







Heat equation 
20171123 

From Max: What does du\dt=a(triangle)^2u mean. Can it be solved for t. Answered by Penny Nom. 





How many miles did he drive in one hour? 
20171121 

From Ava: Graham drove 42 1/3 Miles in 1 1/3 hours. How many miles did he drive in one hour? Answered by Penny Nom. 





An expression for the area of a triangle 
20171119 

From hari: why is area of a triangle drawn from centre of a circle i.e radii forming the sides is
1/2 *r^2 sin theta where r is radius Answered by Penny Nom. 





Jesse has dimes and nickels in his piggy bank. 
20171118 

From Dee: Jesse has dimes and nickels in his piggy bank.
The number of nickels is 3 times the number of dimes.
If the total amount is $8.50, how many coins are there in total? Answered by Penny Nom. 





Blair is 12 years younger than Serena right now. 
20171118 

From Dee: Blair is 12 years younger than Serena right now.
Three years ago Serena’s age was five times Blair’s age. What are their ages? Answered by Penny Nom. 





The mass of a length of tree trunk 
20171113 

From SM: What is the mass of a length of 1m of trunk a tree trunk of uniform cross section of area 0.5 sq.m is made of wood of relative density 0.8? Answered by Penny Nom. 





Splitting twice 
20171111 

From Terry: 4 people are splitting 1/3 of something. 1 is to receive twice as much as the other 3. what it the fractional interest for each? Answered by Penny Nom. 





The graph of graph y= 2x1 
20171111 

From Natividad: How do you graph y= 2x1? Answered by Penny Nom. 





A triangle with sides measuring 6, 8 and 10 inches 
20171111 

From rukhsar: A certain triangle has sides, which are, respectively, 6 inches, 8 inches, and 10 inches long. A rectangle equal in area to that of the triangle has a width of 3 inches. The Perimeter of the rectangle, expressed in inches, is Answered by Penny Nom. 





math 
20171111 

From rukhsar: A certain triangle has sides, which are, respectively, 6 inches, 8 inches, and 10 inches long. A rectangle equal in area to that of the triangle has a width of 3 inches. The Perimeter of the rectangle, expressed in inches, is Answered by Penny Nom. 





Five coins 
20171110 

From Allan: I have five coins..a penny,a nickle,a dime,a quarter and a loonie.....how many different amounts of money could i pay using ny combination of this coins Answered by Penny Nom. 





Mathematical ideas in everyday life 
20171108 

From Ricita: Mathematical ideas to solve various problems of our everyday life ,environment
related problems. Answered by Penny Nom. 





Scale factor 
20171103 

From Hannah: I do not understand it...... What is the scale factor for 9 cenimeters = 1 meter Answered by Penny Nom. 





Formula when i know the GST total 
20171031 

From Duncan: HI  I've added up the GST from a pile of receipts and would like to know what the total cost of goods would be without GST. I don't want to add up 100's of receipts again with the cost before GST but I do need this total cost.
i.e.) I know I paid $400 GST, what would the formula be to find out the cost of what I purchased before taxes? Your help is much appreciated! Answered by Penny Nom. 





formula when i know the GST total 
20171031 

From Duncan: HI  I've added up the GST from a pile of receipts and would like to know what the total cost of goods would be without GST. I don't want to add up 100's of receipts again with the cost before GST but I do need this total cost.
i.e.) I know I paid $400 GST, what would the formula be to find out the cost of what I purchased before taxes? Your help is much appreciated! Answered by Penny Nom. 





Surface area of a hemisphere 
20171028 

From Shaina: If the total surface area of a hemisphere be 36.22/7 cm then its radius will be 3 cm is it true or false Answered by Penny Nom. 





Adding fractions 
20171027 

From Sandy: virinchi distributed 4/7 of cake to his friends 1/3 of it to his family members which part of cake is remaining? Answered by Penny Nom. 





f(x)=x^26x find f(x2) 
20171027 

From Kenneth: f(x)=x^26x find f(x2) Answered by Penny Nom. 





Solve 2cos^2 x + sin x = 2 
20171025 

From Yamama:
hello ! I need help to solve this equation :
2cos^2 x + sin x = 2
Thank you very much
Regards Answered by Penny Nom. 





11% of a central angle 
20171022 

From Hope: How do you turn a percentage in to a central angle eg. 11% Answered by Penny Nom. 





A tangent to a curve 
20171022 

From Jasem:
Suppose that
f(x)=(3x3)^1/2.
(A) Find an equation for the tangent line to the graph of f(x) at x=2
(B) Find all values of xx where the tangent line is horizontal, and enter them as a commaseparated list (e.g., 2,3,6). If there are none, enter none.
Values of x Answered by Penny Nom. 





Sampling distribution 
20171016 

From Esther: I need 4digits combination of 235689 and without replacement. Thanks Answered by Penny Nom. 





Salary plus commission 
20171016 

From Natasha: Veronika works at Future Shop and earns ₱10.50/h plus 6% commission on sales. Last week Veronika worked 40 hours. What was Veronika’s weekly gross salary if her total sales were ₱2050? Answered by Penny Nom. 





The distance between the origin and a moving point on a graph 
20171016 

From Paulina: Find the rate of change of the distance between the origin and a moving point on the graph of y=x^2 +1 if dx/dt=2 centimeters per second Answered by Penny Nom. 





Three consecutive odd integers 
20171010 

From Johanna: Three consecutive odd integers are such that the sum of the first and second is 31 less than 3 times the third Answered by Penny Nom. 





27000001 
20171009 

From Tulashiram: If a× b =27000001, then what is the value of a & b ? Answered by Penny Nom. 





Five bales 
20171008 

From John:
two answers were given... I believe both to be incorrect.
five bales weighed two at a time: weightx2 given: 110,112,113,114,115,116,117,118,120, and 121. It stated all combinations ie: ab,ac,ad,ad,bc,bd,be, etc. to arrive at the above 10 combined weights. I come up with the following...
Bale A= 54lbs, Bale B=56, Bale C=58, Bale D=59. and Bale E=62 pounds.
A+B=110, A+C=112, A+D=, B+C=114, B+D=115 ,A+E=116 ,C+D=117, B+E=118 ,C+E=120, and D+E=121 Answered by Penny Nom. 





An enclosure for some remote control boats 
20171003 

From Roberto: I am trying to build a "ring" for our remote control boats, using irrigation pipe.
I'd like to use full 20' long sticks for the long sides and use eight of what we call
45s, which are actually 135' fittings to make the six short sides. If I know the length
of the two long sides, what would be the formula to find the exact lengths of the short sides?
Thank you. Answered by Penny Nom. 





The volume of a cone without calculus 
20171002 

From Akash: How to find the volume of a cone without the knowledge of calculus? Answered by Penny Nom. 





The square root of 6 is irrational 
20171002 

From John: http://mathcentral.uregina.ca/QQ/database/QQ.09.06/sylvia1.html
In the initial assumption of that proof, root 6 is assumed to be a/b where a and b have no common factors, but why does having a common factor make it irrational? Answered by Penny Nom. 





The importance of a comma 
20170930 

From carolyn: the equation 2y + 53 = 165 represents the situation joel spent 165 dollars on a pair of jeans and two shirts at the same price what does y represent
price of a pair of jeans
price of a shirt
amount joel spent on the shirts
number of shirts joel bought Answered by Penny Nom. 





Macy and Camile's ages 
20170930 

From carolyn: macy is 2 years older than Camille twice the sum of their ages is 52 which equation can be used to find camilles age x Answered by Penny Nom. 





How many pet dogs? 
20170926 

From Michelle: In 2016 there were about 135 million households in the United States. 36.5% of the households own at least one dog. On average, these households have 1.6 dogs. How many millins of pet dogs were in the United States in 2016? Answered by Penny Nom. 





Four multiples of 10 
20170923 

From Laudacir: Four multiples of 10 are added together.the total is a 3 digit number with three consecutive digits. What could the four number be? Answered by Penny Nom. 





Changing a mixed number to a decimal 
20170923 

From karla: to change an improper fraction into a decimal 5 3/4 equals Answered by Penny Nom. 





Walking up and down a hill 
20170919 

From Justina: At 2:20 p.m. Jack is at the top of the hill and starts walking down at the exact same time that Jill, who is at the bottom of the hill, starts walking up. If they maintain the uphill speed of 2mph and downhill speed of 4mph and the distance from the bottom to the top of the hill is 1.5 mi, at what time will Jack and Jill meet? Answered by Penny Nom. 





Up a hill and down again 
20170917 

From justina: Jack and Jill travel up a hill at a speed of 2mi/h.they travel back down the hill at a speed of 4mi/h.what is their average speed for the entire trip? express your answer as a mixed number Answered by Penny Nom. 





An alphabetic sequence 
20170917 

From malik: find the letter of the following series....?
ZOTTFFSSE Answered by Penny Nom. 





The surface area of a sphere 
20170917 

From penny: The surface area of a sphere is 1519.76cm. Taking 3.14 , find the radius of sphere Answered by Penny Nom. 





How many guests were present? 
20170917 

From SM: How many guests were present at an Italian dinner if every 2 guests shared a bowl of salad, every 3 guests shared a bowl of pasta, and every four guests shared a bowl of meatballs, and there were 65 bowls used altogether? Answered by Penny Nom. 





Peanuts in 5 bags 
20170917 

From Maria: There are a total of 270 peanuts divided up into five different bags. The first two bags contain 174 peanuts between the two of them. The second and third bags contain 130 peanuts between the two of them. The third and fourth bags contain 86 peanuts between the two of them. The fourth and fifth bags contain 42 peanuts between the two of them. How many peanuts are in each bag? Answered by Penny Nom. 





An equilateral triangle inscribed in a circle 
20170915 

From sumit: what is the area (in sq. unit) of an equilateral triangle inscribed in the circle x^2+y^24x6y23=0. Answered by Penny Nom. 





Complementary angles 
20170915 

From SM: The measure of angle A is 60 degrees more than its complement. Find the measure of angle A. Answered by Penny Nom. 





Average price 
20170915 

From Annette: If I sold a widget at $15.50 17.5% of the time and $16.50 88.5% of the time what is the algebraic expression for that. How do I arrive at an average price Answered by Penny Nom. 





An impossible problem 
20170915 

From Fay: Given math homework problem of: Gary and Larry given 2 numbers and told to add together. Gary subtracted and got 14. Larry multiplied and got 799. I tried substitution:
XY=14 and X x Y=799
X= Y+14
(Y+14) Y=799 and here I'm stuck at Y squared+14 Y= 799
using substitution I got 47x17=799 but not 14b when subtracted. HELP????? Answered by Penny Nom. 





The angle between two planes 
20170912 

From Arthi: Hello. hope you are having a good day.
I am stuck on a maths question in which it is asking, how to find the angle between two given planes. These planes are in a 3D shape such as a prism.
How can I do this?
Please reply as soon as possible
Thank You Answered by Penny Nom. 





Quadrilateral ABCD is inscribed in a circle 
20170911 

From Joie: Quadrilateral ABCD is inscribed in a circle such that side DA is the diameter. AB=2m., BC=4m., CD=6m., angle BAD=75.93degrees. Find the area of the quadrilateral. Answered by Penny Nom. 





A pool with a dome 
20170911 

From Bruce: A round 24 foot pool. A dome 3 feet above pool in center. How many feet across is the dome touching top rail straight across of pool? Answered by Penny Nom. 





Simultaneous equations with fractions 
20170909 

From Farah: Hi, my name is Farah. I hope you can help me with this question . X/2 + g/5= 3 and 2g  f = 10 Answered by Penny Nom. 





The volume of an attic 
20170907 

From paul: trying to determine volume of an attic base is rectangular 29 ft by 37 ft
peak runs parallel to longest base side and is 7 ft long
roof lines run from each end of the peak to the respective corners
the peak is 3.5 ft above the base
(so seen from above there are 5 visible lines: the peak and 1 line to each of the 4 corners) Answered by Harley. 





Simultaneous equations 
20170902 

From keto: xy=2,x^2+xy=12 Answered by Penny Nom. 





Prisms 
20170901 

From Christa: What do all prisms have in common? Answered by Penny Nom. 





Annual salary 
20170901 

From Lisa: I am applying for a job that pays $16.00 per hour, plus 5 hours of overtime every 2 weeks. I live in California, where overtime is 1.5 times the regular rate of pay after you work 8 hours a day. What would the gross annual salary be with all the overtime hours added in? Answered by Penny Nom. 





A rope formed in a semicircle 
20170829 

From Janna: How do I find the total length of a piece of rope formed in a semicircle that has a diameter of 8 inches? Answered by Penny Nom. 





A car on a rough road and a concrete road 
20170827 

From Ken: A car is driven on a rough road at a speed of 25km and then on a concrete road with a speed of 70kph. The car has 5.5 hours to travel 225km. How long did the car travel on concrete road? Answered by Penny Nom. 





Factors 
20170816 

From Gemma: Why do 315 and 525 have the same number of factors? Answered by Penny Nom. 





A 4 sided lot 
20170815 

From Micheal: If one side of .4 acre is 25 feet what would the other three sides be Answered by Penny Nom. 





Two circles 
20170813 

From Ladines: Find the equation of the circle passing through points of intersections of circles x²+y²=4y and x²+y²=2x and the center is on line y=2 Answered by Penny Nom. 





A rectangle and a circle 
20170812 

From Ramzan: a diagram shows the shape of rectangular framework with length (2x+20)cm and with (y+10)cm . The outline is made of wire . If a circle with diameter 56 cm is to be made from the wire and the area of the rectangle is 420 square centimeter ,find the possible lengths and width of the rectangle Answered by Penny Nom. 





1 billion x 1 billion 
20170811 

From Kona: 1 billion x 1 billion
1 trillion x 1 trillion Answered by Penny Nom. 





The perimeter of a sector of a circle 
20170811 

From Alisa: find the perimeter of the sector with radius 7 cm in which the angle at the centre is 60 degrees leave your answer in terms of pi Answered by Penny Nom. 





Two digit numbers that contain 5 
20170811 

From Irish: How many two digit numbers contain the digit 5? Answered by Penny Nom. 





(x18)/7=6 
20170808 

From David: (x18)/7=6 Answered by Penny Nom. 





A pair of linear inequalities 
20170808 

From Hempstone: Solve the inequalities 3x5<2x+5>4x+9 Answered by Penny Nom. 





Significant digits 
20170806 

From Pat: The directions for a problem are: "Solve the problem, expressing your answer
using the correct number of significant figures."
Problem
0.0043 divided by 2.04
Answer before using the correct number of significant figures is
0.002107843
Is the correct number of significant figures the number below?
2107843
Pat Answered by Penny Nom. 





Teams of 4 from 20 people 
20170804 

From Christopher: math team has 20 people on the team but only 4 can enter the competition. The team captain has to pick 4 of them but he knows that he cannot put James, Bill or Todd on the team with one another or there will be problems. what would the formula be to find the solution to how many possible team combinations the are Answered by Penny Nom. 





Ratios and proportions 
20170801 

From khurram: what is ratio and proportion? please give a detailed note on this topic, i am really panic of these calculations Answered by Penny Nom. 





A lock with 3 tumblers 
20170729 

From Carol: I have a lock that has 3 tumblers. The numbers are 0  9. I cannot recall what I set the combination to. How many combinations will there be with three numbers? Answered by Penny Nom. 





A 4 digit safe combination 
20170729 

From Donna: I lost my safe combination :( it is 4 digit # with the last digit being 2.
I do not think the 1st digit is 1, 2 or 3
Can u help? Thank u :) Answered by Penny Nom. 





Factorials 
20170727 

From dinesh: Is there any shortcut formula for multiply series numbers.
like
1x2x3x4x5.......x100 =? Answered by Penny Nom. 





A semi ellipse 
20170725 

From Ian: The arch of the bridge is in the shape of semi ellipse,with its major axis at the water level.suppose the arch is 20ft. High in the middle,and 120 ft. Across its major axis. How high above the water level is the arch,at a point 20 ft.from the center (horizontally). Round of 2 decimal places Answered by Penny Nom. 





An arched window 
20170724 

From Gerry: Looking to make a full size template for an arched window. Need increments every 16". The radius is 138' 0 9/16" , the chord is 226" and the rise at center of chord is 43" Answered by Penny Nom. 





Some 4 digit numbers 
20170724 

From Camille: I need all of the 4 digit combinations that starts with number 3 and digits can't be repeated Answered by Penny Nom. 





3 consecutive multiples of 11 
20170722 

From nisha: using the multiples formula shown at ypur site how can we solve finding 3 consecutive multiples of 11 whose sum is 363 Answered by Penny Nom. 





A police officer spots a speeding car 
20170720 

From Josh: Marie, a police officer, spots a speeding car and starts chasing it. The speeding
car travels at a speed of 130 feet per second. Marie's car reaches a constant speed
of 145 feet per second 1725 feet from the start of the chase. During that time, the
speeding car has traveled 3150 feet. Write a system of equations to represent this
situation. Answered by Penny Nom. 





Catherine, Molly and Tom 
20170719 

From liezel: what is the answer of this problem, If Catherine and molly has 320pesos altogether, Molly and tom have 360 in all. Tom and Catherine have 240pesos altogether.How much does each of them have? Answered by Penny Nom. 





((a5)/a)/(4/a) 
20170718 

From Michael: Find the Quotient:
((a5)/a)/(4/a) Answered by Penny Nom. 





Parallel and Perpendicular lines 
20170717 

From Karen: Find an equation for the line with the given properties. Perpendicular to the line 7x + 2y = 6; containing the point (2, 1)
Find an equation for the line with the given properties. Parallel to the line 5x  3y =6; x intercept = 3 Answered by Penny Nom. 





An arithmetic sequence 
20170717 

From abbi: hi there im a student in 11 grade
ive been trying to do this task but i have no idea how to do it
the question is
Find the common difference and the n^th term of the arithmetic sequence if the first term is 4 and the twentieth sum of the terms is 1030 Answered by Penny Nom. 





Squares and rectangles 
20170715 

From Tront: So, there's a general rule that all squares are rectangles but not all rectangles are squares. Im trying to find a term that would describe this relationship. I've found that if all of A is B but not all B is A then I'd say that A is a subset of B, but is there a term that describes the relationship as a whole? I don't want to describe the components, I want to describe the relationship as a whole. Answered by Penny Nom. 





Two consecutive odd integers 
20170714 

From Adeeb: Find two consecutive odd positive integers, sum of whose square is 290. Answered by Penny Nom. 





Exponential form 
20170706 

From estela: what is exponential form of 9×1000 Answered by Penny Nom. 





Of cows and men 
20170704 

From Akash: In a group of cows and man the number of legs is 32 more than the twice the number of heads.The number of cows is? Answered by Penny Nom. 





The equation of a circle 
20170703 

From Chen: Find the center radius and equation of a circle in standard form given the following conditions:
1. Tangent to 3x+2y=0 at the point (0,0) and passing through (1,1) and (6,0) Answered by Penny Nom. 





y = g(x + 1) 
20170627 

From Shamsudiin: HI there i am currently doing a level maths AS
I don't understand how to graph this Question y=g(x+1) i really need help please
please respond to this problem Answered by Penny Nom. 





How fast am I travelling? 
20170624 

From corey: if i travel 2 miles in 10 seconds, how fast am i travelling please Answered by Penny Nom. 





The number of truckloads to fill a hole 
20170618 

From Jennifer: How many full size truck bed pickup loads do in need to get to fill a hole that is 18' x 30' that is 4" deep? Answered by Penny Nom. 





Long division with decimals 
20170616 

From Kenneth: Hello:
Why is it recommended to move the decimal from a divisor when dividing so that the divisor is a whole number?
I know how to divide by moving the decimal from the divisor, but I cannot explain the reason.
I thank you for your reply. Answered by Penny Nom. 





The surface area of a hexagonal pyramid 
20170616 

From Emilie: Hello, I need help with this question:
A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6. Find the total area of the pyramid.
Thank you in advance if you can help me... Answered by Penny Nom. 





What percentage did I take? 
20170614 

From david: you have $5.85 I took $1.06 from you,what percentage did I take? and the formula to solve it. Thank you Answered by Penny Nom. 





The smallest and largest 4 digit integers 
20170613 

From Avneetpal: Difference of the smallest and biggest 4digit number Answered by Penny Nom. 





Three consecutive natural numbers 
20170611 

From Anita: Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the square of the other two by 60. Find the numbers. Answered by Penny Nom. 





Solve the equation completely cos 2x = 1 
20170608 

From Lava: Solve the equation completely cos 2x = 1 Answered by Penny Nom. 





A man drives 48km in 45 minutes 
20170603 

From Jamal: A man drives from Ibadan to Oyo a distance of 48km in 45 minutes. If he drives at 72km/h where the surface is good and 48km/h where the surface is bad. Find the number of kilometers of good surfaces Answered by Penny Nom. 





Simultaneous equations with fractions 
20170602 

From Jamal: 1/x + 1/y =5 and 1/y  1/x =1 Answered by Penny Nom. 





The maximum area of a rectangle with a given perimeter 
20170602 

From Bob: How would I go about finding the maximum area of a rectangle given its perimeter (20m, for example)? Answered by Penny Nom. 





4 digit codes with repeating digits 
20170601 

From Morgan: what are all possible 4 digit code repeating numbers? cuz i know that you have one website on it but, it doesn't repeat 2 numbers in a code. Answered by Harley. 





A cylindrical water tank with a leak 
20170601 

From Alexander: if a cylindrical water tank has diameter of 90cm and leak starts at the bottom 10 litres in an hour. how long will it take for the level to fall by 20cm Answered by Penny Nom. 





Five rational numbers between 2 and 1 
20170531 

From Prince: Five rational numbers between 2 and 1 Answered by Penny Nom. 





3rd Grade math problem 
20170530 

From Angela: Following is a problem from my 3rd grader's homework assignment:
Solve. Draw a diagram to represent the situation.
Rachel has 20 oneinch beads. She wants to use all of them to make a square picture frame. What will be the length of each side?
Find Perimeter, Area, and Side Length Answered by Penny Nom. 





A square peg in a round hole 
20170529 

From bill: bill wants to put a 2 foot square peg into a round hole What must be the circumference of the hole? Answered by Penny Nom. 





A 25 acre strip 
20170529 

From Va: hello, can you pls help me....i have a property which has 300 ft width road frontage and my lot is 4700 ft deep to the back line of my property which i am told 27 acres. I want to only sell 25 acres...and go to the rear line with 4700 feet, but decrease the front width using the 300 ft measurement. how do i decrease the 300 ft width measurement by 2 acres? i am confused what the measurement would be..thank you....so to sum it i want to make 25 acres out of a measurement of 300 x 4700 ft long reducing the front measurement..thank you so much. Answered by Penny Nom. 





Algebra 
20170528 

From Kerim: I need to solve this equation.
y=at^2  2at
x =2a√t
Express y in terms of x and a
Give in the form y=(x^p/ma^3)  (x^q/na) where p,q,m and n are integers Answered by Penny Nom. 





A polygon inscribed in a circle 
20170527 

From Levan: This was the closest to what I am trying to solve.
http://mathcentral.uregina.ca/QQ/database/QQ.09.06/s/dj1.html
So in the answer linked, we figure out what is "c".
But what if we know "c" and want to find out "n" based on specific "r=1".
It might be simple math, but I have not had any relationship with math for 20 years now
but this question puzzles me for a reason. Answered by Penny Nom. 





Ordering fractions 
20170525 

From Esmeralda: How May i order this 30%,3/100,7/20 and 0.33 from least to greatest Answered by Penny Nom. 





Initial velocity 
20170523 

From Annelle: a body is thrown vertically downward from a height above the ground. determine the initial velocity and the height of the starting point if after 4 secs it reaches the ground with velocity of 68 m/s. Answered by Penny Nom. 





A trapezoid inscribed in a circle 
20170517 

From Kameron: I have been given a challenge problem that states that Diameter AB is drawn in a circle if 10 inch. Chords AC and BD are drawn so that each is of length 12inch and ACDB is a trapezoid. Find the height, in inches, of the trapezoid Answered by Penny Nom. 





A 40 acre square 
20170514 

From Richard: How many feet on each side of 40 acre square ? Answered by Penny Nom. 





A limit 
20170514 

From Soham: Find out the value of the following:
lim (x+x^2 +x^3 +.........x^n–n)/(x–1)
x→1 Answered by Penny Nom. 





Two wires between two buildings 
20170511 

From Bill: I need to find the height of the intersection point of two building wires< br />
Building A is 860 feet high and building B is 480 feet high. The wires existent from the top of one building to
The bottom of the other < br />
The distance between is 32 feet Answered by Penny Nom. 





What is the regular price? 
20170511 

From Saira: If the sale price is 55.50$ and the discount is 12% what is the regular price Answered by Penny Nom. 





Canada's population as a percentage 
20170511 

From bethmarie: What percentage of the world population (7.5 billion) is Canada's population (36 million).
Thank you very much! Answered by Penny Nom. 





Yards per second to miles per hour 
20170511 

From Scott: If a soccer ball travels 30 yards or roughly .017 miles in 2 seconds how fast was the ball going in mph? Answered by Penny Nom. 





Slicing an inverted bowl at various heights 
20170430 

From Joel: Find a formula to calculate the circumferences of an inverted bowl at various heights.
E.g. Take an inverted bowl with a diameter of "x" cm and a depth / height of "y" cm.
How can I calculate the circumferences at distances of various heights above the base?
Alternately, what would be the formula to calculate the distance of the line segment resulting from a line which intersects both sides of a parabola in which that line is drawn parallel to the tangent of the vertex of the parabola at any given distance from the vertex? Answered by Penny Nom. 





Jamie has twice as many video games as Mel. 
20170427 

From John: Jamie has twice as many video games as Mel. Together, the boys have 24 games. how many games do each boy have Answered by Penny Nom. 





1 acre as a 2 foot wide strip of land 
20170425 

From alan: How can one convert 2 acres (a square  area) of land into a strip of land that is 2 feet wide and (?) feet long? Answered by Penny Nom. 





Filling cinder blocks with concrete 
20170424 

From Katherine: I am looking to construct a 10 X 10 dance floor using 8 x 16 cinder blocks.
I have figured that I will need about 120 blocks, however I am not sure
how much concrete I will need to fill the total empty space.
Thank you Answered by Penny Nom. 





Selling price and markup 
20170424 

From Julie: What would the cost of an item be, if the sell price was $50 and the markup 48% Answered by Penny Nom. 





The length of a train 
20170424 

From Stefano: If a freight train is coming towards you and you were traveling at 85 miles an hour and it takes 35 seconds for the train to pass you how long is the train
Figure 50mph for train Answered by Penny Nom. 





Baseball Cards 
20170420 

From Raquel: A minor league baseball team gave away baseball cards to each person entering the stadium. One group receives 28 baseball cards. A second group received 68 baseball card. If each person entering the stadium receive the same number of cards, what was the greatest possible number of baseball cards that each person could have received? Answered by Penny Nom. 





A lost iPhone pass code 
20170417 

From Sam: I have a locked iPhone and it has all my of my holiday photos on it. I changed the password and then I think I did a incorrect number pattern but anyway I know it ends with 99 and the first 4 digits are 235 and 6 could you please send all of the combinations for this password (without the 99) Thx and plz get back ASAP I need it for school Answered by Penny Nom. 





sin x/ 1+cos x = 1cos x/ sin x 
20170416 

From duiren: sin x/ 1+cos x = 1cos x/ sin x Answered by Penny Nom. 





A function which is onto but not onetoone 
20170416 

From Avinash: Define a function f(x):N>N which is onto but not oneone.Where N is set of natural numbers. Answered by Penny Nom. 





A word problem about the dimensions of a lot 
20170416 

From Charlotte: If a house is 66x78 ft, how many feet out from the house around would be an acre to not include the house Answered by Penny Nom. 





Forming a cone from a circle 
20170415 

From Tasha: A sector of a circle subtends an angle of 216 degrees at the centre, If this sector is used to form a cone of vertical height ,8cm, calculate the base radius of the cone Answered by Penny Nom. 





Express x/a 2a/x =1 in terms of a. 
20170414 

From tony: express x/a 2a/x =1 in terms of a. Answered by Penny Nom. 





The cost of a piece of sheet metal 
20170414 

From Mohammed: I bought a 2 mm sheet plate of 1.2m × 2.4m in fijian $95. I used 1.95m × 0.4m from that sheet plate. What will be my total cost for the sheet plate I used. It was a mild steel plate. Answered by Penny Nom. 





Why does 10x10x10 give 1,000.0000000000001? 
20170412 

From Randolph: Hi, On your calculator I found that a box 10 by 10 by 10 inches has a volume of 1,000.0000000000001 cubic inches. Can you explain the numeral 1 thirteen places past the decimal? Thanks, Randy Answered by Penny Nom. 





Acres and perimeter 
20170412 

From Peggy: How many acres in 2700' circumference or perimeter Answered by Penny Nom. 





A rectangular box filled with oil 
20170411 

From morpal: we want to calculate volume of rectangular box height 1275mm and lengths 2400mm and breadth 1270mm and oil s. gravity is .950 how much kg. of oil i can store Answered by Penny Nom. 





Rational numbers between 2 and 3 
20170408 

From Medha: Find 12 rational numbers between2 and 3 Answered by Penny Nom. 





A circle inscribed in a 30690 triangle 
20170407 

From Kameron: i have been given a problem with a 306090 triangle and a circle inscribed with a radius of 2 and was told to find the perimeter of the triangle Answered by Penny Nom. 





Successive Differences 
20170406 

From Twaha: Please find the equation of the sequence 1 2 4 7 11 16 22 Answered by Penny Nom. 





The height of a isosceles trapezoid 
20170403 

From Riham: Hi
How can I find the height in an isosceles trapezoid if I have the measurements of all of its sides ?
Thank u in advance. Answered by Penny Nom. 





How to find last two or three digits of a large exponent like 17^256? 
20170330 

From Raginee: How to find last two or three digits of a large exponent like 17^256? Answered by Penny Nom. 





A puzzle with some integers 
20170330 

From Glen: Use 7,7,5,5 to equal 3 only using each # once and each math function once Answered by Penny Nom. 





13  3x = x times the square root of 5 
20170329 

From Kevin: A student I am tutoring was sent this question from his teacher.
Solve for x: 13  3x = x times the square root of 5 Answered by Penny Nom. 





Is the square root of 2 plus the square root of 2 irrational? 
20170329 

From haya: how can i prove the the square root of 2 plus the square root of 2 is an irrational number? Answered by Penny Nom. 





How much money do I make per sq ft? 
20170328 

From jackie: If I make $12.00 per hour and I cover 750 sq ft in one hour, how much money do I make per sq ft? Answered by Penny Nom. 





Is a large integer divisible by 2^n? 
20170328 

From Sahand: You are given number x that is very large (that large that it can't be divided by hand)
can we find out that x is divisible by 2^n or not? Answered by Penny Nom. 





Quadratic Equations 
20170328 

From Natalie:
Hi Maths Central,
I am having trouble with quadratic equations. The question is:
Calculate the length 'l' of a rectangular pool by creating and solving a quadratic equation.
1. The rectangular pool is of equal area to a square pool, and a circular pool (5.70m^2).
2. The length of the rectangular pool must be 2m longer than the width 'w'.
Thank you so, so much for your help, Maths Central! Answered by Penny Nom. 





The sum and difference of two numbers 
20170320 

From Olivia: The sum of two numbers is 87 and their difference is 29. What are the two numbers Answered by Penny Nom. 





Differentiate y = x^x^x 
20170319 

From Nafis: differentiate y = x^x^x Answered by Penny Nom. 





Is infinite a number? 
20170318 

From Divyansh: Is infinite a number? If yes why as i think that numbers are used for counting but infinite is undeterminable? Answered by Penny Nom. 





Faster than as a percentage 
20170318 

From Maximilian: Hi, i have a strange issue with the phrase "faster than" in percentage, ie. if i have a 10MB/s connection, and somebody has a 7MB/s connection, is it 30% faster or 50% faster.
which ( affirmation, phrase, sentence ) is the right one:
a:) My 10MB/S connection is 50% faster than the 7MB/s ?
or
b:) My 10MB/S connection is 30% faster than the 7MB/s ?
Thanks in Advance, and please if you can teach me why ! Answered by Penny Nom. 





2^a, 2^b, 1^1 and 1^0 
20170317 

From Émile: If you had 2^a = 4 and 2^b = 4 you could assume that a = b right? Yet we can observe that 1^1 and 1^0 both equal 1, yet 1 = 0 isn't true. So if given a log base 1 number 1 the would the answer be 1 AND 0? Answered by Penny Nom. 





Percentage change in productivity 
20170315 

From Sunni: I'm working on a graph and I need to find the percentage of increase from one figure to another. How do I do that? For instance our department started with a workload of 1773 in Jan and ended with 341 in Dec. In addition to that we received 2088 new items from Jan  Dec with an average of 5 workers. How do I find the percentage of increased productivity if any? Answered by Penny Nom. 





Solve 3x^219x14=0 for x 
20170315 

From nick: I'm an 8th grader and am quite confused with this equation:
3x^219x14=0
The answer is:
2/3 , 7
But I'm not sure how to solve for it. Answered by Penny Nom. 





The ratio of two ages 
20170315 

From Angel: The sum of Keith's age and Alan's age is 36. Four years ago, the ratio of Keith's age to Alan's age was 4:3. Find the ratio of their present age Answered by Penny Nom. 





What is the grade of the incline? 
20170312 

From Jon: If I am climbing 16 feet in elevation over 80 feet horizontal. What is the grade of the incline Answered by Penny Nom. 





A regular tetrahedron 
20170312 

From Jeramie: When we have a regular tetrahedron, is it always true that all the angles of the triangles measure 60 degrees? Answered by Penny Nom. 





How much does the fish weigh? 
20170308 

From Jeri: Fish is caught that weighs 5 pounds plus half its weight. How much does the fish weigh? Answered by Penny Nom. 





More on calculating the area (acreage) of a foursided lot 
20170306 

From Kerri:
Can you please show the formula used to calculate areas as provided on this page:
Calculating the area (acreage) of a foursided lot Answered by Penny Nom. 





Exponential form 
20170304 

From michael: I was teaching my student about exponent when we stumbled across this problem.
"write (125)^3 in exponent form"
The problem is with the number "125". I think 125 = (5)^3. But one of my student thought that it is 125= 5^3.
Both of them is equal to 125 but they totally different in structure. I wonder which one is correct and why it is. I am worried if they get this wrong, it might spell problem in the future when we start substituting the numbers with variable.
Thank you very much for reading my question and answering it. Answered by Penny Nom. 





Tons of sand 
20170301 

From Elizabeth: Hello my arena is 132.23 feet width by 132.23 feet length. I need to put 4 inches of sand. How many tons of sand do I need ? Answered by Penny Nom. 





The inside diameter of a silo 
20170228 

From JOHN: I need to find the inside diameter of a cement silo with an outside circumference
118 ft and a wall thickness of 7 inches. thank you John Kerr. Answered by Penny Nom. 





Building a hexagon enclosure 
20170226 

From Kenneth: Hello, I have a question for you. I have a special needs daughter and I want to install a ceiling fan into her room. The fan is 42 inches in diameter. I would like to build a wooden hexagon enclosure to protect the fan. I would like the enclosure to be at least 2 inches wider than the fan on each side measuring from flat surface across to flat surface. How do I figure out the length of each panel so that I can miter them and assemble it? Thank you for your time. Answered by Penny Nom. 





Covering a ceiling with tablecloths 
20170224 

From DEANNA: I am trying to cover a 16 x 31 foot ceiling with tablecloths. For sale, are 90 x 132 inch tablecloths for $4.97 a piece and 60 x 102 inch tablecloths for $3.85 a piece. Which would be my cheapest option to cover the entire space? Answered by Penny Nom. 





Filling a pool with two hoses 
20170220 

From Charlene: A large hose will fill a pool in 40 minutes while it takes a smaller hose 60 minutes to fill the same pool. The same pool takes 80 minutes to drain if the drain is open. Suppose one day both the hoses are turned on, but by accident the drain was left open. How long would it take to fill the pool that day? Answered by Penny Nom. 





Covering the ceiling of a garage 
20170220 

From DeAnna: I am trying to drape a 15 x 30 garage with yards of fabric. If the yard of fabric is 60 inches wide, would 10 1/4 yards be enough for my space? Answered by Penny Nom. 





A total amount of $27,500 invested at 5% and 7% 
20170219 

From Brad: Kristina invests a total of $27,500 in two accounts paying 5% and 7% simple interest, respectively. How much was invested in each account if, after one year, the total interest was $1,645.00. Answered by Penny Nom. 





A block base for a plywood rectangle 
20170218 

From Joe: How many cinder blocks 16x8 would i need to build a solid base for a plywood base 54inches wide and 30 inches deep Thank you Answered by Penny Nom. 





Addition and subtraction base 5 
20170129 

From BABAWALE: Simplify 342five +132five223five Answered by Penny Nom. 





Vinculum 
20170127 

From Dick: What is the line or bar over a Roman Numeral called?
Eg. V with the bar over it representing 5,000 . Answered by Penny Nom. 





Feet per second to miles per hour 
20170127 

From ron: if a vehicle travels 50 feet in 2.5 seconds what is the speed in mph.
3600 sec in hour /5280 feet in a mile i get .68181818. how do i figure the 2.5
seconds. all the calculators I've used show 34 mph is that correct or am i forgetting the 2.5 second. please help. Answered by Penny Nom. 





The volume of a slab 
20170121 

From Russell: Working with a segment of a circle. The O.D. is 3.440" the length of the chord is 3.130 I need information on the volume of the largest area. I would like to know (in thousands of an inch) how tall would the largest area need to be to equal .1143 cubic inches If you need more info I can send it Thanks in advance Answered by p. 





Angular speed 
20170121 

From Kenzi: A wheel of radius 14 inches is rotating 45°/sec. What is the linear speed in in/sec and the
angular speed in RPM? (Round your answers to three decimal places)
I already found the linear speed. I got 10.996 in/sec. I don't know how to find the angular
speed. Answered by Penny Nom. 





The ratio of students to teachers 
20170120 

From Dylan: The ratio of students to teachers at a school is 19:1. How many students are there in each total number of people? Answered by Penny Nom. 





The average rate of change of cot(t) 
20170118 

From Brianna: Hello!
It's been a while since I've taken a math course, and I'm stuck on a problem in my calculus course.
The question is this:
Find the average rate of change of the function over the given interval.
h(t)=cot(t) a) [5pi/4, 7pi/4] Answered by Penny Nom. 





Five equations 
20170116 

From Muhammed: A x 4 = E
B ÷ 4 = E
C + 4 = E
D  4 = E
___________
& A + B + C + D = 100
what is the value of E Answered by Penny Nom. 





Form the quadratic equation which has given roots 
20170116 

From Tharshini: Given a and B are the roots of the quadratic equation x^2+4x+7=0. Form the quadratic equation which has the roots
3a1 and 3B1 Answered by Penny Nom. 





One millionth of one percent of 90,000,000,000 
20170116 

From Gene: What absolute number is one millionth of one percent of 90,000,000,000 Answered by Penny Nom. 





How do I establish the original List Price? 
20170115 

From Bob: (1) I have a net price item at $4,664.66 but do not have the discount percentage. I have been told I received 40%? How do I establish the original List Price and to confirm what discount I received? Answered by Penny Nom. 





A circle inscribed in an isosceles triangle 
20170114 

From Sal: There is a right isosceles triangle. Inscribed inside of it, is the largest possible circle.
Ho do you find the value of the radius?
I want to find out a way of only using the rules/laws of geometry, or is that not possible. Answered by Penny Nom. 





8^3/2(2+2) 
20170113 

From Mary: 8^3/2(2+2) Answered by Penny Nom. 





A rectangle with a given perimeter and area 
20170111 

From Joe: i have a math question for homework that i don't understand.
can you draw a rectangle that has 18cm in perimeters and 20cm in areas.
i tried but i can't. Answered by Penny Nom. 





An angle and its complement 
20170110 

From Ysa: If the measure of an angle is twice the measure of its complement, what is the measure of the angle? Answered by Penny Nom. 





Renting an electric cart 
20170107 

From Desiree: Vacation Rentals rents electric carts for travel on their grounds. The economy plan rents
carts for $26 per day and the premium plan rents a carts for $12 per day plus a one time fee of $126.05
For how many whole days would it be cheaper to rent from the economy plan then from the premium plan? Answered by Penny Nom. 





A tolerance limit is 0.5% 
20170106 

From Joe: Dear Sir/Madam,
How can I describe the following.
My volume tolerance limit is 0.5%,regardless of quantity.
Say , My total volume output is 344,714 Litres and benchmark volume is 348,194
Difference of 3480Litres, this would give me a percentage of 0.999.
Which is above my tolerance.
How can I explain this high tolerance limit even though volume difference is minimal.
Regards
Joe Answered by Penny Nom. 





A parabolic arch 
20170105 

From Rand: It is most likely already been answered but I can not seem to find the right key words for the search engine?.
What I am looking for is, if you have an have arch/arc and you know the degree of slope and the height of the arch/arc from ground lvl; how do you factor the decreasing angle/#’s to get the distance tween the two feet on the assumption that the arch/arc is curved all the way to ground lvl?
a. where the legs widen continuously (till they hit ground) so yes parabolic &
b. where the legs come down straight after a ½ circumference run.
What I am focusing is the parabolic.
Many Thanks Answered by Harley Weston. 





Plans for dog kennels 
20170104 

From Pat: So... I'm trying to draw up a plan for my new kennel buildings. They are going to built
out of grain bins. I know, cool,... right. Anyway the kennels will be along the outside
of the circle and be shaped like wedges. the center will be a play area. All of the kennel
sides are 6 ft in length so the size of the gate will determine how many kennels I can
fit in each bin. If I want to put an odd number of kennels in and I cant draw
a straight line across to make all of the wedges the same size... how do I figure out the
angles...degrees ? maybe i'm making it too hard but i'd like to give the dogs as much space
as i can. I did up some ... attached. Answered by Harley Weston. 





A rational number between 4 and 5 
20170103 

From Anshika: Write rational number between 4 and 5 Answered by Penny Nom. 





Cutting a wire into 18 cm lengths 
20161229 

From Shambhavi: A long wire of some length is cut into small pieces of 216 cm leaves a small piece of length of 89 cm of this part were cut into equal pieces each of 18 cm the length of the left over wire would be Answered by Penny Nom. 





Water leaking from a trough 
20161228 

From Kathryn: A trough is 6 m long, and has uniform crosssection of an equilateral triangle with sides 1 m.
Water leaks from the bottom of the trough, at a constant rate of 0.1 m3/min.
Find the rate at which the water level is falling when the water is 0.2m deep. Answered by Penny Nom. 





An octagon from a square 
20161226 

From Chris: We have a square piece of wood (30 inches x 30 inches) that we need to cut into an octagon. Is there a simple way to figure out where to make the marks/points to cut? I mean like really simple?
Thanks! Answered by Penny Nom. 





20+30*0+1=? 
20161226 

From Mr: 20+30*0+1=? Answered by Penny Nom. 





Write these numbers from greatest to least 
20161222 

From lsaiah: write the following numbers from greatest to least
3 1/2, 7/3, 80%, 2.5, 0.94 Answered by Penny Nom. 





Simultaneous equations with fractions 
20161221 

From Kimi: I am stuck on this,can someone please help me????
1/2x+1/3y=11
8x+2/5y=102
Can someone please explain how to solve questions like these??
Or else I will never learn...
Thank you Answered by Penny Nom. 





Two concentric circles 
20161221 

From shrestha: Two concentric circles have radii of 14 cm and 7 cm respectively. Find the area of space between them. Answered by Penny Nom. 





The inverse of y=x^2+x+c 
20161221 

From Sam: What is the inverse of y=x^2+x+c for x? Answered by Penny Nom. 





The inverse of y = x(x  2) 
20161221 

From Sasha: Hello, I recently stumbled upon this question and I haven't been able to figure it out.
Why is the inverse of y=x(x2) not a function?
Suggest a domain restriction which would ensure that the inverse is a function.
Thank You :) Answered by Penny Nom. 





The area and radius of a circle 
20161219 

From india: How do you find the radius of a circle if only the area is given to you? Answered by Penny Nom. 





Joining a fitness center 
20161218 

From Salem: A fitness center offers a special price for groupclass students. The cost of registration is 30 dollars and then you have to pay 25 dollars per month. What is the rule of the equation in the light of c=m+? Answered by Penny Nom. 





980 cubic yards of dirt 
20161217 

From Jondi: I am trying to visualize 980 cubic yards of dirt by using a metaphor.
Would this be the size of a car?
A fire engine?
A semitrailer?
How many trucks would you need to haul away 980 yards of dirt? Answered by Penny Nom. 





1/1cosine(2x)  1/1+ cos(2x) 
20161214 

From Sean: 1/1cosine(2x)  1/1+ cos(2x) Answered by Penny Nom. 





Divisibility of 3n^5+7n 
20161214 

From Parag:
Question from Parag, a student:
if n is a natural number,then 3n^5+7n is divisible by
a)2
b)3
c)5
d)7
i got the answer but still i need a valid alternate approach. Answered by Penny Nom. 





3^2x5=27 
20161214 

From danaja: solve for the following 3^2x5=27 Answered by Penny Nom. 





How far apart are the boats? 
20161213 

From Halley: Two boats leave port at the same time. Boat A travels east at a speed of 12 km/hr. Boat B travels southwest at a speed of 14 km/hr. After two hours, how far apart are the boats? North is 0 degrees. How do I figure this out.
Thanks Answered by Penny Nom. 





x^2 = 16 
20161212 

From A student: x to the second power = 16
what number solves the equation? Answered by Penny Nom. 





The area of a city block 
20161208 

From Miura: A city block is three times as long as long as it is wide.if the distance around the block is 0.48 kilometers, what is the area of the block in square meters? Answered by Penny Nom. 





A sales tax of 7% 
20161207 

From Kenneth: Hello:
If a sales tax of 7% is placed on every $1.00 of merchandise for sale, is it correct to indicate
the tax as 7%/ per $1.00 or 7%/$1.00? If the calculation is expressed as 7%/$1.00 X $5.00,
the tax is not $0.35 but 0.35. Is a tax rate of 7% incorrectly represented as 7%/$1.00
since the dollar unit cancels from the multiplication?
I thank you for your reply. Answered by Penny Nom. 





The sum of three integers is 30 
20161206 

From Vaishnavi: _+_+_:30. Blanks are to be filled by(1,3,5,7,9,11,13,15) and numbers can be repeated. Answered by Penny Nom. 





Profit and loss on two shirts 
20161206 

From Mahesh: A man purchases one shirt and one TShirt for Rs. 6000. He sells the shirt at a profit of 20% and TShirt at a loss of 10%, as a result he gains 2% on whole transaction. what is the cost price of the TShirt ? Answered by Penny Nom. 





Two boys on the same route 
20161206 

From Abbey: Starting from the same spot, one boy completed a route in 9 minutes and another boy completed it in 15 minutes. When will both boys be at the same starting point at the same time again? Answered by Penny Nom. 





Three friends bought 13 books 
20161206 

From alexis: Marina bought 4 books José bought as many books as Ben bought together the 3 friends bought 13 books how many books did Ben buy Answered by Penny Nom. 





Gallons and cubic inches 
20161205 

From Theresa: If I did not know the cubic inches in a liquid gallon how would I find it?
In other words what is the formula for this? Answered by Penny Nom. 





A pie chart 
20161205 

From vickie: Determine the central angle needed to form a pie chart for the following housing characteristic data: 63% owner occupied, 27% renter occupied, and 10% vacant Answered by Penny Nom. 





Covering a floor with plank flooring 
20161204 

From sandra: my bathroom is 5'x6'.2"
i want to purchase plank flooring which covers 19.8 sq ft per box.
how many boxes would i need. Answered by Penny Nom. 





The diagonals of a cube 
20161202 

From Peter: when u have a cube and the inner diagonal is 41.6 how long is the outside diagonal Answered by Penny Nom. 





Building a pyramid 
20161201 

From Jesse: I'm trying to build a 30"by30"by 18.25"tall pyramid,what should my cutting measurements be? Answered by Harley Weston. 





Acres and miles 
20161130 

From Carolyn: If I am running a pipeline of 1,100 miles, how many one acre plots will it take to cover this distance?
Carolyn Answered by Penny Nom. 





Is every rectangle a rhombus? 
20161128 

From Robert: not every rectangle is a rhombus.true or false? if false please leave a short explanation. thank you:) Answered by Penny Nom. 





A stone walkway around a garden 
20161127 

From Abigail: A garden measures 12 feet by 16 feet. The family would like to add a stone walkway around the garden. This would increase the total area of to 302.25 square feet. what will be the width of the of the walkway Answered by Penny Nom. 





Two tangent circles 
20161127 

From mikee: find the equation of a circle tangent to the circle x2+y2=4
and with the center at (0,5) Answered by Penny Nom. 





A circle inscribed in an equilateral triangle 
20161127 

From jo: what is the radius of the inscribed circle of an equilateral triangle with altitude 12 units? Answered by Penny Nom. 





2^x= 2x  11 
20161127 

From Kathy: I don't know how to start this problem:
2^x= 2x  11 Answered by Penny Nom. 





The weights of two boxes 
20161125 

From dearbhla: One box weighs 3 3/7kg. Another box weighs 1 5/6 as much. How heavy is the second box? Answered by Penny Nom. 





Simultaneous equations 
20161125 

From Rohan: x2/3 + y  1/4 = 13/12
2x/2 + 3 + y/3 = 11/6 Answered by Penny Nom. 





Radius angle and arc length 
20161124 

From pavidthra: Length or arc 11 and angle of subtended 45.need to find a radius Answered by Penny Nom. 





Multiplication and repeated addition 
20161123 

From Anandmay: Hello
I was looking closely at early arithmetic where I found how we discovered properties of Arithmetic.
Like:2 x 3 = 3 x 2.
This can be proved by considering a 2D figure(actually,quadrilateral) having length consisting of 2 boxes of
1by1 dimensions and breadth of 3 boxes of the same dimensions.
Now,consider it again,but,this time,length of 3,and breadth of 2 of such 1 by 1 boxes.
We now notice that we can fit the 2 types of rectangles formed on each other precisely.
So the multiplicative property of commutativity is true for all natural numbers as we can generalize the result(in our mind,for self satisfaction).
Now,can you find me a nice satisfactory reason of why a fraction times a natural number equals the number times the fraction?
I mean, for example,i can understand the meaning of 3 x 2/3 to be three times 23rd,that is, 2/3+2/3+2/3.Fair enough.
But here is the problem:By definition and actual meaning of multiplication, a x b means the repeated sum of b,done 'a' times.
So what is the meaning of doing 2/3 x 3?The repeated addition of 3 how many times??2/3 times??Not making sense,right?And even
we have not proved yet the commutative property of numbers INCLUDING fractions.So how can we resolve this problem and make these things meaningful?
Thanks Answered by Penny Nom. 





Why are equivalent fractions equal? Part 2. 
20161122 

From Anandmay: Hi!
I saw one of your answered questions:Why are equivalent fractions equal?
The same question I had for why i searched and ended up entering this wonderful site.
The answer was so much experimental based.I mean,for example,it was explained how
3/4 was equal to 6/8 by dividing a unit into 4 equal parts and taking four of the parts,and then dividing the
same unit into 8 equal parts and then taking 6 of them.The result was that both the taken parts were equal.
(That is,3 out of 4 equal parts were equal to 6 of the 8 equal parts.)
But,this was very much nongeneralized and experimentalbased result(proof).
And we all know that in mathematics,we confirm some particular thing for all the numbers iff we generalize
it.
So,can you explain more clearly 'HOW' the 3 parts of the 4 equal parts and the 6 of the 8 equal parts of the unit
equal(that is the same)?I don't want experimental proof.I want clear proof,and thus please give a generalized
proof for all fractions and their equivalents.
Thanks! Answered by Penny Nom. 





A square inside a circle inside a square 
20161113 

From Jeff: Greetings,
I came across a question from a textbook from years ago. I've been trying to solve it, but am not sure if my approach is correct.
There are 2 squares (1 inner, 1 outer) & 1 circle.
The inner square is the largest square that will fit inside the circle. It has an area of 1 unit.
The circle is the biggest that will fit in the outer square.
What is the area of the outer square? Answered by Penny Nom. 





The amount of material remaining on a roll 
20161111 

From Yoh:
Question from Yoh:
Hello,
I am trying to find impressions on a roll (either full roll or partial).
Let's say I have the following information.
 Outer Diameter of roll
 Inner Diameter of roll (cardboard core)
 thickness per layer
 Each cut off length (impression length)
Now let's say a roll has a 40in outer diameter, the cardboard core has a 3.75in diameter and a thickness of .002. Each impression has a cut off of 14inches.
With this the roll will have approximately 2,700 impressions. How would I find the remaining impressions if the outer diameter of the roll is only 6.5inches?
Thank you. Answered by Penny Nom. 





A fish and eight parakeets 
20161111 

From Cindy: Cindys fish weighs 8 times as much as her parakeet. Together the pets weigh 63 ounces. How much does the fish weigh? Answered by Penny Nom. 





4444 base five 
20161111 

From John: If 4444 is a number in Base5, is 624 its value? Answered by Penny Nom. 





An equation with fractions 
20161109 

From Tina: How do you solve x+1/3=x+2/5. X+1 divided by 3= x+2 divided by 5. What's x= Answered by Penny Nom. 





Volume of liquid remaining in a tilted cylinder 
20161108 

From Brian: I am trying to determine the amount of a liquid remaining in a 55 gallon drum when it is tilted at 45 degrees and the liquid level is low enough so that the liquid does not completely cover the bottom of the drum.
Your help is greatly appreciated. Answered by Harley Weston. 





The area of a rectangle 
20161105 

From Ivan: If the vertices of a rectangle are a(1,3),b(3,4),and c(1,4),find it area. Answered by Penny Nom. 





A key for a lock with five tumblers 
20161102 

From Aeriel: A lock works by having a key turn a sequence of tumblers. Consecutive tumblers have different heights, and in order to unlock the lock, the sequence of heights on the key must exactly match those of the lock. The picture below shows a lock with four tumblers.
How many different keys can be made for a lock that has 7 tumblers with 5 possible heights each? Answered by Penny Nom. 





A problem with a recipe 
20161031 

From Ted: Recipe calls for 3 1/2 c of sugar & 4 c of water. I only have 3c of sugar how much water do I use Answered by Penny Nom. 





Three circles 
20161030 

From yolani: two equal circles with centre A (1;1)and B (4;5)touch a third circle with centre P as shown in the diagram. If P ,A and B Lie on a straight line find the coordinates of P Answered by Penny Nom. 





A pattern rule for a sequence 
20161028 

From Grace: Here's a Grade 7 question, we need to find the pattern rule:
1  1
2  3
3  6
4  10
......
It may involve exponents, but we can't seem to figure it out.
thank you.
Grace. Answered by Penny Nom. 





The derivative of the inverse of a function 
20161028 

From Kate: Hi, I'm in a College level Calculus course and I can't seem to figure out the answer to this question.
Find the derivative of f^1(4) if f(3)=4 and f'(3)=1/7 Answered by Penny Nom. 





Parallel lines 
20161026 

From Jordan: (7,5) 3x 4y=5 Answered by Penny Nom. 





A word problem at the fair 
20161025 

From Rick: Have 48 tickets to spend, have to spend them all in exactly 10 events.
Rides cost 6 tickets games cost 4 tickets & treats cost 3 tickets Answered by Penny Nom. 





The volume of a hexagonal pyramid 
20161021 

From Elizabeth: Find the height of a hexagonal pyramid with a volume of 1320 ft ^3. The area of the base is 120 ft^2. Answered by Penny Nom. 





How many marbles does Haley have? 
20161019 

From Pat: Sabrina has 1/4 the marbles as Haley.
They have 305 total. How many marbles does Haley have? Answered by Penny Nom. 





A mixed number as a percent 
20161018 

From Jayda: how go you change a mixed number into a percent
Ex. 3 3/4 Answered by Penny Nom. 





y = mx + c and Ax + By + C = 0 
20161018 

From Erick: please explain to me how to convert an equation from the form y=mx+c to Ax+By+C=o form. Answered by Penny Nom. 





The degree of 2x + 7 
20161017 

From Deejay: How about when the given has no degree and the other has a constant only, For example 2x + 7,
where's the leading term and what is its leading coefficient? Answered by Penny Nom. 





Travelling upstream and downstream 
20161017 

From Kathleen: It took a boat 2 hours to reach town A going upstream. The way back was 1h20 min. What is the speed of the boat in still water if the speed of the stream is 3 mph? Answered by Penny Nom. 





A circle formed from bending a wire 
20161016 

From Deszaree: The same piece of a wire is bent to form a circle
calculate:
a, the radius of the circle
b, the area of the circle Answered by Penny Nom. 





A probability question concerning eggs 
20161016 

From Brian: Two participants are alternatively selecting eggs from a basket of 6 hardboiled eggs and 6 uncooked eggs.
Alternatively they are smashing the eggs on their foreheads. One participant gets 4 hard boiled eggs in a row and the other person gets 4 uncooked eggs in a row.
What is the probability of this occurring (I watched this happen).
Thank you
Brian Answered by Penny Nom. 





A linear relationship 
20161016 

From Bianca: x represents the number of hours since 8am. y represents the number of children the school nurse has seen during the school day. The nurse has seen 3 children by 8am and 27 children by noon.
How many children has the nurse seen at 2pm?
If the nurse has seen 18 children, what time is it? Answered by Penny Nom. 





An airplane schedule 
20161014 

From Stephanie: Starting at 8:00a.m., a passenger plane leaves from an airport every 6 minutes and a cargo plane leaves every 7 minutes. When is the next time these kinds of planes will leave at the same time? Answered by Penny Nom. 





Selina saved $6 on a 20% off sale 
20161014 

From Myra: I don't know how to help my child answer this question  Selina bought a shirt on sale that was 20% less than the original price. The original price was $6 more than the sale price. What was the original price? Answered by Penny Nom. 





A five digit number 
20161012 

From Massa: Explain why any four digit number is less than any five digit number? Answered by Penny Nom. 





Subtraction of two numbers in different bases 
20161007 

From Wica: Hello,
So happy I found this site. I am having problems with bases. My question is :
Please perform the subtraction between two number over different bases :
A. (5874)base 12  (216)base 9
B. (216)base 9  (5874)base 12 Answered by Penny Nom. 





How far is the boat from the harbour? 
20161006 

From Karabo: a boat sails 30 km due east from a harbour. Then it sails 40 km due north. How far is it from the harbour? Answered by Penny Nom. 





A kinky curve 
20161006 

From tammie: Koch’s kinky curve is created by starting with a straight segment and replacing it with four segments, each 1/3 as long as the original segment. So, at the second stage the curve has three bends. At the next stage, each segment is replaced by four segments, and so on. How many bends does the curve have at the third stage? Answered by Penny Nom. 





The remainder theorem 
20161004 

From A student: need help with this
f(x)=4x^415x^24; x2
using the remainder theorem to find the remainder Answered by Harley Weston. 





A triple product 
20161003 

From sam: Let a and b are vectors such that
Vector a = (1,1,2)
Vector b = (2,1,1)
And let vector c be a unit vector such that triple product of a,b,c is
minimum . We have to find the value of c.
[Thoughts]
I thought triple product of a b, c means the volume occupied by
parallelepiped. And we have to do volume minimum Answered by Penny Nom. 





The equation of a line 
20161001 

From Miriam: write the equation of the line that passes through (6,7) and is perpendicular to 3x+5y=0 Answered by Penny Nom. 





The equation of a circle 
20160930 

From Trent: write the equation of circle B with center B(2,3) that passes through (1,2) Answered by Penny Nom. 





Hexagonal pyramid bevel angles 
20160930 

From Peter: I have seen your response to a similar question from Steve which Chris and Harley responded to, however I am not familiar with some of the terms. Is there a formula that I can enter my details in which will give me the specific angles I require. The item I am constructing is much larger than the one you responded to previously. Thank you for any assistance you are able to provide. Answered by Penny Nom. 





Powers 
20160929 

From Ezra: i cant figure out this question. Can you please help
ezra
product of power (6x4)3 Answered by Penny Nom. 





A 2 million gallon tank 
20160928 

From Kimberly: I have a tank that is shaped like a cylinder, and it has to hold 2 million
gallons of water. There is a height limit of 30 ft.
I know the equation is V=pi x r squared x h but I don't know if I need anything
For the square foot of water. Answered by Penny Nom. 





Jenny, Charles and Chase have some butterflies 
20160926 

From Kyla: Jenny cares 7 times as many butterflies as Charles.
Charles catches 2 times as much as Chase.
All together they have 560 butterflies.
How many butterflies does each person have?
Please help, I am very confused on how to solve the problem.
Thank you! Answered by Penny Nom. 





A car chase 
20160925 

From Ms.: Car 1 is traveling down the road at 50 mph and passes Car 2 is
sitting on the side of the road. Car 2 needs to catch Car 1 one half mile
down the road. How fast must Car 2 drive to catch Car 1 if Car 2
waits 10 seconds before pursuing Car 1?
Yes, the assumption is that the Car 2 can accelerate from a standing position and over take Car 1 rate. What is the answer or formula for this type of question?
Respectfully
Befuddled Mom? Answered by Penny Nom. 





How fast and how far must Car 2 travel before catching Car 1? 
20160925 

From Ms.: Car 1 is traveling down the road at 50 mph and passes Car 2 is
sitting on the side of the road. Car 2 needs to catch Car 1 one half mile
down the road. How fast must Car 2 drive to catch Car 1 if Car 2
waits 10 seconds before pursuing Car 1?
Yes, the assumption is that the Car 2 can accelerate from a standing position and over take Car 1 rate. What is the answer or formula for this type of question?
Respectfully
Befuddled Mom? Answered by Penny Nom. 





2,0061234...484950 
20160924 

From Mimi: Compute the following:
2,0061234…484950 Answered by Penny Nom. 





The length of stock on a roll 
20160923 

From Ken: I have a roll that is 13.5 inches wide ( OD) , and is wound on a 3 inch core. the thickness of the material is 3.5 thick.
Do you know of a formula that can calculate the linear feet on that roll?? Answered by Harley Weston. 





Standard form 
20160922 

From anna: ok. i have b=2/3x+5/7. im supposed to change it to standard form. how do i do that? Answered by Penny Nom. 





The width of a 300 foot long rectangular acre 
20160921 

From Debbie: If 2 sides of a 1 acre plot is 300 feet each what are the other 2 sides? The acre is a rectangle. Answered by Penny Nom. 





The distance around a warehouse 
20160921 

From Chuck: How far do I walk when I walk around a 751,000 sq. ft. warehouse? Answered by Penny Nom. 





Two equations 
20160917 

From Nilesh: How to solve (xy)^1/2 + 3(xy) = 30 ; xy + 3(xy) = 11? Answered by Penny Nom. 





Integrate (x^2  4x + 4) ^4/3 
20160915 

From Ifah: Hi i have questions please answer
Integral 2 sampai 3 dari (x²  4x + 4) ^4/3 dx Answered by Penny Nom. 





20/2 + 2 * 2^2 + 6 = 8 
20160915 

From Simone: 20/2 + 2 * 2^2 + 6 = 8
insert brackets to make this true Answered by Penny Nom. 





The radius of a coffee cup 
20160912 

From Brett: What is inside radius, in centimeters of a coffee cup if it holds 350g of coffee when filled to a depth of 9.5 cm? Assume coffee has the same density of water, 1.00g/cm3. A numeric value is expected and not an expression. Answered by Penny Nom. 





Four digit numbers 
20160908 

From ning: 00009999 there is ten thousand 4digit numbers. How to find the number of ways that 4 digit are the same? How to prove it by using formula? Answered by Penny Nom. 





The equation of a ski slope 
20160831 

From Hannah: The information provided is
A ski slope has a slope of 0.2. You start at an altitude of 10,000ft.
Then the question is "Write the equation giving altitude (a) as a function of horizontal distance moved (d).
I know this is probably a very simple question but I didn't take a math class my senior year and now I'm a freshman in college, so some of it is very frustrating to me.
Any help is much appreciated, thank you! Answered by Penny Nom. 





The dimensions of a rectangle 
20160831 

From Hazym: How do I find the length(which is 15m longer than the breadth) and the breadth of a rectangle just by its perimeter which is 70 m? Answered by Penny Nom. 





Exponential form 
20160831 

From Lily: Hi! I was wondering, I was having a little issue understanding this one problem. It was "write 81 in exponential 2 different ways" and I already got 9(2) but I was wondering what the second one could be! Thanks! Lily Answered by Penny Nom. 





Todd Matt and Jeff 
20160830 

From Lisa: Three brothers spent different amounts of money on their recent vacation.
Matt spent $25 less than Todd.
Jeff spent 3 times as much as Matt.
How much did each brother spend if they spent a total of $275?
Check answer required
T= Todd Answered by Penny Nom. 





Two sequences 
20160820 

From Ting: The first four terms of a sequence are 4, 20, 56 and 120. By comparing with the nth term of sequence 1,5,14 and 30 which is 1/6n(n+1)(2n+1), find a formula for nth term. Can you precisely show out how you do this questions ( with the steps please) Answered by Penny Nom. 





I bought 3 books for $150.00 
20160820 

From Shavon: if i bought 3 books for $150.00 and 1 of the books cost 50% more than both other books combined what's the price of the more expensive book? Answered by Penny Nom. 





A suspension bridge 
20160818 

From sai: The main cable of a suspension bridge has the shape of a parabola. The cables are strung from the top of two towers, 61 metres apart, each 15.25 metres high above the roadway. The cable is 1.5 metres above the roadway at the point that is directly between the towers.
h(x)=a(x30.5)^2+1.5
where a is the constant and its value to be determined.
a) determine the value of the constant a by using that the fact that height of the suspension cable, h(x) is 15.25 metres at each tower. Hence, write the updated model equation. Answered by Penny Nom. 





The ages of 10 children 
20160817 

From Diann: Sum total of the ages of 10 children 10 children is 110, what are their ages if all are 2 years apart?
thank you Answered by Penny Nom. 





5/8 of 16 
20160814 

From Michael: What is the fraction of 5/8 of 16 Answered by Penny Nom. 





A search area 
20160813 

From tammy: if your searching an area and you go 300 km from point A and search 380° what or how much area would you search? Answered by Penny Nom. 





Covering an octagonal region with sand 
20160813 

From Lynn: How much sand is needed to fill a 20 ft. wide octagon area 6 inches deep? Answered by Penny Nom. 





The area of a circle 
20160812 

From sandeep: if circumference of a circle is πd what is the area? Answered by Penny Nom. 





Five consecutive even integers 
20160812 

From Marcelle: The average of 5 even consecutive numbers is 112. What is the largest numbers? Answered by Penny Nom. 





A ship and a light 
20160811 

From Kirby: A ship is sailing due west when a light is observed with heading 297°50' from the ship. After the ship has travelled 2250 feet, the light heads 311°55' from the ship. If the course is continued, how close will the ship approach the light? Answered by Penny Nom. 





A 15% discount 
20160809 

From eunice: brian brought a printer sale at the store. the discount was 15%, and brian saved 550. what was the printer original price? Answered by Penny Nom. 





Two lots 
20160808 

From Deniece: I have 2 lots that are joined together. One lot is 38' X 105' and the other is 45' X 105'. What is the total in acre size. Or, how close are these lots to make one full acre? I want to sell both lots and want to advertise using the total lot size. Thank you. Answered by Penny Nom. 





Carlos, Mark, Jeremy, and Alan collect Yugioh cards 
20160808 

From justin: Carlos, Mark, Jeremy, and Alan all collect Yugioh cards. Mark has twice as many cards as Jeremy. Carlos has 3 times as many cards as Jeremy, and Alan has collected 12 less than 3 times as many cards as Jeremy. Together the four players have collected 456 cards. How many does each person have? Answered by Penny Nom. 





Spraying an acre 
20160807 

From Sara: I have a spray rig that is 80' wide. How many feet must I go to have sprayed an acre? Answered by Penny Nom. 





A cone inscribed in a hemisphere 
20160807 

From anonymous: A cone is inscribed in a hemisphere. the slant height of the cone is 20cm. When cut along its slant height, the cone forms a sector of a circle.
find the angle of the sector, to the nearest 1 decimal place. Answered by Penny Nom. 





The diameter of a cylindrical tin 
20160804 

From Scott: a cylindrical tin is 15 inches high and holds 5 gallons of paint when it is full. Find the diameter of the tin.
(1 gallon = 0.1605 cubic feet) Answered by Penny Nom. 





The sequence 13 17 23 27 33 37 
20160729 

From Shriya: The first term of a sequence is 13.
The following terms are found by alternately adding 4 and 6 to the previous term.
The first six terms are 13 17 23 27 33 37.
Find the 80th term. Answered by Penny Nom. 





The modulus of a complex number 
20160729 

From Cheyenne: There's a question on my Summer Assignment I cant figure out. Here it is:
Find the absolute Value of the complex number. 5i
Please help? Answered by Penny Nom. 





The circumcentre of a triangle 
20160728 

From Raj: If the vertices of triangle ABC are A(4,1) B(1,2) C(4,3) then find coordinates of circumcentre of triangle Answered by Penny Nom. 





The dimensions of a rectangle 
20160725 

From Krunox: A rectangle is twice as long as it is wide. Its perimeter (the sum of the lengths of its sides) is 60 cm. Find its length and width. Answered by Penny Nom. 





A cubic equation 
20160725 

From Chinmay: x³2x²7x+5 Answered by Penny Nom. 





The number of sides of a polygon 
20160723 

From Shriya: All the angles of a polygon are either 155° or 140°.
There are twice as many angles of 155 °or 140°.
Find the number of sides of the polygon Answered by Penny Nom. 





The temperature inside and outside a greenhouse 
20160722 

From Mehzad: Every day, the temperature in a greenhouse is at its low temperature, 70 degrees Fahrenheit, at 2 a.m. and at its high temperature, 84 degrees Fahrenheit, at 2pm. Its temperature increases linearly between 2 am and 2pm , and decreases linearly from 2 pm and to 2am. The outside temperature follows the same linear patterns, but has a low temperature of 60 degrees Fahrenheit at 2 am and a high temperature of 78 degrees Fahrenheit at 2 pm. At which of the following times will the temperature inside and outside the greenhouse be the same?
a) 8:00 am
b) 12:00 noon
c) 4:00 pm
d) The two temperatures will never be the same Answered by Penny Nom. 





Two equations with fractions 
20160722 

From kanesh: p/2+q/3=3
p/4+2q/3=3 Answered by Penny Nom. 





Which term of this sequence has value 8? 
20160720 

From Lauren: Hi there
Which term in the sequence 2; 5/3; 4/3 ; 1; ... has a value of 8.
Since term 2 and 3 of this sequence contain fractions which can be converted to recurring decimals. What is the best way to work out the common difference here.
I do however understand that to work out the nth term of an arithmetic series, the following formula Tn = a + (n1)d. In this series a = 2 Answered by Penny Nom. 





Writing numbers in the form a/b 
20160717 

From Edward: How to write these numbers in form of a/b: 7, 0.175, 3.25, 37/10, 16, 1/3, 2.04 Answered by Penny Nom. 





A congruence theorem for two right angled triangles 
20160717 

From Sayari: Hello.
Is it possible for two right angled triangles to have the same length of base and height and a different hypotenuse? If not so, then why in the congruence criteria RHS the hypotenuse is given more importance? It can also be like 'two triangles are congruent if they are right angled and have the same base and height.'
Thank You. Answered by Penny Nom. 





The composition of a function with itself 
20160717 

From Mel: If f(1 + 3x) = 1 * x, solve f(f(x)) Answered by Penny Nom. 





If x+y=7 and x^2+y^2=42, then xy equals? 
20160717 

From Mehzad: If x+y=7 and x^2+y^2=42, then xy equals? Answered by Penny Nom. 





A train from Erie to New York 
20160714 

From carol: a train leaves Erie with twice as many women as men. At York, 17 men get on and 16 women . How many men and women were originally on the train?off. There are now the same number of men as women Answered by Penny Nom. 





Lisa went for a run 
20160714 

From Olive: Lisa ran 3km north and then 4 km east what was her total distance Answered by Penny Nom. 





The perimeter and area of a shape 
20160630 

From Scott: If I have a 16 x 32 rectangle the square feet is 512. So if I take a rope 96 feet long , which is the lineal feet of the rectangle, and manipulate it to any shape I want does the square footage inside the rope stay at 512 square feet? Thanks in advance! Answered by Penny Nom. 





A 1.4 acre square 
20160628 

From Jamie: Dear Faithfullness,
I was previously to be purchasing a square 1 acre plot, which I believe was to have 209feet, 4 sides perimeter.
How big would a 1.4 acre site be?
In sq feet length ie original 209ft + (the adeed 0.4) Answered by Penny Nom. 





Triakis 
20160627 

From Gordon: Some authorities treat "triakis" (and related terms "dyakis", "tetrakis", etc.) as attached prefixes; others treat them as separate adjectives. Thus I see one of the Catalan solids described as both "triakistetrahedron" and "triakis tetrahedron". Which usage is correct? Answered by Chris Fisher. 





Slope 
20160627 

From Ashiq: What is 1% slope if length 101 feet? Answered by Penny Nom. 





Subsets 
20160626 

From Kats: How Many sub sets are in set k={6,7,3} Answered by Penny Nom. 





find f+g 
20160626 

From yzabelle: find f+g
f(x)=x^21
g(x)=square root of x+2 Answered by Penny Nom. 





An equation involving pi 
20160626 

From Diaz: How would you solve :
( pie*X)/ 4 = pie/2
I have no idea.what to do! Answered by Penny Nom. 





Simultaneous equations 
20160625 

From sena: 2x/3+3y/2=1
4x5y=22
simultaneous equation Answered by Penny Nom. 





Sin squared (x) + Sin (x)  2 
20160625 

From Sree: Reduce the below to a single term
Sin squared (x) + Sin (x)  2
Thanks Answered by Penny Nom. 





An open ball is an open set? 
20160623 

From Aqeel: Theorem: The open ball is an open set? Answered by Harley Weston. 





Cubic feet of soil 
20160619 

From H: A garden is 8 ft x 7 ft that needs to raised 6 inch's How many cubic feet of soil required ? What am I missing ?
Thanks
H Answered by Penny Nom. 





Profit 
20160615 

From Toyia: 12.87 profit from 21.99 sale. What is the percentage that was taken off the 21.99 Answered by Penny Nom. 





Quadrilateral 
20160614 

From Muhib: Is there a quadrilateral with 0 sets of parallel sides. Answered by Penny Nom. 





A ratio of boys to girls 
20160612 

From Jasper: There are 600 pupils in a school. The ratio of the boys to girls in the school is 3:5 how many girls and how many boys are in the school Answered by Penny Nom. 





The difference between the ares of two rectangles 
20160609 

From Ingrid: I am trying to help my son with an area question.
I have the answer, from the solutions, but I cannot figure out how to teach him.
Question:
Two rectangles have lengths 13cm and 19cm respectively.
Their total area is 376cm squared.
If both their widths are whole numbers, what is the difference in their areas?
I know that this is solvable once I determine the widths of the rectangles ,
but how do I go about finding that?
Thanks for your help Answered by Chris Fisher and Harley Weston. 





Implicit differentiation 
20160606 

From Pranay: Is a circle x^2+y^2=2 a function? If it is not a function,
why is it possible to do implicit differentiation on it?
Thanks. Answered by Penny Nom. 





The lateral side length of a cone 
20160605 

From Diane: Question is find the lateral side length of a right cone with area of 372 sq. cm and base circle radius of 9 cm. Answered by Penny Nom. 





20 things taken 8 at a time 
20160530 

From Jessie: I need all of the 8 digit combinations using the numbers 120.
i.e 1 2 3 4 5 6 7 8, 2 3 4 5 6 7 8 9 like wise
no number should be repeated in one combination.
Thanks
Jessie Answered by Penny Nom. 





John and Max walk to meet each other 
20160529 

From abhay: The speeds of John and Max are 30 km/h and 40 km/h.Initially Max is at a place L and John is at a place M. The distance between L and M is 650 km. John started his journey 3 hours earlier than Max to meet each other. If they meet each other at a place P somewhere between L and M, then the distance between P and M is? Answered by Penny Nom. 





A barn roof 
20160529 

From Joe: Is it possible to build a barn roof (irregular pentagon?) with a 12' base and the other 4 sides 4' each? Thanks. Answered by Penny Nom. 





Placing a sphere in a cylinder of water 
20160527 

From Fiona: Hi the question i have is, if I have a cylinder filled with water and the volume of the water is 150Pi what would the rise in the level of the water be if you put a sphere into the cylinder with a volume of 500/3Pi? Sorry if it's a bit long winded Answered by Penny Nom. 





A cylinder in a cube 
20160525 

From Sonia: A cylinder has the same height and diameter as the sides of a cube use 3.14~ which has the greater volume Answered by Penny Nom. 





The area of a 4sided lot 
20160525 

From prasad: How to find area of a land whose sides are 41ft,33ft,32.3ft and 33.2 ft. Pl give me the formula and proof. Answered by Penny Nom. 





Two pieces of rope 
20160521 

From Render: Fred cuts a 12 inch piece of rope. Then he cuts a second piece of rope that is 3/2 longer than the first piece. Is the second piece shorter or longer than the first piece? Explain. Answered by Penny Nom. 





A trough with a triangular cross section 
20160521 

From Clarice: A trough having an equilateral triangle end sections has sides equal to 0.4 m and 7m long.what is the volume of the liquid in the container if the depth of the water is one half the depth of the trough? Answered by Penny Nom. 





Euler's polyhedron formula 
20160520 

From Antonia: why does not cylinders follow Euler's polyhedron formula ( VE+F=2) ??
if a cylinder has 3 faces, 2 edges and 0 vertices it doesn't follow Euler's formula??? Answered by Penny Nom. 





The tens digit of a number is five times the unit digit 
20160519 

From sanjeev: The tens digit of a number is five times the unit digit. Find the number? Answered by Penny Nom. 





Filling a pit with glass pebbles 
20160517 

From Sam: I need to know how many pounds of glass pebbles are needed to fill a 24 inch across circular fire pit, if 5 pounds covers 4"H x 4"W x2"D? Thank u for any assistance, Sam Answered by Penny Nom. 





A puzzle embedded in a table top 
20160513 

From Aaron: I want to make a table with a puzzle embedded in it. The table top would be a
36" circle and the puzzle is 20"x27" I'm thinking that it's not going to fit,
but not sure. Any help would be appreciated.
Thanks,
Aaron Answered by Penny Nom. 





The volume of a truncated rectangular pyramidal pond 
20160513 

From Paul: How do you calculate a partially filled truncated rectangular pyramid if you always know the bottom rectangle, the maximum height top rectangle perimeter, but have a varying height. Similar to filling up a pond you know the current height and dimensions at the max rectangle how do you calculate it half full i.e. 10x30 outside perimeter with a 2x8 base and a max height of 6ft how do you calculate it at 3ft without remeasuring the top perimeter.
Thanks,
Paul Answered by Harley Weston. 





A pair of equations with fractions 
20160511 

From tiya: hello, i want to know how to solve this question.
m/6+2n/3=6
m/10=2n/5=2 Answered by Penny Nom. 





A 70% off sale 
20160511 

From virginia: If the sale price is $129.99 @ 70% off  what was the original price? Answered by Penny Nom. 





At what time will Sara catch up with Jake? 
20160507 

From Laura: At 11:00 a.m., Jake started driving along a highway at constant speed of 50 miles per hour. A quarter of an hour later, Sara started driving along the same highway in the same direction as Jake at the constant speed of 65 miles per hour. At what time will Sara catch up with Jake? Answered by Penny Nom. 





A rectangular field 
20160507 

From Jan: A rectangular field is 63m long and 21m wide. A fence of 2m in height is needed to fence the field and fencing is also required to divide the field in three square sections. There are three wooden gates measuring at 1.5m to the three sections of the field. What is the total surface area of the fence needed for fencing and diving the field? Answered by Penny Nom. 





A 3 hour river cruise 
20160506 

From Jan: A 3 hour river cruise goes 15km upstream and then back again.The river has a current speed of 2km/h.what is the boat's speed and how long was the upstream journey? Answered by Penny Nom. 





A six digit code 
20160506 

From Ralph: How many combinations are possible if a "safe" has four buttons and you can use a six digit code? (these are just single press buttons..)For example, this could be one possible combination: Button 4 Button 1 Button 1 Button 3 Button 2 Button 4. Thanks! Answered by Penny Nom. 





Trigonometry 
20160430 

From Joel: I am bored with what I'm learning in 6th math class and want a challenge. I decided to look at trig. I couldn't find a good resource to teach me. Could someone either explain trig to me or show me a resource? Please don't say I'm too young to learn trig. I just am trying to learn. Answered by Penny Nom. 





Converting ml to g 
20160428 

From Lerato: I would like to know which formula should I use to convert ml to g? Answered by Penny Nom. 





A patio slab 
20160427 

From Heaven: Allie used 11.7m^3 of cement to make a square patio. If the thickness of the patio is 15 cm,what is the length of the patio? Answered by Penny Nom. 





Solve 2^2x + 3(2^x)  4 = 0 
20160427 

From Lloyd: Solve the equation 2^2x + 3(2^x)  4 = 0 Answered by Penny Nom. 





Covering a site with 6 inches of rock 
20160426 

From Carla: if a pump house that measures 20'x16' sits in the middle of a site that is 50'x60' and you apply crushed rock to the site at depth of 6", how many yards will you need to haul? Answered by Penny Nom. 





One million is six percent of what number? 
20160426 

From Colleen: One million is six percent of what number?
Thanks! Answered by Penny Nom. 





Dimes and pennies 
20160426 

From Renae: Charity has 42 more pennies than dimes. Hope has 7 times as many pennies than dimes. Hope and Charity have the same number of dimes. Together they have $5.46. How many dimes and pennies do each have? Answered by Penny Nom. 





sin 2x  sin x = 0 
20160424 

From lilly: sin 2x  sin x = 0 0 Answered by Penny Nom. 





The inverse function for f(x)=2x^2+5x 
20160423 

From Ashini: The inverse function for f(x)=2x^2+5x Answered by Penny Nom. 





A triangle inscribed in a circle 
20160422 

From Olyana: I am struggling with this question! Help!
So, there is a circle. In the circle, there is an equilateral triangle inscribed.
Each side of the triangle is 20. There is no other info given, other than
the triangle is inscribed in the circle and the sides of the triangle are 20.
I am supposed to find the radius of the circle! Please help! Answered by Penny Nom. 





600(1+0.05)^7 
20160421 

From chelsey: I am unsure on how to solve this problem, 600(1+0.05) 7 ? Answered by Penny Nom. 





Two tax rates 
20160421 

From Vishal: Total amount paid annually $444 for 2014 which is inclusive for tax.
tax rate for first six month is 7% then it is changed to 15% for second six months.
calculate the total basic amount paid before tax.
the basic amount on which tax paid in first and second six month is same. Answered by Penny Nom. 





A sector of a circle 
20160421 

From mustafa: In a sector of a circle, the arc length is equal to half the perimeter of a sector.find the area of a sector in terms of r Answered by Penny Nom. 





15.86 acres 
20160421 

From Ronald: If a rectangular piece of land is 1320 ft. on one side, how many feet would be required on the other side to equal 15.86 acres? Answered by Penny Nom. 





A square of side length 4x3 units 
20160420 

From Bryan: Find an expression that represents the area of a square with side length 4x3 Answered by Penny Nom. 





External and interior angles of a regular polygon 
20160419 

From pearl: a polygon has n sides.The exterior angle is 8 times the interior angle
find the value of the interior angle
find the value of n Answered by Penny Nom. 





The derivative of x! 
20160416 

From Sang: How to find the derivative of x! and integral of x! Answered by Penny Nom. 





Heights at various points along an arc 
20160415 

From Isiah: So I am working on a problem with a few friends; you have an arc with the center of its chord at 0,0. We also have a known sagitta and a known radius of curvature.
How do we calculate the height extending in both the positive and negative directions?
Central sag: 2.48
Chord length: 9.6 Answered by Penny Nom. 





Sloping my yard away from my house 
20160415 

From Harold: I need to slope a area of my yard away from my house and garage. The length of my house is 80 feet long and i need to slope it 22 feet away. I want to raise the dirt at the foundation by 6 inches and slope it down to nothing at the width of 22 feet. How much soil would i require? Answered by Penny Nom. 





A scale factor 
20160413 

From tonya: What is the scale factor for the two figures regular octagon with 15 and 9 written in decimal form Answered by Penny Nom. 





Mrs. Gibson has 3 children 
20160412 

From MJ: Mrs. Gibson has 3 children. The older ones are twins. The youngest one is 3 years
younger than the twins. If the sum of their ages is 102, how old is the youngest
one? Answered by Penny Nom. 





The area and the perimeter of a rectangle 
20160412 

From kimberly: is there a relationship between the are and the perimeter of a rectangle?
explain. Answered by Penny Nom. 





tan15° 
20160411 

From JOHN: find the exact value of tan15° in surd form. Answered by Penny Nom. 





The diagonal of a 10 acre square 
20160411 

From Derrick: I own 100 acre square of land. I want to run from farthest corner of property to farthest corner, Diagonally. How many miles would I have traveled? Answered by Penny Nom. 





Conversion of an equation 
20160411 

From Marie: How to you convert the equation of a line from xintercept form
(y=(xx1)(xx2)) to general form (y=ax^2+bx+c) if it involves square
roots?
For example:
Convert this equation to general form: y=(x+the square root of 5)^2
Thanks for the help! Answered by Penny Nom. 





A road trip word problem 
20160410 

From Marc: While on a road trip I imagined this random word problem. Suppose I start a trip of 75 miles. My initial speed is 75 miles per hour. After every mile traveled I decrease my speed by one mile per hour. After the first mile I decrease my speed to 74 miles per hour and so on for each subsequent mile traveled. How long will it take to complete the 75 mile journey? Answered by Penny Nom. 





The area of a circle and a square 
20160410 

From Richard: I cannot understand why if you have a perimeter say of 4 units as the circumference of
a circle then you reshape it into a square you lose very approximately some 20% of its
volume but the perimeter length stays the same.
Can you please explain this to me as to why the volume decreases. Answered by Penny Nom. 





A stained glass cone lamp 
20160409 

From Edwin: In making a 16" dia. cone lamp (stained glass), how many square feet of glass do I need. Answered by Penny Nom. 





Setting up a pool 
20160409 

From BETH: i am trying to cover an area for a 15x15 foot round pool with play sand before I set up the pool. My playsand bag is 50 lbs , says it covers .5 cubic feet per bag. How many bags do I need? Answered by Penny Nom. 





Filling a hole with 14 tons of rock 
20160408 

From Barry: If I had 14 tons of inch and one half sized aggregate rock, how large of a square or rectangular shaped hole would I need to hold that amount? Answered by Penny Nom. 





4 carpenters can build 8 houses in 10 days. 
20160405 

From Kenneth: Hello:
Here is my question:
4 carpenters can build 8 houses in 10 days. 2 carpenters can build how many houses in 15 days?
Here is one solution:
The number of houses built is jointly proportional to the number of carpenters and the number of days. So h = kcd where k is a constant. Substituting the given: 8 = k*40, so k = 1/5. Our formula is then h = cd/5. I'm not sure how to determine whether or not one unit is jointly proportional to any other unit.
However, if 2 carpenters are unknown as in 4 carpenters can build 8 houses in 10 days. How many carpenters can build 6 houses in 15 days? What is the solution using this method? And likewise, if days are unknown, as in 4 carpenters can build 8 houses in 10 days. 2 carpenters can build 6 houses in how many days?
I thank you for your assistance. Answered by Penny Nom. 





Pizza delivery 
20160403 

From Andrew: Suppose you own a local pizza restaurant, Pizza with Pizzazz, and in order to compete with the big pizza chains in your area you are considering an advertising campaign offering customers a free pizza if their pizza is not delivered in 30 minutes or less. Even though your pizza restaurant is known for its fast and friendly delivery service, you are not sure if you can afford to give away too many pizzas for free. Looking over your past 12,421 pizza deliveries you find out 97% of the pizzas were delivered in 30 minutes or less.
Calculate the probability that all 100 randomly selected pizza deliveries will have been made in 30 minutes or less? Hint: Use the multiplication rule. (Round 4 decimals)
I'm really stumped on how exactly to do this problem. I don't need the answer just the steps broken down to show me how to get it!
It would be gladly appreciated if you could help! Answered by Penny Nom. 





Maximizing the area of a two lot region 
20160403 

From yousef: A man wishes to enclose two separate lots with 300m of fencing. One lot is a square and the other a rectangle whose length is twice its width. Find the dimensions of each lot if the total area is to be a minimum. Answered by Penny Nom. 





The last two digits of a phone number 
20160403 

From Joshua: I want to find the last two digits of a phone number whose first eight numbers of a ten digit phone numbers are known. Answered by Penny Nom. 





20 mangoes 
20160401 

From Mussharat: I have 20 mangoes and have to put them in 5 boxes such that
the numbers will be odd numbers.Also I can't cut or take the seed
out from the mango . What should I do. It's really confusing.
I'll be more than happy if you could help me. Answered by Penny Nom. 





The volume of a cone 
20160331 

From Odum: Find the volume of a cone with radius 6.5cm and height 12.6cm Answered by Penny Nom. 





When does sqrt(x^2+y^2)=x+y? 
20160330 

From Margret: when does sqrt(x^2+y^2)=x+y Answered by Penny Nom. 





A tilted cylinder tank 
20160328 

From Astri: I have a problem determining the fluid level for tilted cylinder tank.
Actually I've found some solution here for horizontal cylinder tank. What if the cylinder
is tilted at a certain degree, for example 30 degree from the vertical axis.
Thank you. Answered by Penny Nom. 





The remainder theorem 
20160327 

From Pratyasha: A quadratic polynomial when divide by x+2 leaves a remainder of 1 and when divided by x1 leaves a remainder of 4. What will be the remainder if it is divided by (x+2)(x1)? Answered by Penny Nom. 





The volume of a box with a hexagonal base 
20160327 

From Frank: how many gallons of water in an 8" hexagon shaped box. 6" sides x 12.5" high ? The walls are 1" thick , beveled @ 30 degrees, so inside dimensions are 6" Answered by Penny Nom. 





A square based box and a cylinder 
20160326 

From rajpal: i m trying to calculate an area required to hold 4.4 mln cubic metres of volume.
I used square and I get below result
A box shape that has dimensions 1500 meters (1.5km) by 1500 meters (1.5km) by 2 meters depth has a volume of:
= 4,500,000 cubic meters (4.5 mln cubic meters)
but when I use a cylinder shape, i get below result
A cylindrical shape that has a radius of 850 meters and a depth of 2 meters has a volume of:
= 4,539,600 cubic meters (4.54 mln cubic meters approx)
why is it that the cylinder, though of same depth holds more volume than a square?
kindly clarify. Answered by Penny Nom. 





An isosceles triangle inscribed in a circle 
20160325 

From NIHAL: A isosceles triangle is inscribed in a circle having sides 20cm,20cm,30cm. find the radius of circle Answered by Penny Nom. 





Polynomial division 
20160325 

From Ashley: (4x4+6x^3x^2)/(3x2)
The instructions say to "perform the division". Answered by Penny Nom. 





A problem in base x 
20160325 

From Malith: determine the value of base x of (211)x = (152)8
please mentioned the steps
Thank you Answered by Penny Nom. 





Travelling in a spacecraft 
20160325 

From julie: if i was travelling in a spacecraft at the speed of light and i turned on my headlight would i see the beam ? Answered by Robert Dawson. 





A rotating schedule for a softball team 
20160325 

From Caroline: I couldn't find a similar question, hopefully there isn't one!
I have a softball team of 18 people (7 girls and 11 boys), but am limiting each game to 13 players (6 girls and 7 boys). The season is 10 games long. How do I create a rotating schedule which allows members to play evenly? I tried separating the boys and girls to create rotation for each but I got confused. Some are unable to attend all games but for the simplicity of a rotation schedule can you please help? Answered by Robert Dawson and Victoria West. 





The inverse of a function 
20160320 

From Billy: f(x) = Square root(x^2 + 2x)
What is the inverse? Answered by Penny Nom. 





Biking and jogging 
20160317 

From alondra: Ricky went on a bike ride. After 6 miles he got a flat tire and had to jog home. He jogs 3mph slower than he bikes, so the jog took 1 hour longer than the bike ride. At what rate did he travel each way? Answered by Penny Nom. 





The perimeter of a rectangle 
20160317 

From Linda: Noel correctly adds the length of three sides of a rectangle and gets 88 cm her brother Ryan correctly adds the lengths of three sides of the same rectangle and gets 80cm. What is the number of cm in the perimeter of the rectangle Answered by Penny Nom. 





A block wall 
20160315 

From Robert: I have a wall 40 ft. long and 4 ft. tall as well as another one that is 30 ft by 3.5 ft. tall that I am trying to build. how many 6 inch by 12 inch landscaping blocks do I need? Answered by Penny Nom. 





The sides of a triangle 
20160315 

From Hitarth: Why we cannot construct a triangle ofngiven sides 5cm,5cm and 10cm? Answered by Penny Nom. 





tan inverse 1/4 
20160314 

From nazz: prove; tan inverse 1/4=1/3 cot inverse 52/47 Answered by Chris Fisher. 





Angles 
20160312 

From Laurynn: What are angles in general (please include the 'angle of incline')
Thank you
Laurynn Answered by Penny Nom. 





The integral of a sum 
20160310 

From Rahul: How to solve definite integral of a sum. The specific problem is as follows,
Integral of ( 1+ sum of x^k, k=1 to k=n), x=0 to x=b *dx.
The answer is b + sum of b^(k)/k, k=2, to k=n+1. I understand only the integral
of first term. But integral of the sum I do not understand at all. Answered by Penny Nom. 





A circle and a chord 
20160310 

From Mujtaba: The distance of a chord of length 16 cm, from the centre of the circle of diameter 20 cm Answered by Penny Nom. 





A word problem 
20160310 

From Sam: Jo is 10 cm taller than Ruth. Pam is 16cm taller than Ruth .Rod is 8cm taller than Pam.
How much taller than Jo is Rod? Answered by Penny Nom. 





An equation with fractions 
20160309 

From Ed: 7/10___ +3/2=6/5 Answered by Penny Nom. 





Can you construct a regular 21gon? 
20160308 

From Peter: hi, i know that if i use a compass to draw a circle, i can use the same setting to mark 6 intervals along the circle circumference, how would i go about marking out 21 equally spaced points around the circumference?
if there an online calculator i can us, or some other interesting trick?
tia
peter Answered by Robert Dawson. 





Tiling a floor 
20160305 

From joanne: How many floor tiles 20x20 inch do I need for area of 8x 12 ft.? Answered by Penny Nom. 





The area of a rectangle 
20160303 

From Lucas: The area of a rectangle is given by A=x2+18x+72
use factoring to find an expression for the dimensions of the rectangle.
if the area of the rectangle is 7 square feet, what are the possible values of x?
what are the dimensions of a rectangle? Answered by Penny Nom. 





A geometric progression 
20160303 

From Pauline: A woman measures the height of her child at birth and at monthly intervals afterwards.The child's height increases by 5% per month. Find the number of measurements she has made before the child's height is twice what it was at birth Answered by Penny Nom. 





Corrosion inhibitor in a pipeline 
20160302 

From Edu: I have a 12 in pipeline and 5 miles long. I need to coat it with corrosion inhibitor how much chemical will I need Answered by Penny Nom. 





Compressed Earth blocks 
20160302 

From John: how many 14"x10"x4" blocks do I need for a 1300sq foot house 8 foot high Answered by Penny Nom. 





A percentage problem 
20160302 

From jehanzaib: if x is a percentage: e.g. 40%
than what does "x/(1+x)" = 29%. what is the explanation. Answered by Penny Nom. 





A rectangular prism 
20160302 

From Paula: Trying to help with a math problem. I don't know how to set up the equation for this.
A rectangular prism has a volume of 7.875m3rd and a height of 3.5 m. What is the area of the base of the prism?
Thanks for your help! Answered by Penny Nom. 





An algebra problem with a sphere 
20160229 

From Sania: If the number of square centimeters on the surface area of a sphere is equal to the number of cubic centimeters in its volume find its diameter Answered by Penny Nom. 





A deck that is half an ellipse 
20160228 

From Steve: On your website, I was reading a question and your response from a girl named Angela in which you provided a formula by which her father, a welder, could figure out points on an arc corresponding to equal 3' intervals on a 30' chord where the vertex was 1' off the chord. Is there an equivalent formula when working with an ellipse? I suspect this change will make the calculations significantly more complex. I am building a deck that is half an oval, and would like to be able to mark out the perimeter by measuring the distance from regular intervals on the primary access to a corresponding point on the perimeter. I will then connect the points on the perimeter and cut a reasonably smooth arc. The length of the primary access will be 22' and width of the deck at the vertex is 9'. I would like to be able to know the distance from the primary axis to a point on the perimeter at equal intervals of 6" along the primary axis. Can you help? Answered by Penny Nom. 





A 13 game bet 
20160228 

From farah: I'm trying to calculate the odds of a 13 game bet. Each game has 2 teams with 3 possible outcomes (win,draw,lose).
What are the odds. Answered by Penny Nom. 





10800 sq. ft equal approx what part of an acre? 
20160227 

From David: 10800 sq. ft equal approx what part of an acre Answered by Penny Nom. 





A word problem 
20160227 

From KRK: amrutha thinks of a number, multiplies it by 5 & 6, devides the result by 3
and takes away the number first thought of to get an answer 36. find out
the number Answered by Penny Nom. 





Solve for x and y 
20160227 

From ntshidi: Y=1/2x+4and1/4x6 Answered by Penny Nom. 





A place value drawing 
20160224 

From Kristin: Make a place value drawing of a number that has
double the number of tens as ones and three times
the number of thousands as hundreds write the number. Answered by Penny Nom. 





The sum of the angles of a triangle 
20160224 

From Sophia: Does every triangle add up to 180 degrees? (Such as a unique triangle) Answered by Penny Nom. 





The weight of some dirt 
20160224 

From Michael: How many tons of dirt are in a triangle 14M x10M x 8.1M x .8M deep? Answered by Penny Nom. 





Converting a fraction to a percentage 
20160222 

From Preitty: How can I turn fractions into percentages when the denominator is not a number that can multiply to 100? Answered by Penny Nom. 





How can I express Sin 4A in term of Sin A? 
20160222 

From Odukoya: How can I express Sin 4A in term of Sin A? Answered by Penny Nom. 





A bonus of 8% of sales 
20160222 

From Barghavi: A man earns $325 per week plus an additional 8% on any sales over $500.
If he makes $6,250 in sales, how much money in total does he earn that week?
thank you! Answered by Penny Nom. 





The evaluation of a 3 by 3 determinant 
20160219 

From Kristen: What is the stepbystep process on how to evaluate the determinant of a 3*3 matrix, using the expansion method (not the diagonal method) Answered by Penny Nom. 





The domain and range of a function 
20160219 

From Genius: State the domain and range
g(x)=x(x1) Answered by Penny Nom. 





The interior and external angles of a regular polygon 
20160217 

From percy: a regular polygon has n sides .The size of each interior angle is eight times the size of each exterior angle .
1.find the size of each exterior angle
2.calculate the value of n Answered by Penny Nom. 





Shooting a ball at a target 
20160216 

From Thys: Hi
I have a problem with the formula that i use .(for programming)
I have looked all over the web to find a solution but no luck.
I have a cannon that shoots a ball at a target
I use this formula to calculate what my initial velocity must be to hit the target
at a angle of 30 degrees and a distance of 15m (the cannon and target position is known)
It works perfectly if both is at same height but if one is higher or lower it miss.
In an example I am working with the range is 30m, the angle is 45 degrees and the target is 10m higher than my position.
Please help
Formula = V0 = √RG / Sin(2α) Answered by Harley Weston. 





0/0 
20160214 

From Noni: Q. 0÷0=1 Why it is wrong when 4÷4=1; 3÷3=1; 2÷2=1: 1÷1=1 ? Answered by Penny Nom. 





Speed and velocity 
20160214 

From kechi: A boat sails south through Chesapeake Bay. It takes 10 hours to sail 110 kilometers. Describe the boat's motion. Calculate the boat's speed and velocity, showing the calculations. Explain how the boat's speed is different from its velocity Answered by Penny Nom. 





Perpendicular lines 
20160214 

From Brendon: points A (4; 6) , B (1;2), C (5;3) and D (4; 1) are given
prove that AC and BD are perpendicular to each other Answered by Penny Nom. 





Calendar arithmetic 
20160214 

From Jenalee: January 1, 2001 is Julian Day 2 451 911 (the number of days that have passed since Day 0, January 1, 4713 BC).
If Julian Day 0 was a Monday, what day of the week was January 1, 2001? Answered by Victoria West. 





Two equations in two unknowns 
20160213 

From Anumba: 4x + 2y = 4
7x  y = 11 Answered by Penny Nom. 





Todd is 3 years older than his brother Jack 
20160213 

From Victoria: Todd is 3 years older than his brother Jack. If Jack is x years old and Todd is y years old, write a rule that relates their ages over time. When Jack is 28 years old, how old will Todd be? Answered by Penny Nom. 





Travelling with and against he current 
20160209 

From Lloyd: A boat travelled 210 miles downstream and back. The trip downstream took 10hrs, the trip back took 70hrs
1. what is the speed of the current?
2. what is the speed of the boat in still water? Answered by Penny Nom. 





A 2 digit number 
20160208 

From Lloyd: The sum of digits of a certain 2 digit number is 7.
Reversing its digits increases the number by 9.
Find the number Answered by Penny Nom. 





Backfilling a rectangular hole for a shop foundation 
20160208 

From Jeremy: Hello, I'm going to be backfilling a rectangular hole for a shop foundation and need to know how much concrete and gravel I'm going to need to fill it in. The shop foundation is 38 feet wide by 30 feet long and 4 feet deep, there is also a concrete perimeter going inside the foundation that measures 16 inches wide and goes all the way around the inside of the foundation Answered by Penny Nom. 





The equation of a vertical line 
20160207 

From Kagiso: The equation for a vertical line that goes through the point (7; 3) is? Answered by Penny Nom. 





38 is what percent of 400? 
20160207 

From chris: 38 is what percent of 400? Answered by Penny Nom. 





An exercise with factorials 
20160207 

From vidhi: find the value of n: (11/2) (22/3) (33/4)...(1515/16) = n!/16 Answered by Penny Nom. 





How many acres? 
20160206 

From JOHN: How many acres of land is in a strip that is 5000 foot long and 100 feet wide? Answered by Penny Nom. 





A metal gate 
20160206 

From Carl: I am a welder and I build gates. I have to put holes in a rail and then bend the rail
in a curve. The problem is that the holes in the curved rail must line up with holes
in the other straight rails. How do I calculate where to put the holes in the rail
before I bend it? I will send a drawing if necessary. Answered by Harley Weston. 





The midpoints of the sides of a quadrilateral 
20160205 

From Andrea: The segments, joining, in order the midpoints of consecutive sides of a quadrilateral form a parallelogram. Answered by Penny Nom. 





When will Scott and Jill have earned the same amount? 
20160204 

From kalia: Scott starts with $10 and earns $5 and hour. Jill starts with $40 and earns $3 and hour. when will the two have the same amount of money in the same hours? Answered by Penny Nom. 





The height of a triangle 
20160203 

From Brooklyn: How do I figure out the height of a triangle when it only tells me the base of he triangle? And vice versa. Answered by Penny Nom. 





A two car competition 
20160202 

From Christian: Question: Two cars are racing to a fixed point and back. One car travels 70 MPH both ways
While the other travels 60 MPH there and 80 MPH back, which car won the race?
It is not a tie. Answered by Penny Nom. 





Division base 5 
20160201 

From Jenalee: I am having problems with a dividing bases question. I reviewed two that I could find in the database and tried the question as shown but I am still getting the wrong answer.
My question is 32\24043 to the base of 5 for both. Answered by Penny Nom. 





Golf for 6  2 three balls 
20160201 

From Andy: We are shortly having a golf holiday in Phoenix. There are 6 people playing 6 rounds, so we will play in 2 three balls. Is there a combination of pairings that ensures everyone plays with each other the same number of times. Many thanks for your help ! Andy Answered by Victoria West. 





Which term of the series 2+7+12+...is 152? 
20160201 

From francis: whice term of the series 2+7+12+...is 152? Answered by Penny Nom. 





Simplify 
20160201 

From Sabira: Simplify step by step
5x/8 + 7y/18 = 6 Answered by Penny Nom. 





Subtraction in a base larger than ten 
20160131 

From Jenalee: Hello,
So happy I found this site. I am having problems with bases. My question is 97B9  6A3A base 16 for both.
Please help. Answered by Penny Nom. 





Percentage reduction 
20160130 

From Kuuku: The daily production targets in 2000 was 60,000 units this declined to 48,000 units in 2001 but was projected that further 300units reduction would be experienced in 2002. Calculate the percentage reduction by 2002. Answered by Penny Nom. 





Prove the earth is round 
20160130 

From Kevin: Working on a project for a science fair.
To prove the earth is round without the ability to get way above the surface.
How could we set up and experiment to see the curve.
My thought is using a telescope at the beach?
Form what we see so far the curve is 8 inches per mile?
So thought is set up a telescope and a target 1 mile away? Answered by Robert Dawson and Chris Fisher. 





A quadrilateral inside a square 
20160130 

From Subrahmanya: In a square ABCD of side 6 units P, Q are mid points of BC, CD respectively. The line segments BQ, DP intersect in R then find the area of the quadrilateral ABRD using only plane geometry. Answered by Chris Fisher. 





The diagonals of a polygon 
20160129 

From Sofia: What are diagonals and if you drew an octagon and drew all the diagonals how many would there be? Please explain because this is pretty confusing! Thank you! Answered by Harley Weston. 





Consecutive angles of a parallelogram 
20160128 

From Hanna: The consecutive angles of a parallelogram measures Answered by Penny Nom. 





Two increases of 20% 
20160127 

From Z: How do I find how many books are in a library given a problem like this... The number of books increase after buying 20% more in May. The number increased again by 20% after they were given 300 books. How many books did it start with?. Answered by Penny Nom. 





Two increases of 20% 
20160127 

From Z: How do I find how many books are in a library given a problem like this... The number of books increase after buying 20% more in May. The number increased again by 20% after they were given 300 books. How many books did it start with?. Answered by Penny Nom. 





Exponential form 
20160126 

From Jufe: What is the exponential form of ³√11x² Answered by Penny Nom. 





A chord of a circle, the central angle and the radius 
20160126 

From Nishan: If chord length is given along with angle then how to calculate the radius. Answered by Penny Nom. 





Exponential growth 
20160126 

From Paul: The value of a stamp was 0.03 in 1851. The value in 2011 is $50,000. If the value increased exponentially, what is the annual growth rate? Answered by Penny Nom. 





I was paid 67% of the total owed 
20160125 

From Julie: I was paid $27000. This is 67% of the Total Owed. The Total Owed is unknown. How do I calculate the amount of the Total Owed? Answered by Penny Nom. 





The range of a function with a finite domain 
20160125 

From Hannah: Solve y=(1⁄4)x1 if the domain is (4,2,0,2,4).
I don't get how to do this. Can anyone help? Answered by Penny Nom. 





A system of linear equations 
20160124 

From kareem: my name is kareem
and i am a student i have a math puzzle and i tried to solved it but it always have same mistake
xy=9
x+z=12
zn=14
y+n=2 Answered by Penny Nom. 





The diameter of the top of a truncated cone 
20160124 

From Peter: I am trying to calculate the diameter of a truncated cone given
one diameter the height of the cone and a 10% taper from one end
to the other. For example a butter churn is 18" tall and 9" in
diameter at the base. the sides need to slope inward at 10%
What is the diameter at 9" and 18" Answered by Penny Nom. 





A quadratic equation with equal roots 
20160123 

From abdiwahid: X^2+2ax+4x+9a=0 is quadratic equation which has equal roots. Find the possible value of a? Answered by Penny Nom. 





Fractions of two quantities 
20160122 

From Melody: Kate ate 1/4 of her orange. Ben ate 2/4 of his banana. Did Kate and Ben eat 3/4 of theit fruit? Explain. Answered by Penny Nom. 





The length of an 80 acre piece of land 
20160121 

From Eugene: Have to clear a piece of land 80 acres by 500 feet wide. What is the length of the property? Thanks Gene Answered by Penny Nom. 





Find two values of x satisfying f(x)=1 where f(x)=sin(ln(x)) 
20160121 

From Ruth: I'm trying to find two values of x satisfying f(x)=1 where f(x)=sin(ln(x)) Answered by Penny Nom. 





The volume of a silo 
20160118 

From Clinton: Can you show me how to calculate the ground corn capacity in a steel silos of 10' x 10' high and 10' x 20' high and 10' x 24' high and 10' x 28' high Answered by Penny Nom. 





A Max/Min problem with an unknown constant 
20160117 

From Guido: Question:
The deflection D of a particular beam of length L is
D = 2x^4  5Lx^3 + 3L^2x^2
where x is the distance from one end of the beam. Find the value of x that yields the maximum deflection. Answered by Penny Nom. 





The perimeter of a square 
20160116 

From dennis: If I have eleven Square Acres, what would the perimeter dimensions be? Answered by Penny Nom. 





A limit of a rational function 
20160116 

From selvamani: F (x) = x^3+3x^29x2 / x^3x6 and limit x tends to 2, f (x) exist then limit x tends to 2, f (x) is equal to ? How to answer this problem. Answered by Penny Nom. 





The perimeter of a one quarter acre square 
20160115 

From Kerry: If you have a perfect square that is one quarter of an acre what are the length of the sides and how do you arrive at the solution? thank you, Kerry. Answered by Penny Nom. 





Complex numbers in standard form 
20160115 

From Michael: express the following complex numbers in standard form (2+3i)+(52i) Answered by Penny Nom. 





Solve 1/3 ( x5 ) + 4 =1/6 ( 2  3 x ) +1 for x 
20160115 

From edwin: 1/3 ( x5 ) + 4 =1/6 ( 2  3 x ) +1 Answered by Penny Nom. 





A rectangular enclosure 
20160115 

From Amber: A rancher wants to use 300ft of fencing to enclose a rectangular area of 4400 square feet. What dimensions should the rectangle be? Answered by Penny Nom. 





Countable and uncountable sets? 
20160115 

From wilson: what are the countable and uncountable sets? Answered by Penny Nom. 





The range of a function defined piecewise 
20160113 

From sarah:
f(x)={x2, x<2
{x^24, 2_<x_<2
{x+2, x>2
find the range Answered by Penny Nom. 





A triangular shaped garden 
20160113 

From Demetrie: Dwayne's garden is triangleshaped with two equal sides and a third side that is 4 ft more than the length of an equal side. If the perimeter is 49 ft, how long is the longest side? Answered by Penny Nom. 





Sue's favourite number 
20160112 

From Maria: This is my son's homework. He is 7. Can you help?
Sue has a favourite number.
It is an even number.
It has 3 digits.
The digits add up to 15.
Find 10 numbers that could be Sue's number? Answered by favourite number. 





The perimeter of a triangular plot of land 
20160111 

From Janelle: I need to fence off 6.5 acres. The plot is triangular shape. How many feet would I be fencing off? Answered by Penny Nom. 





Three discounts 
20160110 

From Tiffany: Khairul wants to buy a sofa set. He is offered 3 successsive discounts of 10%,20% and 25%, and he can arrange them in any order he wants. Which order will benefit him the most? Explain your answer. Answered by Penny Nom. 





Water flowing through a rectangular drain 
20160108 

From Tiffany: the cross section of drain is a rectangle 30 cm wide. If water 3.5 cm deep flows through the drain at a rate of 22 cm/s, how many litres of water will flow through in one minute? Answered by Penny Nom. 





The area of a rectangle 
20160108 

From ranjan: if we make a rectangle with a 100cm of wire, then its area will be? Answered by Penny Nom. 





Integration of dx/(x^2+1)^3 
20160107 

From Ishank: Integration of dx/(x^2+1)^3 Answered by Penny Nom. 





A pipe is installed with a 2% grade 
20160107 

From peter: a sewer ditches to be 148 feet long. the pipe is installed with a 2% grade.
what would be total amount of fall be? Answered by Penny Nom. 





Three consecutive integers 
20160107 

From ronn: Three consecutive integers whose sum is 186 Answered by Penny Nom. 





Two transport companies 
20160106 

From Brynleigh: The Sugar Sweet Company will choose from two companies to transport its sugar
to market. The first company charges $5096 to rent trucks plus an additional fee of
$200.75 for each ton of sugar. The second company charges $5500
to rent trucks plus an additional fee of $175.50 for each ton of sugar.
For what amount of sugar do the two companies charge the same?
What is the cost when the two companies charge the same? Answered by Penny Nom. 





A ratio word problem 
20160106 

From Nina: The length and the width of the rectangle is in the ration 5:3. Its area is 375m2. Find its perimeter. Answered by Penny Nom. 





A sequence 
20160105 

From Mia: the next three terms in each sequence. 0.4, 0.54, 0.68, 0.82, Answered by Penny Nom. 





A graph of the water level of a river 
20160105 

From emoni: Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Answered by Penny Nom. 





Four consecutive integers 
20160105 

From sherica: my teacher gave us an assignment and it says here that;
THERE ARE FOUR CONSECUTIVE INTEGERS.IF THE SMALLEST ONE IS x ,FIND THE SUM OF THE FOUR INTEGERS. that is the question ...thanks hope that u can answer it Answered by Penny Nom. 





Find the quadratic equation whose roots are 4 and 7 
20160103 

From sadiya: Find the quadratic equation whose roots are 4 and 7 Answered by Penny Nom. 





Markup as a dollar amount 
20151230 

From Lori: Hello,
I am trying to figure out mark up as a dollar amount. Is it the same as profit or is it a different number? And what is the formula to get to it, please? Thank you Answered by Penny Nom. 





The height of a parabolic arc 
20151230 

From Tom: Is there an algebraic means to determine the highest point of a parabolic arc if the base and perimeter are known? Answered by Penny Nom. 





Number of bricks needed 
20151230 

From trudy: if I have 250 sq ft of space that I want to fill with bricks that measure 7.5 in by 11.5 in how many bricks do I need to fill the 250 sq ft. Answered by Penny Nom. 





Book sales 
20151230 

From Sandra: Your finance text book sold 56,500 copies in its first year. The publishing company expects the sales to grow at a rate of 20.0 percent for the next three years, and by 8.0 percent in the fourth year. Calculate the total number of copies that the publisher expects to sell in year 3 and 4. Answered by Penny Nom. 





How can he raise his average to 90? 
20151229 

From Raj: Harris has an 87 in a class where daily works count 20%, quizzes count 20% and tests count 60%.
If there are only two test scores what must the score on his second test to raise his average to 90? Answered by Penny Nom. 





A relative maximum and a relative minimum 
20151228 

From kemelo: show for the following function f(x)=x+1/x has its min value greater than its max value Answered by Penny Nom. 





A circle is inscribed in a hexagon 
20151228 

From Lalitesh: A circle is inscribed in a regular hexagon ABCDEF
Prove that AB+CD+EF=BC+DE+FA Answered by Penny Nom. 





A troublesome word problem 
20151228 

From Linda: James is now 3/5 John's age. Three years ago, he was 1/2 John's age. Three years from now, he will be 2/3 John's age.
How old are they now? Answered by Penny Nom. 





Constructing simultaneous linear equations 
20151228 

From Deborah: Linda thinks of a twodigit number. The sum of the digits is 8. If she reverses the digits, the new number is 36 greater than her original number. What was Linda's original number?
Thank you! Answered by Penny Nom. 





Strings of characters 
20151228 

From Ali: If I have an app and offer a two, three and four digits name and it can be only number, letters or both?
I want to know how many options will I have for each?
For example
the two digits: aa, 11, a1 or 1a
the three digits: 111, a2a, 222
the four digits: 1111, 2ge3 or 1234
So if I used all the letters and all the numbers but nothing starts with a zero
How can I calculate them separately? Or what's the result for each?
Thank you
Ali Answered by Penny Nom. 





A diameter of a circle 
20151227 

From sahil: Find the equation of diameter of circle x2 +y26x +2y8 which passes through the origin. Answered by Penny Nom. 





Converting a fraction to a percent 
20151222 

From Sharon: How do you turn a fraction into a percentage? I'm beyond confused with this. Even though I think of myself as a good math student doing 8th grade math at a young age, this just makes me want to scream! I get the way you turn 1/4 into 25%, but when it comes to something like 7/9 = ? I just can't figure out the answer. Answered by Penny Nom. 





The angles of a triangle 
20151217 

From Faith: Does the measure of angle determine the length of its side? For example two angles are congruent then the sides are also congruent because from my understanding the angle determine the shape of triangle. Answered by Penny Nom. 





The perimeter of a 4 acre square 
20151216 

From samantha: What is the distance in miles or how many laps to make a mile, if one was walking around 4 acres of land which is like a square? Answered by Penny Nom. 





A bus trip 
20151215 

From Michelle: I do not know what equation(s) should be used in order to obtain the answer(s) to this word problem.
A bus was rented for a trip, the cost was dived equally amongst the passengers. During the trip, someone mentioned that if there were 9 more passengers, they would have paid each 5$ less. Another mentioned that if there were 6 less passengers, they would have each paid 5$ more. What is the cost of renting the bus and how much must each passenger pay. Answered by Penny Nom. 





Proof that an erroneous algebraic statement is false 
20151214 

From Berteanu: I need help with this proposition:
"It exists x a real number that for every y real number 5*x2*y*y=1
This is false.
Let x be from R.
And I need an y real number that 5*x2*y*y!=1
Please,could you help me? Answered by Penny Nom. 





Sierpinski Pyramid 
20151214 

From victor: Is a tetrix (a Sirpienski Pyramid/Tetrahedron) its own hyperplane?...alternatively, is it a hyperplane? Answered by Robert Dawson. 





The positive root of sin(x) = x^2 
20151213 

From Kemboi: Find the positive root of the equation sin(x) = x^2 Answered by Penny Nom. 





Linear equations in two variables 
20151213 

From priya: I have problem in solving these equations please help me today itself very urgent:
I)2x+y=y
II)pie*x+y=9 Answered by Penny Nom. 





The dimensions of a rectangle given its area and aspect ratio 
20151213 

From colum: Can you work out the length and width of a rectangle where you know only the area and aspect ratio Answered by Penny Nom. 





Constructing a cross country district schedule 
20151213 

From David: Retired math teacher trying to help soninlaw schedule a cross country district schedule. The would like to have four trimeets each week for five weeks and one week of dual meets. The score the trimeets as three duals, i.e. 1v2, 2v3, 1v3 constitutes one trimeet. After many hours, not sure its possible, but I have forgotten a great deal! Thanks Answered by Victoria West. 





Building a dreamcatcher 
20151210 

From Faye: I have been asked to build a dreamcatcher, which is round into a 3x3foot area. What would the circumference be that I would need to make the hoop? I am thinking it is 9.42 feet long but am not good in math. Answered by Penny Nom. 





Matthew skateboards around the school 
20151209 

From Abigail: Matthew skateboards 4km each hour.
How long will it take him to skateboard around the school yard measuring 300m by 200m.?
Thank you. Answered by Penny Nom. 





The line of intersection of two planes 
20151209 

From Rabz: Determine the vector equation for the intersection between the two given planes
2x+7y equal to 14,x+z equal to 7 Answered by Penny Nom. 





The original price before a discount and taxes 
20151209 

From Michelle: Good day,
I would like to know if there is a particular equation to validate the following information:
I had to find the original cost of an item sold for 759.36$ before a 25% discount and 13% taxes.
I know we must use separate question to obtain the answer but I am unsure how to write the equation to validate my answer. Answered by Penny Nom. 





20 golfers playing a 20 week season 
20151207 

From Jeff: We have 20 golfers playing a 20 week season. We play in foursomes. How best to set foursomes so everyone can play with every without playing with the same person multiple times? Answered by Victoria West. 





Travelling in opposite directions 
20151206 

From Roselyn: Jenny and Mark commute to work, travelling in opposite directions. Jenny leaves the house at 8 AM, and averages 35 kph. Mark leaves at 8:15 AM, and averages 40 kph.At what time will they be 40 kilometers apart? Answered by Penny Nom. 





Compacted and uncompacted soil 
20151205 

From J.H.: I am negotiating with a company to sell them land that they would use for excavating soil to be used in construction. I would like to value the land based on the volume of soil they are likely to remove. I have seen several answers, giving the calculation based on 43,650 sq. ft./acre x number of acres x number of feet in depth, divided by 27 to convert the number to cu. yds. However, that is the number when compacted. They pay $.50/yd. of soil removed, but that yd. is not compacted. How do you calculate the number of yds. of uncompacted soil in 1 acre of land? Answered by Harley Weston. 





A word problem with percentages 
20151205 

From Caedryn: After giving 25% of her stickers away, May had 50% as many stickers as Rose. If they had 200 stickers altogether at first, how many stickers did Rose have? Answered by Penny Nom. 





A schedule for a league with 15 teams 
20151205 

From Zac: Hello,
I have a league schedule question. We have a league where we have say have 15 teams. Each team is to play each other twice during a 10 week session.
However each team tries only to play 3 matches(teams) per night(week).
How would we set up a random schedule for the 10 week session? Answered by Victoria West. 





Drawing an arc 
20151204 

From hassan: how to draw a curve long 1m with an angle of 22.5? Answered by Penny Nom. 





The height of a truncated cone 
20151204 

From Jack: I need to build a truncated cone that has a top of30 inches and a base of 64 inches . The sides need to be at a 64.5 degree angle. This will determine the height. Can this be calculated? Answered by Penny Nom. 





A tangent line to a parabola 
20151202 

From pei: Given that the line y=mx5 is a tangent to the curve y=2x^2+3 find the positive value of M. Answered by Penny Nom. 





Riding a mountain bike up and down a mountain 
20151202 

From sam: Michael, can climb a mountain at 2.5km/hr on his mountain bike. he descends the mountain at 5.5km/hr. he completes the whole circuit in 7 hours. how long is the trail to the top of the mountain? Answered by Penny Nom. 





A parabolic arch 
20151130 

From Muhammad: An arch over a road has a parabolic shape it is 6 meter wide at the base and is just
tall enough to allow a truck 5 meter high and 4 meter wide to pass
a):
assuming that the arch has an equation of the form y=a(x)^2+b use the given
information to find a & b. explain why this assumption is reasonable.
b):
sketch the graph of arch equation Answered by Penny Nom. 





Pouring a foundation 
20151127 

From Lisa: Hi im building a house 30ft long 18 ft wide I would like to pour a foundation of 6 inches
deep. How much sand, cement , 1/2" gravel do i need. Answered by Penny Nom. 





The sweep angle of a video camera 
20151125 

From Franc: a television camera is 30ft from the sideline of a basketball court 94 ft long. The camera is located 7 ft from the mid court. through what angle must it sweep in order to cover all action on the court? Answered by Penny Nom. 





The angle at the vertex of an isosceles triangle 
20151125 

From Karan: I have been given an isosceles triangle. the Top angle is what i have to find out and the two sides adjacent to it are both 4.9 cm. i have been told that the area of the triangle is 4 cm^2. i have no idea how to work this out, any ideas? Answered by Penny Nom. 





The range of f(x)=(2x+2)/(x1) 
20151125 

From Nazrul: f : R to R is a function which is defined by f(x)=(2x+2)/(x1).
Is f(x) an onto function? Please explain.
What is the range of this function?
Thank you very much for your previous help. Answered by Harley Weston. 





How much does the Earth curve over a one foot distance? 
20151124 

From Sean: Hi, I am trying to figure out how much the earth curves over a one foot distance. I'd like to be able to draw the exact arc on a piece of paper. I am an artist and am looking to make glass vessels with the exact curvature of the earth. I read on your site that it curves approximately 8 inches per mile. can I just use simple ratios to break it down into inches?? Thank you so much for your help. Answered by Harley Weston. 





The measure of an angle in terms of its complement 
20151122 

From Pam: Can you please help me so I can help my daughter the equation is the measure of angle v is 4 time the measure of its complement what is the measure of angle v when the equation is 4x+x=90 Answered by Penny Nom. 





Dividing by a fraction 
20151121 

From Jennifer:
Question from Jennifer, a student:
I want to know how to get the right answer for this math problem, dividing a fraction in to a whole number , example 3/8 using the whole number 6? Thanks Answered by Penny Nom. 





20 million as a percentage of 7.3 billion 
20151118 

From Nick: Based on the estimate of the worlds current population (7.3 billion people), I'm trying to work out what percentage of that figure 20 million people would amount to?
(Apologies in advance that I've no idea if the 7.3 billion figure is an American Billion or UK billion)
Thanks for any help.
Nick. Answered by Penny Nom. 





Archimedes, Euclid and "Circular Reasoning" 
20151115 

From Ron: I have read about Archimedes and his work with sphere in cylinder and cone in cylinder and the volume relationships. Did he or any others also extend this to regular based polygon based regular like pillars, and columns? The ratio of 1/3 to 1 whole holds true with all regular based columns as example: a regular pyramid having a regular hexagon base inside a regular hexagon column of equal height. Answered by Chris Fisher. 





A common tangent to two general parabolas 
20151115 

From Kind: Hi,
I want to find the common tangent of two general parabolas, but i don't know if it's possible or not.
If it's possible, please make a tutorial.
The first parabola equation : Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.
The second parabola equation : Gx^2 + Hxy + Iy^2 + Jx + Ky + L = 0.
I need this because i want to find the equation of Beloch fold. (Huzita  Hatori 6th axiom)
However if you know any other method to find Beloch folds equation, I am open for any suggestions. Answered by Chris Fisher. 





A schedule for 12 high school golf teams 
20151115 

From Jason: I have 12 high school golf teams (A  L). There will be 4 games each week for 4 weeks. For each game, 3 teams play at a time (A vs B vs C). I would like it where no team plays the same team twice. Week four is my issue as I seem to always have a team or two playing the same team again. Is it possible to have each team play each other only once? Answered by Victoria West. 





Dealing with surds 
20151114 

From Agnes: simplify (1√3)(1÷3+√3) Answered by Penny Nom. 





The diagonal of a rhombus 
20151114 

From Om: In a rhombus ABCD, angle A=60° and side AB=6 cm. Then diagonal BD is ? Answered by Penny Nom. 





The area of a domed roof 
20151113 

From Brandon: I have a tank with a 13' radius that has a domed roof of 3.5' tall How do I figure out the area in SQFT? Answered by Penny Nom. 





A three digit number 
20151113 

From Tina: The sum of the digits of a 3digit odd number is 13. The digit in the tens place is 4 less than the digit in the hundreds place and 3 more than the ones digit. What is the number? Answered by Penny Nom. 





Working with fractions 
20151112 

From muhammad: There are 1200 pupils in a school, 2/3 of them are girls, 1/4 of the boys are overweight.How many boys are overweight? Answered by Penny Nom. 





A volume in cubic yards 
20151112 

From James: The first formula for figuring cubic yards of concrete need is length in feet, times width in feet, times depth in actual inches, divided by 320. Such as, 150x 50 feet x 4inches divided by 320 = cubic yards. How and why does this formula work? Answered by Penny Nom. 





A concrete container 
20151112 

From Karstin: The exterior of a concrete container will be 10 feet by 8 feet by 4 feet tall. The walls and the bottom are 6 inches thick. What will it cost to construct it if concrete is $98.95/cubic yard? Answered by Penny Nom. 





Fencing around a rectangular field 
20151111 

From Darlene: Question from Darlene, a parent:
A farmer has 10,000 meters of fencing to use to create a rectangular field. He
plans on using some of the fencing to divide the rectangular field into two
plots of land by constructing a fence inside the rectangle that is parallel to one
of the sides. Let X be the width of the rectangular field. Write an equation
to express the area of the field as a function of X. Find the value of X that
maximizes the area of the field. Answered by Penny Nom. 





Roof Square footage 
20151111 

From Todd:
Question from Todd:
Good Day.
I have to figure out the square footage of a quonset style roof that's not playing by the rules The building dimensions (rectangular) are 63'x135' the height of the roof is 9.25'. It not an entire Quonset, It's that style of roof,(curved). There are concrete block walls 10' up to the metal roof.
Thank you!
Todd Answered by Harley Weston. 





The combination to a locker 
20151111 

From Jason: Hi,
I can't seem to open my locker cause I forgot the combination, the numbers are 18
Without repeat for 4 number for example 1234 or 2345 for numbers 18 without any repeat. Answered by Harley Weston. 





The derivative of x^1/3 
20151108 

From omar: hi can help me
am teacher ask me about x^1/3 Derivation definition . Answered by Penny Nom. 





Is 22/7 bigger or smaller than 3.14? 
20151106 

From Natalie: Is 22/7 bigger or smaller than 3.14? Answered by Harley Weston. 





A schedule for 8 golfers over 5 days 
20151104 

From Ged: Hope you can help with the following to save next years arguments !
Schedule for 8 golfers playing as pairs in 2 X 4 balls on 5 days.
No player to pair same player more than once and to have played with each player
In the 4 ball.
Thanks. Answered by Victoria West. 





The domain of cos2x/(sinx2) 
20151102 

From Ameen: Find the domain of:
f(x) = cos2x/(sinx2) Answered by Penny Nom. 





Factoring a trinomial 
20151102 

From Eric: 2v(squared) +11v +5 Answered by Penny Nom. 





A quadratic equation with known roots 
20151101 

From Awudu: Given the roots of the quadratic equation ax^2+5x+c=0 are 5 and 2/3,find the values of a,b and c. Answered by Penny Nom. 





Doubling the area of a pamphlet 
20151031 

From Mariam: A pamphlet has the following dimensions: 4 cm by 6 cm
If the area of the pamphlet is doubled, what will be the length of each side if sides can be integer values only? Answered by Penny Nom. 





A 15 team tournament 
20151028 

From Joseph: We have a 15 team tournament. Each team plays all other teams. We need a schedule were each game has a work team. Thus at each fields we have two teams playing and one working. All teams need to play each other and also be a work team. Any help would be appreciated!! Answered by Victoria West. 





An 8 Team Basketball League Schedule 
20151028 

From Janice: We have an eight team league that play at four time slots each week. It's a seven week season. How do we schedule so that each teams plays each other at least once? Answered by Victoria West. 





A trig identity 
20151028 

From Gail: verify sec(x) =cot(x)+tan(x)/csc(x), the csc(x) is under both the whole term cot(x) + tan(x) Answered by Penny Nom. 





A 4 by 7 array 
20151027 

From star: don breaks a 4x7 array into a 2x7 array and another array.what is the fact for don's second array Answered by Penny Nom. 





The uniqueness of the lub 
20151025 

From Aishwarya: Prove that if the lub and glb of a set exist then they are unique Answered by Penny Nom. 





An example of an irrational number 
20151022 

From Allison: It ask me to find an example of an irrational number less than 5 and I don't
understand what the difference from a rational number and an irrational
number besides the fact that a rational number can be repeated and shown in
a simple fraction and an irrational number can't be written in a simple
fraction.
Can you help me? Answered by Penny Nom. 





The sum of two repeating decimals 
20151022 

From Kaitlin: Here is the question I am struggling with:
Is the sum of two repeating decimals always repeating decimal? Explain your answer and give an example.
I answered this question thinking that no you cannot but only when adding 0.9 repeating, but my professor said this was incorrect.
Thanks for the help!
Kaitlin Answered by Penny Nom. 





A schedule for a pool league 
20151021 

From Hazel: I have to make a schedule for my pool league. I have twenty teams each of which must play all other teams. I have ten tables which must also be rotated to all teams play on all tables. Answered by Victoria West. 





Subtraction in base 8 
20151021 

From Adi: Hi!
Can you help me with a nagging problem, I searched a lot over the web and couldn't find it.
I saw this site I gave it a try and I found it to my liking.
I am confused how to subtract bases from other bases:
567 (in base 8)
 456 (in base 8)
______________
?????????
How do you do this? I do know how to carry and subtract with different bases. Can
you please help me?
Thanks,
Adi Answered by Penny Nom. 





Simplify 3(x7) 
20151021 

From geraldine: simplify: 3(x7) Answered by Penny Nom. 





Scheduling a social curling league 
20151020 

From Tyler: I'm scheduling a social curling league where all skips will play with all thirds, all seconds, all leads. And all thirds will do the same and so on. We have 6 teams of 4 and will be doing 6 rotations. Is it possible that all skips will play with all other players from other positions without anyone doubling up?
My initial thoughts were (1,1,1,1) (2,2,2,2) (3,3,3,3) (4,4,4,4)(5,5,5,5)(6,6,6,6)... then rotate the thirds up and seconds down but don't know what to do with the leads and even with just 3 positions there's doubling (1,2,6,x)(2,3,5,x)(3,4,4,x)...4s have doubled (4,5,3,x)(5,6,2,x)(6,1,6,x) as you can see I'm having problems
If you could let me know if this is even possible it would be greatly appreciated Answered by Victoria West. 





6 teams randomly arranged in groups of 3 
20151019 

From Anthony: im trying to make a game scheduled for 6 teams using a 1vs2vs3 ; 4vs5vs6 format.
all 6 teams randomly arranged in groups of 3. each team will play all teams at least twice, im trying to see how to make the number of times each team play another the same.
schedule should be arranged as such 1vs2vs3 4vs5vs6 so that (1vs2, 1vs3, 2vs3) and (4vs5, 4vs6, 5vs6)
i am limited to having only 2 sets of 3 at a time with 6 teams. Answered by Victoria West. 





An 8 team schedule 
20151019 

From Dean: I need an 8 team schedule for 2 time slots where 3 teams are on the ice per slot. I understand that there will be 2 teams on a bye per day. How do make sure that the byes are fair? Can you help me out? Answered by Victoria West. 





A six team league to play a 20 game schedule 
20151019 

From Kelly: Hi there. Some of your posts are close, but my problem is evening out the home
and away games. We have 6 teams in our league and we are going to play a 20
game schedule, playing everyone 4 times. We will play Fridays and Saturdays,
each weekend. Of course the ideal would be to have each team have a home and
an away game each weekend, but I realize that is impossible, but I would like it as
close as possible. Any help would be much appreciated!! We also were considering
opening with a home and away  Friday then Saturday with the same teams. Then
carrying on with playing everyone else and then possibly finishing up with the same
home and home Answered by Victoria West. 





Acres of cattle waste 
20151019 

From Chris: In my first math problem, I found out that 100 cows will produce 21900 ft3 of waste over a year. However I don't know how to do the second part. How many acres of land would a farmer need to spread the waste on if he wanted it to be more that 6 inches deep? Thank you. Answered by Penny Nom. 





Six teams playing five games 
20151018 

From Aidan: I have six teams that will be playing five games.
I want each team to play each game once and each team to play each other team once.
Is this possible or should I add an extra round and let some teams play each other twice? Answered by Victoria West. 





Exponential form 
20151017 

From Will: What is exponential form of 8? Answered by Penny Nom. 





4 games in 4 time slots with 8 teams 
20151016 

From Paul: I'm trying to set up a game matrix for my kids that will have 4 games in 4 time slots with 8 teams. And every team is playing a different game in a different time slot. I provided the initial matrix and I am trying to ensure that no 2 teams play each other more than once. That's my problem.
8 pm 9 pm 10 pm 11 pm
Crokinole 1 vs 2
Trivial Pursuit 3 vs 4
Darts 5 vs 6
Pictionary 7 vs 8
Please help, I've been at it for hours. Answered by Robert Dawson and Victoria West. 





11 golfers over five rounds 
20151015 

From Leo: 11 golfers over five rounds. Will golf as 443. How to set it up so everyone plays at least once with each player. Answered by Victoria West. 





The sequence 1,2,4,7,11,16... 
20151015 

From HEMANT: what is the next term in the sequence : 1,2,4,7,11,16,? Answered by Penny Nom. 





A schedule for 16 teams 
20151014 

From Ellen: I will have 16 teams. I would like to figure out how I can have 4 groups of 4 teams playing in hour increments, but never meeting more than once. How do I accomplish this? Thank you so much for any help you can give to me. . Answered by Victoria West. 





We are six golfers going away for 3 days of golf 
20151013 

From Mike: We are six golfers going away for 3 days golf. We are playing in 2 no threeballs playing concurrently. How can we arrange things so that everyone plays averydody else at least once. Is this possible.? Answered by Victoria West. 





The flight of a ping pong ball 
20151013 

From Abigail: Hello,
Wondering if there is a way to figure out the quadratic equation of half of a parabola?
Doing an assignment about finding quadratic equations for separate bounces of a ping pong ball, but the first bounce is incomplete (as the ball has presumably been dropped, hit the ground and then went on to make a complete bounce).
Please see attachment for references to the diagram that I am using.
Not sure whether I would have to look at it from a different perspective.
Thanks,
Abi Answered by Harley Weston. 





The area of two lots 
20151013 

From Lynn: I have 2 lots that have mobile homes on them... I was told they were 100 x 200 lots.. I have tried to calculate it on here but was not able to understand how to exactly do it. I would like to know if I have a 1/2 acreage or exactly what the 2 lots are? Answered by Penny Nom. 





2.236... 
20151013 

From Ann: 2.236...
What is the most specific category of numbers does this fall into? Rational or Irrational? Does the .... mean that it repeats? Answered by Harley Weston. 





How can the probability be zero? 
20151013 

From anagha: Hi,
thank you for answering (beforehand)
The other day I was just thinking of circles and I came across this peculiar thing.
Most of'em say that there are infinite number of points on the circumference.
and, if it is true, if we spin the radius, the probability that it will point a a particular point is 1/infinity, right?
It didn't make any sense to me and so, I thought there might be an explanation or something of the kind...? Answered by Harley Weston. 





Mathematics 
20151013 

From anagha: Hi,
thank you for answering (beforehand)
The other day I was just thinking of circles and I came across this peculiar thing.
Most of'em say that there are infinite number of points on the circumference.
and, if it is true, if we spin the radius, the probability that it will point a a particular point is 1/infinity, right?
It didn't make any sense to me and so, I thought there might be an explanation or something of the kind...? Answered by Harley Weston. 





Squash scheduling 
20151001 

From Ed: I have 5 teams and 2 courts. Every Thursday we play at four different times (6,7,8,9 o clock)
Each team will play each other 5 times over 25 weeks.
Everyone should get to play evenly at the best time (6:00) and the worst time (9:00) Answered by Victoria West. 





I was wondering what xy means. 
20150930 

From Eric: I was wondering what xy means. My two things I think it means are the two digits of x and y or x times y. thanks for your time,
Eric Answered by Penny Nom. 





sin(x/2)=cos(3x/2) 
20150927 

From Valentine: sin(x/2)=cos(3x/2)
I was trying to use cos3x=cos(2x+x) but there wasn't any progress Answered by Penny Nom. 





The length of a rectangle 
20150926 

From Tris: Hi,
I'm trying to figure out the length of a rectangle but i forgot how. So, the width is
5cm and the perimeter is 34cm. Answered by Penny Nom. 





The dimensions of a rectangle 
20150925 

From Erick: A rectangular strip of land has a perimeter of 124meters and an area of 385 square meters. Find its possible dimensions Answered by Penny Nom. 





2p^2+4p=16. How do i get p? 
20150922 

From Dohie: How do i solve this?
2p^2+4p=16. How do i get p?
Thanks Answered by Penny Nom. 





A 6person team that has 9 players 
20150921 

From Sheri: I am organizing a 6person team that has 9 players. How do I schedule them fairly over a 9 week league? Answered by Victoria West. 





A hockey roster of 19 kids 
20150921 

From Brian: We have a hockey roster of 19 kids. We only want to play 15 kids for each game. 4 players will not play each game. There are 16 games total. We want to rotate who doesn't play evenly. Can this be done? How many games will each player sit during the season? Answered by Robert Dawson and Victoria West. 





Square roots 
20150921 

From mariana: I have read various articles on how to find the square root of irrational numbers and every article out there seems to be very confusing.
i read you answer to LUKOW about irrational numbers and i am still quite confused. Say i want to find the square root of 326. i know that it is between 18 and 19 because 18 is the square root of 324 and 19 is the square root of 361 im just very confused about the rest of the process. Please help! ( if possible i would appreciate two examples. thanks) Answered by Penny Nom. 





32 golfers playing 6 rounds 
20150919 

From scott: i am looking for a schedule for 32 golfers to play 6 rounds and never play with the same person twice.
I made one for 28 golfers but i am struggling with 32. Answered by Victoria West. 





Partitions into distinct parts 
20150919 

From Brian: Looking for a formula where I can type in a number, 17 for example, and using the numbers 1 through 17 (1, 2, 3, 4 etc....), to come up with all possible combinations, when added, that will equal 17. And each number can only be used once. I've tried a few search engines but my computer stares at me blankly and scratches its head :/. Answered by Chris Fisher. 





A word problem 
20150917 

From Suszanne: Multiplying a number by x yields the same result as dividing the number by 0.125. What is the value of x? Answered by Penny Nom. 





Two price reductions and a coupon 
20150916 

From Suszanne: Mary purchased an item for 45% off the original price, plus an additional 20% off the sale price.She also had a $5 off coupon, which the salesclerk applied after these two discounts. Mary's final purchase price for the item was $50. She paid no sales tax, what was the original price of the item? Answered by Penny Nom. 





Seven switches with 3 stages each 
20150915 

From jeff: We are trying to solve a combination problem. If I have 7 things that can be in 3 states (say on/partially on/off), and all 7 have to a state. How many different combinations can there be? It doesn't seem like we should treat it as 21 independent things, but not sure how to break the problem apart. Answered by Penny Nom. 





Order of operations 
20150912 

From Tanisha: I would just like to double check if something like 5x squared times 4x cubed equals 20x to the power of 5??
It's just that we were told you can only answer an equation like this if the base is the same...so does that mean the x part or the whole thing like 5x?
I'm sorry if that didn't make sense!
Thank you for your help!! Answered by Penny Nom. 





20 golfers for 6 days 
20150911 

From Dave: have 20 golfers for 6 days. Each player should pair with 18 golfers
used a system on your website which is good for 5 days, but cannot get the 6th day.
Thanks for your help Dave Answered by Victoria West. 





18 golfers playing four rounds 
20150909 

From Paul: I have 18 golfers playing four rounds. I want two 3 balls and
three 4 balls each day. I don't want anyone to play in a 3 ball
more than once and I don't want anyone to play with the same
person twice. I realise everybody can't play with everybody, I
just want the best you can do. Answered by Victoria West. 





Scheduling for a bridge club 
20150909 

From margot: Can you help me with scheduling our bridge club?
8 rounds are played with four teams together.
There are 16 teams in total, so our schedule should look like eight 4x4 boxes.
(Each round the four teams play each other over the course of the evening) Answered by Victoria West. 





Division and units 
20150908 

From Kenneth: Hello:
Would there be a reason to divide a number without units by another number with units?
Here is an example:
35 divided by $5.00 or 35/$5.00
The answer cannot have units ($) because $5 X 7 does not equal 35 but instead $35.00.
$35.00 divided by 5 or ($35.00/5) and $35 divided by $5.00 or ($35.00/$5.00) make more sense.
I thank you for your reply. Answered by Robert Dawson. 





An increase in savings 
20150906 

From A student: A man spends 80% of his income. His income increases by 40% and his expenditure also increases by 25%. Find the percentage increase in his savings? Answered by Penny Nom. 





HCF and LCM 
20150905 

From Ally: the HCF of the two numbers is 3, and the LCM is 15.
what could the two numbers be? Answered by Penny Nom. 





A schedule for eight teams and four stations 
20150904 

From Joel: We are having a youth activity where we have eight teams and four stations. At each station there will be two teams competing against each other. We need each team to go through all four stations, but without ever competing against the same team, and, of course, without ever doing the same station twice.
If this possible? Thank you! Answered by Victoria West. 





A tangent line to a circle 
20150903 

From Jamie: Use the Greek method to find an equation of the tangent line to the circle
x^2+y^24x+6y+4=0 at the points (3,2square root 23. Answered by Penny Nom. 





The weight of a pumpkin 
20150901 

From Lisa: A pumpkins weighs 10 pounds plus half of 10 pounds plus half it's own weight, what does the pumpkin weigh? Answered by Penny Nom. 





The diameter and circumference of a circle 
20150901 

From Tracey: Hello,
I own a custom workroom, I am figuring out fabric quantities or an estimate. When
at the job site, I forgot to measure the diameter of the semi circle shape that I have to
make a cushion for!!!
If the circumference of the semi circle is 165" what would the diameter be, maybe half
this measurement????
I appreciate any help...I basically need the width from left to right to see if I can fit
the cushion on one width of fabric that is 52" wide! Answered by Penny Nom. 





Three chickens weighed in pairs 
20150901 

From Shelly: My son brought home a problem of 3 chickens of different weights listing their weights in different groupings of 2. We are to determine the weight of all three together. I think it's a ratio problem, but I am too far removed to formulate a plan to teach him how to solve it. Answered by Robert Dawson and Penny Nom. 





Subtraction base 5 
20150829 

From nakita: can u explain the quinary subtraction ...
(3000) (2342) all the numbers are in quinary number system Answered by Penny Nom. 





Working backwards 
20150827 

From Heather: Tom took a collection of tiles from a box. Sue took 13 and Bob
took half of those remaining. Tom had 11 left. How many did they start with? Answered by Penny Nom. 





A schedule for an 8 person team 
20150827 

From Julie: We have 8 people on our team, but only 4 can play every week. We have 32 weeks, total. How can we divide this so everyone plays evenly ? Answered by Robert Dawson. 





A procedure for finding a square root 
20150827 

From Tracey: Is there a method/process to determine the square root of a large number?
For example, Tiananmen Square's area is 396 900m sq., what is the side length?
Thank you,
Tracey Answered by Harley Weston. 





Factor x^2 + y^2 
20150826 

From Jerome: Factor: x^2+y^2 Answered by Penny Nom. 





A conditional probability problem 
20150824 

From Faustina.: Please I have an exam tomorrow. And I have tried by best in solving this Question. An urn contains 10 white, 5 yellow and 10 black marble. A marble is chosen at random from the urn and it is noted that it is one of the black marble, what is the probability that it is yellow? Answered by Penny Nom. 





Four equations in 3 unknowns 
20150823 

From damien: solve:
S x U  T = 44
T  U x S = 36
U + T  S = 7
U x U / S = 4 Answered by Penny Nom. 





Reinforced steel mesh in a circular foundation 
20150822 

From Padmesh: in a circular foundation we are laying a reinforced steel mesh . i.e., like chords in both ways. the circle diameter is 2.91m and rods are placed 0.1m spacing. so I want to find the number of rods present in that circle. here by I am attaching an auto cad drawing for your reference Answered by Penny Nom. 





Arrangements of the letters STRANGE 
20150822 

From Ravi: In how many ways can the letters of the word STRANGE be arranged to that the vowels occupy only the old places. Answered by Penny Nom. 





A two digit number 
20150821 

From Cameron: Write the 2 digit number that matches the clues.
My number has a tens digit that is 8 more than the ones digit. Zero is not one of my digits.
My number is ________. Answered by Penny Nom. 





The distance over a Quonset 
20150820 

From jane: total base of hemisphere is 30 ft
apex height is 20 feet
what is total length over dome Answered by Penny Nom. 





A probability question 
20150819 

From Omar: Hi my name omar ,
I have an exam tomorrow and i want answer of this question
Thank you
Q:the probability distribution function of a discrete random variable X is given by
P(X=x)=kx^3
For X=0,1,2,3
a)the value of the constant k . Answered by Penny Nom. 





20 golfers playing four rounds 
20150817 

From Paul: I have a party of 20 golfers playing four rounds in fourballs.
I realise that everyone will have 7 players that they do not play
with, however I want to ensure that no one plays with the same
person twice and that the Captain plays with the 12 players of
his choice. Answered by Victoria West. 





Factor 2(x+1)(x3)^23(x+1)^2(x3) 
20150813 

From Bella: The directions are the solve and factor the expression completely:
2(x+1)(x3)^23(x+1)^2(x3)
I was factoring out an (x+1) and and (x3) however the answer showing in my book is different and I can't figure out what I'm doing wrong please help Answered by Penny Nom. 





Parallelogram area 
20150804 

From Nigel: To find the area of a parallelogram you multiply the base by the height of the parallogram, the height being determined by an imaginary line drawn at right angles to the base. However if I made a parallelogram with joints at each corner and maipulated it to an upright position where the base and sides were at 90 degrees to each other,, I could then simply multiply the base times the height to get the area. Since the sloping side of the parallelogram does not vary in my imaginary jointed model, why can I not simply multiply the base by the sloping side to get the area in the same way that I multiply the base times the height of a square to find its area ? I cannot find the answer to this on the internet although I have searched. Answered by Chris Fisher. 





Rotating speakers through a 10 week schedule 
20150803 

From Timothy: I want 15 students to speak 7 times each over the course of 10 weeks.
They each will have 5 minutes.
Thanks Answered by Victoria West. 





An oil field barrel 
20150802 

From Michael: I have a storage tank that is 12' diameter x 22.5' high
it's capacity is 450 oil field barrels (42 gallon)
Which would hold 19,036 us gallons
I'm trying to find out how many inches it would take to make 1 barrel
I was able to get this far by using your volume calculator, but haven't been able to come up with the rest!
Thank you very much for your time, and I really appreciate this site and the tools you all have made available to everyone for free!
Hope to hear back from you soon and God bless you all!! Answered by Penny Nom. 





The length of a shadow 
20150801 

From maaz: Hello
I am having trouble with this question:
Lizzie, who is 6 feet tall, stands in her driveway at night, exactly
24 feet from the base of a spotlight, and casts a shadow that is 12
feet long if her friend Hannah who is 5 feet tall decides to stand
next to lizzie how long will her shadow be? Answered by Penny Nom. 





The distance between two boats 
20150726 

From mohammad: Two boats leave the same dock at the same time,one traveling due east at 10 mph and the other due north at 24mph,how many miles apart are the boats after 3hours ? Answered by Penny Nom. 





Scale 
20150724 

From Kenneth:
Hello:
Can you explain mathematically how the following scales become inches to feet?
For example, how does the scale of 1:160 become 1/16" = 1'?
(1:160) (1/16" = 1 foot) scale
(1:87) (1/8" = 1 foot) scale
I saw more of these different scale examples at the following:
http://www.oakridgehobbies.com/hobbyshop/modelinginscaledimensionsfaqs.html
I thank you for your reply! Answered by Robert Dawson and Harley Weston. 





Mary, Julie and Peter when on a trip 
20150710 

From Edward: How do you solve and set up a problem where: Mary pays one third of the cost of a trip, Julie paid half of what Mary paid, and Peter paid the remaining $75, Answered by Penny Nom. 





Golf for 12 with a proviso 
20150707 

From Ken: I hope you can help me. I'm trying to put together a draw for 12 players in 3 groups over 4 days. One proviso, 2 players must play together in each round because they require the use of a golf cart. We are due to play in September this year.
Thanking you in advance for any assistance you can give. Answered by Victoria West. 





The nth term 
20150704 

From ujjal: What is the nth term in the order 6,8,10.... Answered by Penny Nom. 





Why is the area of square not conserved when it changes to a rhombus? 
20150628 

From shubham: Why is the area of square not conserved when it changes to a rhombus, both have equal sides still rhombus have less area than square.?? Answered by Penny Nom. 





Why are bags of soil measured in litres? 
20150619 

From Cheryl: Why are bags of soil measured in litres? Answered by Penny Nom. 





My final exam score 
20150619 

From Deirdre: Hi,
I got 69% on a question worth 20%
68% on a question worth 20%
And the final exam was worth 60%
My final grade overall was 63%
Did I do very bad in the exam???? Answered by Penny Nom. 





1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 x 0 + 1 = ? 
20150618 

From Sharon: 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 x 0 + 1 = ?
I got 1 as my answer despite BODMAS making it 12 because logic tells
me I ought to place brackets around the first set of repeated addition. Could you
please clarify this for me? Thank you 😊 Answered by Harley Weston. 





4 digit strings using the digits 1, 2, 3 and 4 
20150614 

From Gary: What is the number of possible combinations using the following fact pattern?
A. Each combination must have 4 numbers.
B. The possible numbers to choose from are 1, 2, 3, 4
C. The numbers can be included in the combination more than once. For example, it can be 1111.
Is it possible to generate a schedule of the possibilities? Answered by Penny Nom. 





2^48  1 
20150613 

From Soham: The number 2^481 is divisible by two numbers between 60 and 70. The sum of
the two numbers is? Answered by Penny Nom. 





A waste oil tank 
20150613 

From Angela: a waste oil tank is 5 feet wide and 20 feet long, the empty tank on your truck holds 5000 gallons. If 7.48 gallons are in every cubic foot, what is the maximum depth the oil can be to completely fit into your truck? Answered by Penny Nom. 





The amount before profit and overhead 
20150612 

From kelly: I have an existing amount of $22,750.00. this includes the profit at 10% and overhead at 10%.
How do I remove the profit and overhead in order to come up with the original starting figure? Answered by Penny Nom. 





The area of an isosceles triangle 
20150611 

From Pradipta: Find the area of an isosceles triangle having two equal sides of 20 cm each and angle between them 45 degree ? ( solve without trigonometric function). Answered by Chris Fisher. 





A fantasy football league 
20150611 

From Jason: Hello. We have a fantasy football league with 14 teams. The season is 13 weeks long and we would like to figure out a way to have two divisions of seven teams each with each team playing their interdivision opponents twice. Is there a way to set this up? I cannot seem to find a way to do it. Thanks! Answered by Victoria West. 





8 golfers playing 5 round 
20150611 

From Simon: We have 8 golfers playing 5 rounds, and want to make the pairings as even as possible (ie all play against everyone else)
2 of the players however must play together each day  due to a buggy being required.
If anyone has a formula to work this out I'd be appreciated Answered by Victoria West. 





An equilateral triangle inscribed in a circle 
20150611 

From Casey: I have an equilateral triangle inscribed in a circle  this triangle
has been bisected to give me 2 right triangles. I know the length
of the line bisecting the equilateral triangle is 36 inches. How do
I figure out the circumference of the circle and the length of the
sides of the equilateral triangle? Answered by Penny Nom. 





Is 22/7 is an irrational number? 
20150607 

From Sayak: Is 22/7 is an irrational number Answered by Penny Nom. 





The surface area of a round bar 
20150606 

From chirag: Please tell me the formula for finding round bar surface in square inches/ mm Answered by Penny Nom. 





Manipulating an equation 
20150605 

From Leigh: Hi, I'm having trouble trying to find out how the equation y=mx+b for b comes up with the answer b=ymx. Could you please assist me with this Answered by Penny Nom. 





A two digit number 
20150605 

From Madison: Trini took some photos. The number of photos she took is a two digit number.
The sum of the digits is 11. The tens digit is 3 more than the ones digit.
How many photos did Trini take? Answered by Penny Nom. 





The surface area of a triangular prism 
20150603 

From Alex: Find the surface area of a triangular prism with Isoceles triangles and dimensions 4 feet by 6 feet Answered by Penny Nom. 





The volume of a pipe 
20150602 

From gordon: What is the formula to find out how many gallon of water in a length of pipe tried your answer on 8inch at 50feet did not work out Answered by Penny Nom. 





A tangent to y = x^3 
20150531 

From Brayden: Show that a tangent line drawn to the curve y=x^3 at the point (d,f (d)), where d>0, forms a right triangle with the x and y axes in quadrant 4 whose area is (2/3)d^4. Answered by Penny Nom. 





A pentagon inscribed in a circle 
20150530 

From Victoria: find the area of a regular pentagon inscribed in a circle with radius 3 units Answered by Penny Nom. 





A stone walkway around a pool 
20150529 

From Jerri: I have a rectangular pool 15x30 and it will require stone placed around it 4 feet out and 4 inches deep how much will I need? Thanks, jerri Answered by Penny Nom. 





The perimeter of a rectangle 
20150528 

From Imran: The length of a rectangle is x+3 centimetres.
The width of the rectangle is x1 centimetres.
Find an expression in terms of x for the perimeter of the rectangle.
The perimeter of a rectangle The perimeter of a rectangle
Give your expressions in it's simplest form.
The perimeter of a rectangle The perimeter of a rectangle
Thank You. Answered by Penny Nom. 





Two concentric circles 
20150528 

From Shannan: Two concentric circles have radii of 24cm and 26cm. What is the length of the chord that is tangent to the inner circle? Include a sketch Answered by Penny Nom. 





Prove that you cannot factor x squared + 5 
20150528 

From lily: the question is: prove that you cannot factor x squared + 5 Answered by Robert Dawson. 





y=f(x) and y=3/2f(x) 
20150527 

From Kevin: Could you please show me what change y=f(x) to y=3/2f(x) has gone through and please graph.
y=f(x) points: (3,0) ,(0,2), (2,2), (3,4)
how does (0,2) change? Answered by Penny Nom. 





A path 30 feet wide by 2 miles long 
20150524 

From Doug: If I make a path 30 feet wide by 2 miles long how many acres am I covering? Answered by Penny Nom. 





The perimeter of a quarter circle 
20150521 

From Bethany: The perimeter of a quarter circle is 3.57. What is the quarter circle's radius? Answered by Penny Nom. 





Golf for 14: 2 fourballs and 2 threeballs 
20150520 

From martin: I have to organize 14 players to play four rounds of golf. Each round comprise two fourballs and two three balls .
What's the best combination to ensure that each persons plays with as many of the others as possible without playing with somebody more than twice? Answered by Victoria West. 





Manipulating an expression using logarithms 
20150518 

From Katie: Solve x=At^be^ct for b in terms of c.
The e is Euler's number, not a letter or random placeholder. v
I've tried 2 methods on my calculator, and I am unsure as to why they give me different answers, and which one is correct.
For some reason, when placing a multiplication sign in between the A and the first t, I get a completely different answer. Why is this?
Also, which is the right answer for the question I have?
Thank you!
Katie :) Answered by Penny Nom. 





An isosceles right triangle 
20150517 

From Ari: In a 454590 triangle find the ratio of a leg to the hypotenuse Answered by Penny Nom. 





Cubic feet and cubic yards 
20150517 

From Richard: If I have a bag that covers.8cubic ft how many bags are in 2.65 cubic yards? Answered by Penny Nom. 





An octagonal frame around a pool 
20150517 

From James: I have a 20' pool and need to put a frame around it using 2by 4 what r the lengths and angle cuts Answered by Penny Nom. 





The intersection of a plane and a cone 
20150516 

From Tom: Is there a way to derive an equation that describes the perimeter of the intersection of a plane and a cone regardless of the angle of the plane to the cone. Assume that the plane does not cut through the base of the cone, the x, y, z location of the vertex is known, the distance from the vertex to the plane through the axis is know., and that the angle of the cone is known. Answered by Chris Fisher. 





A pile of mulch 
20150515 

From Justin: I have a pile of mulch that measures 19 feet wide at the bottom and has a height of 6 feet. I need to know how many yards of mulch I have.
Please help and help with the formula for further use. Thank you! Answered by Penny Nom. 





Two lorries approaching an intersection 
20150515 

From Nuraini: Two straight roads intersect at the right angles. Lorry A, moving on one of the roads,
Approaches the intersection at 50mi/h and lorry B, moving on the other roads, approaches the intersection at 20mi/h.
At what rate is the distance between the lorry changing when A is 0.4 mile from the intersection and B is 0.3 mile from the intersection? Answered by Penny Nom. 





An angle of depression problem 
20150514 

From haxir: find the height of the balloon directly above a town if the measure of angle of depression of another town 5km from the first town is 20°!6` Answered by Penny Nom. 





A calculus optimization problem 
20150514 

From Ali: Given an elliptical piece of cardboard defined by (x^2)/4 + (y^2)/4 = 1. How much of the cardboard is wasted after the largest rectangle (that can be inscribed inside the ellipse) is cut out? Answered by Robert Dawson. 





Folding a rectangle to preserve the aspect ratio 
20150509 

From Anna: If you fold a rectangular piece of paper in half and the resulting rectangles have the same aspect ratio as the original rectangle, then what is the aspect ratio of the rectangles? Answered by Penny Nom. 





Repeated decimals 
20150509 

From Vir: Years ago I (re?)discovered 'cyclic division'. For example: if you arrange the number along a circle and put the number 142857 at the centre
all the numbers taken cyclically, starting with 1, are fully divisible by 37. Whatever the starting point of this number, it remains fully divisible by 37.
what is more, the number can be formed by taking the digits clockwise as well as anticlockwise..This I call "full cyclic divisibility". In many cases, only clockwise cyclic divisibility is possible. But I have not come across a case where ONLY anticlockwise divisibility occurs. Thus clockwise cyclic divisibility seems to be favoured. Could this be construed as a sign of chirality in mathematics?.. Answered by Chris Fisher. 





A word problem 
20150508 

From JAMES: A businessman bought a number of similar articles for a total of sh. 6000. Three of the articles turned out to be defective with no resale value. He sold the remaining articles at 12.5% each above the cost price making a total profit of sh 480. How many articles had he bought? Answered by Penny Nom. 





A triangle inscribed in a circle 
20150507 

From R2D2: A triangle is inscribed in a circle of radius 10. If two angles are 70 degrees and 50 degrees find the length of the side opposite the third angle? Answered by Chris Fisher. 





A circle is tangent to the yaxis 
20150506 

From Elynna: What does it mean when a circle is tangent to the yaxis?
Thanks, Answered by Penny Nom. 





Sales tax 
20150505 

From Adalyn: Hello i've been having some trouble with math, The question is asking for a GST
and a PST
of a 30.00 dollar shirt. I don't know how to find the GST or the PST please help Answered by Penny Nom. 





The surface area of a hemisphere 
20150505 

From Mandy: How can I show that the total surface are of any solid hemisphere is 75% of the area of the full sphere? Answered by Penny Nom. 





The number of possible musical notes using an nkey instrument 
20150504 

From Farihin: Lets say that i have keys, and each key is for notes of a musical instrument,
So i wanted to find out the number of notes i can get for a certain number keys,
of course in the form of an equation. Notes can use as many keys, it can use 1, or 2, or 3, or even 100.
Notes in real life is not as such, but ignore reality.
I tried doing this but i can't seem to find a formula for it.
For example, i have 4 keys, say A, B, C, and D.
so, for notes that uses one key are 4, which is A, B, C, and D themselves.
for notes that uses two keys are 6,
AB, AC, AD, BC, BD and CD.
for notes that uses three keys are 4,
ABC, ABD, ACD and BCD.
lastly for notes that uses all four keys is 1, ABCD.
So, the total will be 4+6+4+1=15#
The nth term for the first equation is n, the second is [(n^2)n]/2
the third and the fourth, i don't know but the final answer should be like,
n + [(n^2)n]/2 + [3rd] + [4th]
Sorry for the long question though... Answered by Penny Nom. 





13 games, 3 possible outcomes 
20150501 

From Kennedy: Hello, hope it finds you well.
Am not that good with numbers, can you please help me get all the possible outcomes of 13 games, with a home win, draw or an away win as three possible results for each of the 13 games.
Thanks in advance Answered by Penny Nom. 





The method of elimination 
20150501 

From oreanna:
Question from oreanna, a student:
How do u solve 2x+9y=3
7x4y=25 in elimination Answered by Penny Nom. 





A square and a rectangle 
20150501 

From nick: why is the area of a square of a given circumference greater than the area of a rectangle with the same circumference ? Answered by Penny Nom. 





Filling a pool with dirt 
20150501 

From Mike: I have a hole which a 24 ft pool in it is 10" deep in the the centre and goes to 1" inch at the edge want to fill it in with dirt how many yards of dirt would I need to fill it in Answered by Penny Nom. 





The volume of a sphere 
20150430 

From Cassidy: How do you find the radius of a sphere that has volume 36pI? Answered by Penny Nom. 





A fraction with a negative exponent in the denominator 
20150430 

From ellen: 7/ab to the 4 power Answered by Penny Nom. 





The volume of a cube 
20150430 

From megan: What's the volume of a cube with a side length of 6? Answered by Penny Nom. 





The surface area of a cut pipe 
20150427 

From ARUN: dear Sir,
please advise me , how to calculate the surface area of a pipe with diameter of 630 mm and thickness of 67 mm which is cut in a angle of 22.5 degree.
please show me how to calculate the surface area of the pipe which cut in an angle.
Thanking you. Answered by Harley Weston. 





A fivedigit pass code 
20150425 

From Mary:
Question from Mary:
More on your published question:
I have the same type of lock, but set up a 5digit pass code. Is that more or fewer possibilities than a 4digit code. How many digits would make the lock most secure? I don't believe Werner specified this, but each number can only be used once. Thanks, Mary Answered by Penny Nom. 





A piecewise function 
20150425 

From uday:
f(x)={x^2+3x+2 / x+2, x(not equal to)=1
{4, x=1
how to find domain and how the graph looks like Answered by Penny Nom. 





Locating the center of a circle that forms an arc 
20150423 

From Ken:
Find the Cartesian coordinates of the center of an arc with the given location of the beginning and end points and radius length. Not the midpoint of the circumference but the actual point that the arc
is drawn around.
I know their are two answers depending on the direction of the arc. Unless we assume that all arcs are drawn counter clock wise.
Thanks
Ken
Answered by Harley Weston. 





A word problem with fractions 
20150423 

From Cecilia: if one third of a pole is red, one quarter is white and 15m is black what is the height of the entire pole Answered by Penny Nom. 





Expand and Simplify (3x+5)(5x9) 
20150423 

From chloe: Expand and Simplify (3x+5)(5x9) Answered by Penny Nom. 





Two concentric circles 
20150421 

From Juniper: Two concentric circles have radii of 4 cm and 8 cm. A segment is drawn so that it is tangent to the smaller circle and a chord of the larger circle. How long is the segment? Answered by Penny Nom. 





A circle inscribed in a square 
20150419 

From michael: A circle is drawn in a square PQRS. If the total area of the shaded portion of the square is 42 cm square, calculate the radius of the circle Answered by Penny Nom. 





A geometric sequence 
20150419 

From Delfina: In a geometric sequence the second term is 15 and the fifth term is 405. Find the sum of the first eight terms Answered by Penny Nom. 





An inequality 
20150419 

From mr.: Simplify the inequality √x>x and represent on a number line Answered by Penny Nom. 





A wireless fence 
20150418 

From Dave: I'm buying a wireless fence to keep my pet in my yard. It has a half acre range. In a straight line how far would that be? Answered by Penny Nom. 





Two cars approaching an intersection 
20150416 

From Engabu: Car A is traveling west at 50km/h & car B is traveling north at 60km/h. both are headed for the intersection of the two roads. At what rate are the cars approaching each other when car A is 3km & car B is 4km from the intersection? Answered by Penny Nom. 





How many boats total are in the marina? 
20150415 

From Carla: In a marina, 3/4 of the boats are white, of the remainder 4/7 are blue, the rest are red. There are 9 red boats. How many boats total are in the marina? My answer is 84 because if 1/4 of the boats are divided into sevenths, that makes the whole marina a 28 part item. 3/28 are red so 84 is the total number of boats. My child thinks I am wrong. Answered by Penny Nom. 





Two airplanes 
20150414 

From john: two planes leave an airport at the same time, one going northwest (N35*W)at 400 mph and the other going east at 332 mph. How far apart are the planes after 4 hours to the nearest mile? Answered by Penny Nom. 





Constructing a box of maximum volume 
20150414 

From Margot: I need to do a PA for maths and I'm a bit stuck.
The PA is about folding a box with a volume that is as big as possible. The first few questions where really easy but then this one came up.
8. Prove by differentiating that the formula at 7 does indeed give you the maximum volume for each value of z. Answered by Penny Nom. 





Team selection 
20150413 

From Peter: I manage a football team with a list of 28 players.
Only 24 can play each game.
The season is 16 games.
How do I fairly select 24 players each week. Answered by Robert Dawson. 





Some nondecreasing sequences 
20150413 

From Sky: Hi I'm a Student and i'll try my best to state the problem perfectly.
The number of nondecreasing sequences of size at least 1 and at most N,
such that each element of the sequence lies between L and R, both inclusive.
Eg: N=1 L=4 R=5
ans= 2. [{4},{5}]
N=3 L=4 R=6
ans= 19. [{4},{5},{6},{4,4},{4,5},{4,6},{5,5},{5,6},{6,6}
{4,4,4},{4,4,5},{4,4,6},{4,5,5},{4,5,6},{4,6,6},{5,5,5},{5,5,6},{5,6,6}
,{6,6,6}] Answered by Claude Tardif. 





The area of a circle given the circumference 
20150412 

From F: How do you find the area of a circumference of 6?
Thanks. Answered by Penny Nom. 





Excavating a basement 
20150412 

From Randy: The cost of excavation is $4.50/ cu yd. Find the cost of excavating a basement 87 ft long, 42 ft wide, and 8 ft deep. Answered by Penny Nom. 





Sharing $600 in the ratio of 2 to 3 
20150411 

From Kenneth: Hello:
If two people share $600.00 in a ratio of 2 to 3, which calculations are correct: 2/3 X $600.00 & 1/3 X $600.00 or 2/5 X $600.00 & 3/5 X $600.00?
The denominator 5 is determined by adding 2 and 3 from the ratio.
I thank you for your reply. Answered by Penny Nom. 





An 8 pointed star inscribed in a circle 
20150410 

From Kermit: How do you find the area of the star that is formed by two squares and surrounded by a circle. The only given information is that the radius of the circle is 10. Answered by Penny Nom. 





The perimeter of a quarter circle 
20150410 

From Riley: How do you find the perimeter of a quarter circle when the radius is 56? Answered by Penny Nom. 





A word problem with fractions 
20150409 

From Lorraine: If the numerator of a certain fraction is doubled and the denominator is increased by 1, the fraction becomes 1/2.
If the numerator of the original faction is squared and the denominator is decreased by 2, the fraction becomes equal to 1.
Let x be the numerator and let y be the denominator of the original fraction.
Write down two simultaneous equation in x and y.
Solve these equations to find two possible values for the given fraction. Answered by Penny Nom. 





The area of the ring between two concentric circles 
20150408 

From Conner: The area of the ring between two concentric circles is 25pi/2 square inches. The length of a chord of the larger circle tangent to the smaller circle is? Answered by Robert Dawson. 





A circle graph 
20150406 

From Davis: i don't know how to answer this question. please help!
a survey about student government shows the following results
110 like the program
120 think the program is unnecessary
210 plan on running for student government next year
if this information is put in a circle graph,what is the central angle for the students who like the program? Answered by Penny Nom. 





On what day of the week did 1994 begin? 
20150405 

From tayyaba: there were 365 days in the year 1993
the first day of the year was friday.
on what day of the week did 1994 begin? Answered by Penny Nom. 





A tangent to y=x^3 passes through (0,2) 
20150405 

From Kevin: Given that the curve y=x^3 has a tangent line that passes through point (0,2). Find the equation of the tangent line Answered by Penny Nom. 





The weight of a steel block 
20150404 

From Mark: the weight of a steel cube 37 inches X 28 inches X 7 inches Answered by Penny Nom. 





n^2 is a multiple of 100 
20150330 

From Rahul: I have to prove that n^2 is a multiple of 100 is necessary or
Sufficient condition (or both) for n being multiple of 10 Answered by Penny Nom. 





The game of 24 
20150328 

From Suzanne: I love this game! Cannot figure out 4,9,10,16 to equal 24? Help! Answered by Penny Nom and Claude Tardif. 





Three consecutive integers 
20150328 

From Aleksey: I need help how do I find the second of three consecutive integers if the sum of the first and third is 26? Answered by Penny Nom. 





Ordering fractions 
20150327 

From latoya: Put the following amounts in order from greatest to least 60%,2/3,0.599 explain answer Answered by Penny Nom. 





A rectangular concrete tank 
20150324 

From mwenge: What is the length ,width and height for the rectangular concrete tank that can have capacity of 50000 liters of water? Answered by Penny Nom. 





Is a rhombus a square? 
20150324 

From Justin: Is a rhombus a square? Answered by Penny Nom. 





Dealing cards to Melissa and Robert 
20150324 

From Karena: 92 cards in all. Melissa has 3 times as many cards as Robert. How many cards does Robert have? Answered by Penny Nom. 





An isosceles triangle inscribed in a circle 
20150323 

From Rachel: Triangle ABC is an isosceles triangle inscribed in circle O. If each leg of the triangle is 13cm and the altitude to the base of triangle ABC is 5cm, find the radius of the circle. Answered by Penny Nom. 





A train trip 
20150323 

From Ngcebo: A train travels a distance of 720 km at a speed of x km/h. on the return journey, it travels at an average speed of y km/h and completes the whole journey in an hour less. if the speed during the return journey was 10 km/h more, what were the speeds in m/s Answered by Penny Nom. 





16 golfers for 18 weeks 
20150322 

From Rose: We could use a schedule to include the following:
16 golfers
4 foursomes
Each person plays once a week for 18 weeks.
No one plays in same foursome more than 1 or 2 times, or the least
amount of time.
Thank you for your kindness. Answered by Victoria West. 





8 golfers playing in 2x2 balls in 5 games 
20150318 

From Brian: We are 8 golfers who will be playing in 2x2 balls in 5 games.
is there a formula to minimize the chances of playing with a partner or opponent
too often please ? Answered by Victoria West. 





The weight of two dogs 
20150317 

From Renee: Darlene's dog weighed 5 times as much as Leah's dog. Together, the dogs
weighed 84 pounds. How much did each dog weigh?
Write an equation and solve Answered by Penny Nom. 





A region defined by three lines 
20150316 

From Lucinda: find the area of the figure formed by the line y=5x+9 and the xaxis and yaxis. Answered by Penny Nom. 





A cone of maximum volume 
20150316 

From Mary: I have to use a 8 1/2 inch by 11 inch piece of paper to make a cone that will hold the maximum amount of ice cream possible by only filling it to the top of the cone. I am then supposed to write a function for the volume of my cone and use my graphing calculator to determine the radius and height of the circle. I am so confused, and other than being able to cut the paper into the circle, I do not know where to start. Thank you for your help! Mary Answered by Robert Dawson. 





Points on the xaxis 
20150314 

From Justin: jamie tells her friend that ordered pairs that have an xcoordinate of O line xaxis. She used the origin as an example. Describe Janine error. Use a counterexample to explain why Janine statement is false Answered by Penny Nom. 





Twotiered GST system 
20150314 

From Ruby: This question showed up in one of my Math assignments and nothing on the internet seemed to help me find a way to calculate it.
A certain country has a twotiered GST system. For the first $1500 of any item, GST is levied at 10% and any amount over $1500 is levied at 15%.
Determine the amounts that give the following GSTs.
a) $350
b) $780 Answered by Penny Nom. 





Average rate for a return trip 
20150314 

From Michael: Jeffrey drove to a town 25 miles away at an average speed of 50 miles per hour. The return trip along the same route took 20 minutes longer than the trip to town. Determine the average speed in miles per hour for Jeffrey's round trip. Answered by Penny Nom. 





The side length of a gazebo 
20150314 

From Dennie: From middle of side to middle of opposite is 14'6". What is the length of the side? Answered by Penny Nom. 





A limit 
20150313 

From arthur: sin(x1)/x^+x2 Answered by Penny Nom. 





Commission 
20150313 

From Rose: A shopkeeper receives 12.5% (12 1/2 %) commission on the sale of books from
the publisher. In a certain month,he receives a commission of rs.250 from the
publisher. How much was his sale for that particular month?? Answered by Penny Nom. 





A fishfinder 
20150313 

From Dave: I have a fishfinder that has a 20 degree cone on bottom of boat going to the bottom of the lake.
How do I know the size of base diameter of the cone on the lake bottom depending on depth...
such as 10 feet deep, for example? Answered by Penny Nom. 





Olivia and Ray walk to school 
20150312 

From Rebeccah: Olivia and Ray walk to school. Olivia walks 1/4 of a mile to school. Her walk is 2/3 of the distance that walks Ray to school. What is the total distance,in miles,that Ray walks to school? Answered by Penny Nom. 





Two sunflowers 
20150312 

From Maurice: Sam and sally planted two sunflowers.Each sunflower grows 1cm each day. Sally's sunflower is 4cm high. Sam's is 12cm high. How high will each sunflower be when Sam's sunflower is twice the height of Sally's? Answered by Penny Nom. 





Constructing a cone 
20150312 

From Levi: While the mathematics at the welding shop page was very helpful there is one vital part missing. If I have never built a cone how do I figure out how much bigger the diameter of my
circle has to be when laying flat on the floor verses the diameter when it has been pulled into a cone. Answered by Harley Weston. 





The height of an equilateral triangle 
20150312 

From anna: I am anna and i am in 7th grade.
i am trying to find the height of and equilateral triangle, all sides equaling 4 inches Answered by Penny Nom. 





The volume of a trench 
20150311 

From Kim: A trench 60m long and 15m deep, 12m wide at the top and 8m wide at the bottom.How many cubic meters of earth have been removed? Answered by Penny Nom. 





The area of a quadrilateral 
20150311 

From Joel: Diagonal ac of quadrilateral ABCD is 60cm and the lengths of perpendiculars to
It from the opposite vertices are 4.2cm and 5.8 cm find the area of the quadrilateral
ABCD Answered by Penny Nom. 





What is 1000 billion billion? 
20150310 

From LeRoy: what does this mean? 1000 billion billion Answered by Penny Nom. 





Two consecutive odd integers 
20150309 

From gowtham: The sum of two consecutive odd integers is 20.find the integers Answered by Penny Nom. 





Angles of elevation and depression 
20150308 

From Timmy: Joel is walking down a street and sees a 115 ft tall building in front of him. He stops 190 feet from the base of the building at the tip of the building's shadow. Round answers to three decimal places.
A. If there was a piece of rope from the top of the building to Joel, how long would it be?
B. What is the angle of elevation from Joel to the top of the building?
C. Margaret says that she could find the angle of depression from the top of the building to Joel by subtracting the angle of elevation from 90°. Is she correct? Explain. Answered by Penny Nom. 





Extraneous solutions 
20150307 

From Emily: I have a question about Extraneous Solutions, Because I was recently researching to figure out
on how to determine that a solution is extraneous and many of the answers talked about how if a answer is negative
that it should always be extraneous but now I found out that positive solutions can also be considered as extraneous solutions
so that is why I am really confused Extraneous Solution's.
I would really appreciate it if you could clearly explain to me how to determine an extraneous solution from a normal solution.
Thanks,
Emily Answered by Chris Fisher. 





The definition of percent ( % ) 
20150307 

From Kenneth: Hello:
I saw this definition online from the Free Dictionary (The Free Dictionary.com) regarding the definition of percent (%):
"Noun 1. a percent sign  a sign (`%') used to indicate that the number preceding it should be understood as a proportion multiplied by 100."
What is this "proportion" multiplied by 100?
When I think of a proportion, I think of a/b = c/d. How can a number preceding the percent sign be understood as a proportion X 100?
I thank you for your reply! Answered by Chris Fisher and Claude Tardif. 





A lot on a culdesac 
20150306 

From ana: Julie lives on a culdesac and wants to know if the city calculated the area of her plot of land correctly (see diagram below). We can assume the culdesac is a circle and it has radius 40 feet.The boundary of the lot along the culdesac (the arc from A to B) is 78.21 feet. The city found the area to be 7012.5 square feet–are they correct? Answered by Penny Nom. 





A man is standing on top of a building 
20150306 

From kiki: a man of height 1.5m standing on top of a building of height 48.5m views another building across the square. he observe that the angle of depression of the bottom of the building is 40 degrees and the angle of depression of the top of the building is 5 degrees. Both buildings stand on the same level
a) calculate the distance of the man from the base of the building across the square measured along the line of sight Answered by Penny Nom. 





Two parallel tangents to a circle 
20150305 

From Samantha: The equation of a circle is x^2+y^2=25. Determine
the equation of the parallel tangent lines to this
circle, for which the slope is 4/3. Answered by Penny Nom. 





Integers in different bases 
20150305 

From Michael: Let k be a positive integer so that 28 (subscript)k = 132 (subscript)5 Answered by Penny Nom. 





The length of a ramp 
20150305 

From Jaylynn: Hi, I've been trying to figure out how long my ramp would have to be in order to reach a height of 3.5 feet at a 30 degree angle for a sugar glider enclosure? Answered by Penny Nom. 





Bricks around a fire pit 
20150305 

From Jayson: I have a round fire pit. It measures 25 inches in diameter. I have 12 inch long square bricks to go around it . My question is what degree do I cut the ends of these bricks to make them fit around this circle? The brick dimensions are 12"Lx6"Wx4"D. Answered by Harley Weston. 





Istanbul to Lagos 
20150303 

From Victor: A plane flies from Istanbul to Lagos at 800km/h and then returns to Istanbul at 900km/h. The return trip takes 1 hour less than the flight to Lagos. What is the distance between Istanbul and Lagos? Answered by Penny Nom. 





Two consecutive positive integers 
20150301 

From meha: Find two consecutive positive integers , sum of whose squares is 365. Answered by Penny Nom. 





Solve x=r(tsin(t)) for t 
20150228 

From David: I don't know how to write the function of t(x) by x=r(tsin(t)).
Can you teach me that? Answered by Harley Weston. 





The radius of a cylinder 
20150226 

From Rose: Hi. I want to know how to find the radius of cylinder.
When I have height (35cm) and area of the curved surface(880sq.cm).
I know the formula is 2πr(h+r). But I can't understand how to find it's radius.
Please help me. I really need your help. Answered by Penny Nom. 





Two equations with fractions 
20150226 

From Pulane: Hi math centre I've been trying to solve these equations for days now please help
(6/x)(1/y)=4
(9/x)+1=(2/y)
Please help me solve them simultaneously
Thank you Answered by Penny Nom. 





A question in set theory 
20150225 

From Jared: If a set A={1,2,3} and set B={ {}, 1}
Can B be a subset of A? Since every Set contains an {} ? Answered by Robert Dawson and Claude Tardif. 





Two concentric circles 
20150225 

From Manasi: The area between 2 concentric circles is 6 times the smaller circle. Radius of small circle is 7 cm. Find the difference in the circumference of the bigger circle ad the smaller circle? Answered by Penny Nom. 





3 over "x" plus 5 
20150223 

From Kenny: 3 over "x" plus 5. I don't know this is either a polynomial and if so how would you define it. Answered by Harley Weston. 





f(x)=(x^21)/(x1) 
20150221 

From Ahmed: Is f(x)=[(x^21)/(x1) and x=2 at x=1] differentiable at x=1 ? Why ? Answered by Penny Nom. 





A region described by inequalities in cylindrical coordinates 
20150221 

From Rahul: I am not able to visualize a solid given by inequalities as under (in cylindrical coordinate system)
0=
I know that (can visualize) first 2 inequalities say it is a cylinder of infinite length.
It seems that third inequality poses the restriction to the height as well as it makes us to remove a cone.
But I just can not understand it clearly.
Thanks in advance!
Regards,
Rahul Answered by Penny Nom. 





Column vectors 
20150221 

From jill: A has co ordinates (7,1) and B has coordinates (3,5).write these as column vectors Answered by Penny Nom. 





A limit 
20150219 

From genc: Lim (27x^31) / (3x1)
X> 1/3 Answered by Harley Weston. 





The height of a building 
20150218 

From prateek: the height of a flagpole on top of a building is 6m.
the angle of elevation of the top and bottom of the flagpole are 45 and 30 respectively.
find the height of the building Answered by Penny Nom. 





An isosceles triangle and an arc 
20150218 

From Sreeharsha: The diagram shows an isosceles triangle ABC in which BC = AC = 20 cm, and angle BAC = 0.7
radians. DC is an arc of a circle, centre A. Find, correct to 1 decimal place,
(i) the area of the shaded region, [4]
(ii) the perimeter of the shaded region. [4] Answered by Penny Nom. 





5000 gallons in cubic yards 
20150217 

From Miguel: If I have a cube shaped tank in the ground that holds 5000 gallons and I want to take it out and fill the hole in with dirt, how much dirt will I need in yards? Answered by Penny Nom. 





Tiling a room 
20150216 

From Owen: nicolas room is 56m2 she wants to put tiles down which are 50cm by 50cm each cost £4 how much money will she spend Answered by Penny Nom. 





Two equations 
20150216 

From nigel: 2x+1/2y=1
6x3/2y=21 Answered by Penny Nom. 





A 330 foot long fence 
20150215 

From Marsha: I am putting up a fence 330 feet long and want to put the t post every 4 feet
how many t post do i need? Answered by Penny Nom. 





Distance, time and rate for three people 
20150215 

From Mubashir: Steven left Town A and walked towards Town B at a speed of 100m/min. At the same time, Jason and Melvin started from Town B and walked towards Town A at a speed of 80m/min and 75m/min respectively. If Steven met Melvin six minutes after passing Jason, find the distance between Town A and Town B. Answered by Penny Nom. 





Bearings and a rectangular plot 
20150214 

From Mubashir: A,B,C,D are the four corners of a rectangular plot marked on level ground. Given that the bearing of B from A is 040 degrees and that the bearing of C from A is 090 degrees. Calculate the bearing of
(a)B from C
(b)A from C
(c) D from C Answered by Penny Nom. 





A stone is dropped in a lake 
20150214 

From Wendy:
Hi, I have problems solving this problem. We didn't exactly go over these kind of problems and the book doesn't have an example either. Thank you for your help!
A stone is dropped in a lake, creating a circular ripple that travels outward at a speed of 80 cm/s.
(a) Find a function g that models the radius as a function of time t.
g(t) =
(b) Find a function f that models the area of the circle as a function of the radius r.
f(r) =
(c) Find f compose g.
f compose g = Answered by Penny Nom. 





Stopping distance 
20150211 

From Audrey: A Harley Davidson motor cycle weighing 650 lbs with a rider weighing 175 bs
was going 40 miles per hour. He had to make a sudden stop . Slammed on brakes. How long a distance for him to stop? Answered by Penny Nom. 





A word problem with fractions 
20150211 

From Omokayode: A vehicle tank was 3/5 full of petrol. When 21 litres of fuel was added it was 5/6 full. How many litres of petrol can the tank hold? Answered by Penny Nom. 





A fence post problem 
20150208 

From Nicole: In Susan's rectangular garden plot, she put 12 posts on the long sides
and 8 posts on the short sides. How many posts did she use altogether?
(The answer is not 40.) Answered by Penny Nom. 





A circle and a chord 
20150207 

From Dakota: If the diameter of a circle is 48 cm, find the shortest distance from a chord of length 34 cm to the center of the circle Answered by Penny Nom. 





Speed, distance and time 
20150206 

From Terry: How many seconds would it take to travel 0.18 km at a speed of 130km per hour? Answered by Penny Nom. 





The product of a 2digit number and a 3digit number 
20150206 

From Nathaniel: The product of a 2digit number and a 3digit number is about 50 000 what are the products Answered by Penny Nom. 





2x^22x+1=4x+1 
20150206 

From Caitlyn: 2x^22x+1=4x+1 Answered by Penny Nom. 





The center and radius of a circle 
20150206 

From ariana: I need to find the center and the radius of this circle. I don't know how to put 9/2
than square it into a fraction.
x^2 + 2x + y^2 +9y=5 Answered by Penny Nom. 





The volume of a cone 
20150205 

From Linda: How do you calculate the volume of a cone that is 25cm high and has an angle of 20 degrees? Answered by Penny Nom. 





A parallelogram inscribed in a circle 
20150204 

From narendra: how can we prove that a circular parallelogram is a rectangle? Answered by Chris Fisher. 





Two cars pass each other going in opposite directions 
20150203 

From Caroline: Two cars pass each other going i opposite directions. One car is going 100 km/h and the other is going 80 km/h. How far apart will the two cars be after driving 45 minutes at these rates of speed? Answered by Penny Nom. 





A train from Vancouver to Whistler 
20150202 

From Tea: Serena and Nina are taking a train from Vancouver to Whistler, a 160km trip. If the average speed is decreased by 16km/hr, the trip will be 1/2 hours longer. What is the average speed of the train?
Thanks :) Answered by Penny Nom. 





Jack and Jill climb two poles 
20150202 

From APRIL: Two vertical poles are 3 meters apart. Jack is climbing one pole while Jill climbs the other. If the distance between Jack and Jill is 5 meters, how much higher is Jill than John? Answered by Penny Nom. 





Comparing fractions 
20150202 

From shealla: Please help me with my assignment please I'm having trouble answering this one..
Write the larger fraction in each pair..
A. 2/3, 4/7 B. 1/3, 2/5 C. 5/8, 3/5 Answered by Penny Nom. 





Ratio of gas to oil 
20150202 

From Chris: I would like to find the gas oil ratio for a 2 cycle engine.
I have the gallons of gas and the ounces of oil used by
the engine, but I want to find what the ratio is. For example
I used 5.675 gallons of gas and 5 ounces oil what is the ratio?
Please explain step by step, and I understand there are 128oz in
a gallon. Answered by Harley Weston. 





Shadow angle 
20150129 

From Lorilyn: A pole,110meters high,cast a shadow of 35meters long,what is the angle Answered by Penny Nom. 





The volume of Lake Utah 
20150129 

From Hannan: Lake Utah has a surface area of 3,846 square miles and an average depth of 10.5 feet. In cubic miles, how much water does it hold?
How would you approach this question? Where would you start? Answered by Robert Dawson and Penny Nom. 





128/(16)/(2) 
20150128 

From jackie: 128/(16)/(2) I was wondering if you can show me how to work this question out Answered by Harley Weston. 





What is our cost? 
20150127 

From Johanna: I have a pieces of 3/4" sch40 (round tube) 240" long at $70. What is our cost. We also add 35% to our cost for selling price. How do I figure this out? Answered by Penny Nom. 





The height of an obelisk 
20150127 

From Fabian: Two observers on level ground position themselves 50 meters apart so that an obelisk is due north of position A and due west of position B. The angle of elevation to the top of the obelisk at position A and B is measured to be 29.9 degrees and 37.5 degrees respectively. Use this information to estimate the height of the obelisk. Answered by Penny Nom. 





Is a square a trapezoid? 
20150126 

From Katie: Can a trapezoid sometimes be a square? Answered by Penny Nom. 





Russell is 6 years older than Samantha 
20150126 

From Kelli: Russell is 6 years older than Samantha.
In 4 years the sum of their ages will be 78. How old is Russell now? Answered by Penny Nom. 





A road around a garden 
20150125 

From hahha: a garden 150 m long and 80 m wide has a road 4 m wide all around on the out side find the cost of paving at the rate of 12 per s.q m Answered by Penny Nom. 





A motorbike race 
20150125 

From Pramegh: In a motorbike race of 75 km, the winner completes the race with a lead of 300 meters and 8 seconds before the second rider. Considering the riders ride with an average speed, find the difference between their speeds with which they completed the race.
(Calculate up to 2 decimal places) Answered by Penny Nom. 





Two concentric circles 
20150125 

From nazneen: select the correct answer from the given four options
given are two concentric circles. radii of outer circle & inner circle are r1 & r2 respectively.
the areas of inner circle & shaded ring are equal. the radii r1 & r2 are related by?
1. r1 = r2
2. r1 = r2*square root 2
3. r1 = r2*square root 3
4. r1 = 2r2 Answered by Penny Nom. 





sin x = cos x 
20150123 

From Mubashir: there are two curves y=sinx and y=cosx intersecting at point where x is less than 90 and greater than 0.to find the point I made a equation sinx=cosx
but donot know what to do further .please help me by solving this equation sinx=cosx
also tell me that have you solved this equation by reference to the graph or by other means please do elaborate your solution in your answer. Answered by Penny Nom. 





A schedule for observing our peers 
20150123 

From Jennifer: I am a sales trainer. Each month we need to observe one of our peers and give feedback. What this means is every month, not only am I observing someone, but someone is also observing me. For example, in January, Amy observes Tracy, Tracy observes Rachel, Rachel observes Ryan, and so on. The last person would then observe Amy, bringing it full circle. There are 10 trainers on my team. How do I set it up to where each trainer observes another trainer only once over the course of the year (and in return, each trainer is only being observed once by each person)? I know they will eventually repeat but would that start in the 10th month? Answered by Robert Dawson. 





A schedule for 5 employees working 2 at a time 
20150123 

From Cynthia: We have 5 employees and need only 2 to work on Saturdays. what is the best
way to fairly schedule everyone. PS. from time to time a sixth person will be
thrown in to make things really interesting. Answered by Victoria West. 





Mary gave her sister 5/8 of her nuts 
20150122 

From Valence: Mary gave her sister 5/8 of her nuts. Her sister gave her friend 2/3 of the amount, and her cousin 1/3 of the remainder. If Mary's sister had 50 nuts left, how many nuts had Mary. Answered by Penny Nom. 





Scheduling meetings with pairs of people 
20150122 

From Jacey: I am trying to figure out a formula/system to pair up a list of people so they meet with each other every month, but they rotate who they meet with. Right now I have 13 people and I would like to just type in their names and then have the system put each person with someone else every month and rotate so no one gets the same person twice. Can this be done? Answered by Victoria West. 





The game of 24 
20150121 

From aaron: 24 game whants me to use 11 14 5 and 9 to make 24 allowed (+  dividing and multiplying) Answered by Penny Nom. 





Math in the universe 
20150121 

From GA: I want to find out examples in universe for this equation:
sin(x)/cos(x)=1 or tan(x)=1. I know the mathematical answer of pie/4 or 45 degree angle.
What I need to know is to find examples of this. I found an example in construction, for example, which is the shape of attic in the house.
I want to find examples in universe like in solar system, in quasars or jets coming out of them, in galaxies, in stars, in black holes, etc
Do you know of any such examples? Answered by Robert Dawson. 





The volume of a swimming pool 
20150121 

From kirara: Find the volume of water in a swimming pool with vertical ends and sides. The length measured at the water line is 50 ft. And the breadth is 20 ft. The bottom of the swimming pool is a plane sloping gradually downward so that the depth of the water at one end is 4 ft. And at the other end is 8 ft. Answered by Penny Nom. 





1,4,9,61,52,___ 
20150121 

From Mubashir: 1,4,9,61,,52,___,84,___,18,1,121,___
please tell me its formula and also that rule that is being applied here like adding 3 or subtracting 5 etc. Answered by Walter Whiteley. 





The height of a building 
20150120 

From Emily: A man 2m high observes the angle of elevation to the top of the building to be 70 degrees. And the angle of depression to the bottom of the building to be 19 degrees. How tall is the building? Answered by Robert Dawson. 





Two cars 
20150118 

From taylor: two cars leave the park at the same time, one traveling north at a speed 10 mph faster than the other which is traveling south. after 3 hours the cars are 420 miles apart. find the speed of both cars Answered by Penny Nom. 





Pumping water from a borehole 
20150118 

From patience: An empty tank for storing water from a borehole has a volume of 480 cubic metres. If it is filled by a pump that pumps water at a rate of 16 litres per second, how many hours will it take the pump to fill this tank please show all calculations Answered by Penny Nom. 





1 + cot x divided by sin x + cos x 
20150115 

From Torrie: I need to solve this problem in terms of Sin, but I'm having trouble.
1 + cot x divided by sin x + cos x Answered by Robert Dawson and Penny Nom. 





Largest cone in a sphere 
20150115 

From Alfredo: What is the altitude of the largest circular cone that may be cut out from a sphere of radius 6 cm? Answered by Penny Nom. 





Percentage change 
20150114 

From Jim: When using a scale e.g. 010, what is the formula for calculating percentage change. For example when someone answers a questionnaire where a question has a 010 scale, and they score a 4 first time, and then they answer the same questionnaire a different day, and they score an 8, how do I calculate the percentage change. Answered by Penny Nom. 





A sequence 
20150113 

From cyaz: write a rule for each sequence then find next 3 terms for 7/8, 3 1/8, 5 3/8 Answered by Penny Nom. 





An input/output table 
20150113 

From Rose: How do you create an input/output table when the rule is: the output is a +5? Answered by Harley Weston. 





$xx,xxx million 
20150112 

From sherry:
as a financial editor, for years I've seen $\$$ amts like this:
$\$xx,xxx$ million (ie, with a comma, not dec point)
Isn't that thousands of millions, which would equal 'billions'? Answered by Penny Nom. 





An investment for 20 months 
20150112 

From rose: Darnell wants to have 2700$ to purchase a tv in 20 months. what will he need to deposit today if he earns 5% annual interest compounded monthly Answered by Penny Nom. 





h+h+h = 9 
20150112 

From juanita: How to solve h+h+h = 9 Answered by Penny Nom. 





The length of a roll of paper 
20150112 

From Peggy: roll of paper 3ft wide and roll equals 500 sq ft how long would the roll be? Answered by Penny Nom. 





A difference quotient 
20150112 

From Sasha: Simplify the difference quotient
f(x) − f(a)/ xa
if x ≠ a.
f(x) = x^3 − 12
Answered by Penny Nom. 





The volume of a lake 
20150110 

From Peter: If a lake is 8 acres in size and 10 feet deep how many gallons of water does it contain Answered by Penny Nom. 





Mutually prime composite numbers 
20150109 

From nivedita: Two composite number that is mutually prime? Answered by Penny Nom. 





Selling items at a reduced price 
20150109 

From Kent: I have an item I sell for $19.95 and make a profit of $10.97 for each sale.
If I reduce the price to $14.97, my profit is $5.99 each sale.
Is there a formula to determine how many more I would need to sell
at $5.99 per sale to make the same net cash (profit) as selling at $10.97 per sale? Answered by Penny Nom. 





The units digit of a prime 
20150108 

From Patricia: Every prime number greater than 10 has a digit in the ones place that is included in which set of numbers below 1 3 7 9 or 1 3 7 or 0 2 4 5 6 8 or 1 3 5 9 Answered by Walter Whiteley. 





Missing digits in a phone number 
20150107 

From Janelle: I had a friend try and play a game on me, regarding phone numbers, so I only know the area code , and the last four digits of the phone number. Which means, there are 3 digits that I need to figure out all the possibilities to. Answered by Penny Nom. 





Scheduling 12 for lunch 
20150105 

From Sabrina: I have 12 staff members that need to have lunch together 1 time each week. I am trying to pair them in a way that we each have the same amount of lunches in the same amount of weeks. Please Help! Thanks! Answered by Victoria West. 





The degree of a polynomial 
20150105 

From Nichole: How do I determine the degree of polynomials? I've searched this on sites but they are
all so confusing! Is there a simple explanation or way to find what the degree is? Some
examples are: 6x^4 10x^2yz^5 and 3m^2n^710m^8. I also have to say that I am
under the impression that this symbol ^ means the number after it is an exponent. Answered by Robert Dawson and Harley Weston. 





A silo is composed of a hemisphere and a cylinder 
20150103 

From Ami: A silo is composed of a hemisphere and a cylinder. The total height for the silo is 20m and the diameter of the silo is 8m. What is the volume of the silo to the nearest cubic meter? Answered by Penny Nom. 





Filling a tub 
20150102 

From Mr: The cold tap can fill a bath in 5minutes,the hot tap in 15,and the waste pipe empty the full bath in 10 minutes. All three are fully open for 2 minutes,after which the wastepipe is closed. How much longer will it take to fill the bath? Answered by Penny Nom. 





1 + 2 + 3 + ... + (2n  1) 
20150101 

From Brian: Hi Maths Central
My wife presented me with a query which may have a simple answer, but one that I can’t deduce or explain.
Take the string of numbers, n=1,2,3,4,5…
It seems that n(2n1) = Sum((1…..(2n1))
e.g. for n=5, both 5 x 9 and Sum(1….9) equal 45, and so on for other values of n.
Could you please provide an explanation? Does it have an underlying reason and a name?
Look forward to your response.
Brian Answered by Penny Nom. 





An isosceles triangle 
20141231 

From ahmadmahmoud: an isoseles triangle is such that each of the base angles is twice the vertical angle.Find the angles of the triangle Answered by Penny Nom. 





1.5% of 1 trillion 
20141230 

From Kgosi: How much is 1.5% of 1 trillion? Answered by Penny Nom. 





Rates, percentages and units 
20141230 

From Kenneth: Hello:
If percentages have no units, why are some percentages called rates, as in interest rate, or
perhaps a tax rate of 7% as an example? A rate has units of different quantities.
I thank you for your reply. Answered by Robert Dawson. 





Curvature of the Earth 
20141229 

From Jimmy: Both batteries died in my scientific calculator and I have lost my formula for the heigth of the curvature of the earth between two points on the surface. I used degrees and miles. I only had to enter the distance between the two points on the surface and the formula gave me the hieght the earth raised between the two points. Answered by Robert Dawson. 





196 kilometer in2 hours 
20141229 

From Ekanem: QQ A motorist had planned to reach a place 196km in two hrs exactly. For the first 15km he was able to average only 40km/h. What average speed must he keep up for the rest of the journey if he is to arrive on time. Answered by Penny Nom. 





The perimeter of a quarter circle 
20141226 

From Maisy: This is the question that I got for a math worksheet.
The radius of a quarter circle is 5 miles. What is the quarter circle's perimeter?
Use 3.14 for pi. Answered by Penny Nom. 





A trip to Ottawa from Toronto 
20141222 

From Kristy: A trip to Ottawa from Toronto will take 4 1/2 hours. Assuming we are 2/3 the way there, how
much longer will the trip take? Answered by Penny Nom. 





A tangent to a circle 
20141222 

From azman: Find the equation of the tangent line to the circle x^2+y^2=9 at the point P (2, square root of 5). Answered by Penny Nom. 





Discount 
20141220 

From nirmala: A bag is marked at rs 800 and is sold for rs 68. Find the rate of discount Answered by Penny Nom. 





211basex=152base8 
20141215 

From Humaira: 211basex=152base8 Answered by Penny Nom. 





A line segment of length root 5 
20141215 

From angela: On the dot grid below, draw and label a line segment with length square root 5
the dot grid is 8 by 10 Answered by Penny Nom. 





A cone is 2/3 full of sand 
20141214 

From Janice: A cone with a radius of 3.5 cm and a height of 12 cm is 2/3 full of sand.
What is the volume of the sand inside? Answered by Penny Nom. 





A right triangle 
20141213 

From Katie: the shorter leg of a right triangle measures 2 feet less than the longer leg. the hypotenuse measure 10 feet. find all three sides Answered by Penny Nom. 





Planar curves 
20141213 

From ann: what does planar curve mean in your definition of a cone? Answered by Penny Nom. 





A cuboid 
20141211 

From Nehal: Six cubes have a surface area of 24 cm2. They are joined together to male a cuboid.
What could the surface area of this cuboid be? There are two different answers. Answered by Penny Nom. 





Remainder 
20141208 

From Muqadasah: A number, when divided by136, leaves remainder 36. If the same number is divided by 17, what will be the remainder? Answered by Penny Nom. 





30% profit 
20141205 

From Lyn: I would like to know a formula that I would use on a standard calculator to calculate a 30% profit margin on an item.
If I purchased an item at $7.70 how would I calculate 30% profit for me, not just 30% mark up? Answered by Penny Nom. 





A circle through 3 points 
20141204 

From priyanka: Find the equation of a circle passing through the origin and intercept on axes are a and b. Answered by Penny Nom. 





Shaking hands at a party 
20141203 

From Nazrul: At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
Please help me. Answered by Penny Nom. 





How do you change a decimal to a ratio? 
20141129 

From Esmeralda: How do you change a decimal to a ratio? Express the decimal 0.2 as a ratio. Answered by Penny Nom. 





1999 equations in 1999 unknowns 
20141128 

From Subrahmanya: Solve the following system of 1999 equations in 1999 unknowns :
x1+x2+x3=0, x2+x3+x4=0……., x1997+x1998+x1999=0,
x1998+x1999+x1=0, x1999+x1+x2=0.
(in x1,x2,...................,x1999 the numbers 1,2,.............,1999 are subscripts) Answered by Penny Nom. 





Even and odd 
20141128 

From Subrahmanya: n1, n2, n3....................,n1997 are integers not necessarily distinct. (actually in n1, n2,.............., n1997 the numbers 1,2,.................,1997 are subscripts of 'n')
X= (1)^n1+(1)^n2+............+(1)^n998
Y=(1)^n999+(1)^n1000+............+(1)^n1997
Then
which of the following options is true
A) (1)^X = 1, (1)^Y = 1 B) (1)^X = 1, (1)^Y = 1
C) (1)^X = 1, (1)^Y = 1 D) (1)^X = 1, (1)^Y = 1
E) none of these Answered by Penny Nom. 





Exponential notation 
20141127 

From Jaqui: May sound super easy, but how would you SHOW that you simplified
3x3 to the power of 2 (the little 2)?
thank you!
Jaqui Answered by Penny Nom. 





What is 20 and 3/5 of 10? 
20141126 

From Jeannine: What is 20 and 3/5 of 10? Question is written exactly this way.
Is this 20 3/5 times 10 (103/5 times 10), or is it 20 and (3/5 times 10)? Answered by Penny Nom. 





Mark's book case 
20141124 

From anne: mark has 312 books in his case. he has 11 times as many fiction books as non fiction books. how many fiction books does mark have? Answered by Penny Nom. 





Cutting a hexagon with a sliding miter saw 
20141123 

From Joseph: I need the angles in degrees for a hexagon one side is 18inches on the outside the problem I am having is in the angle of the cut and I am using a sliding miter saw which only goes from0 degrees to 45 degrees so I need help in getting the angle of the cut Answered by Harley Weston. 





A truncated, squarebased pyramid 
20141123 

From Hannah: A designer vase has the shape of a truncated, squarebased pyramid. The base of the vase is a square with a side length of 15 cm. The area of the square opening is 70.56 cm2. Each of the four sides is a trapezium with slant sides 9 cm long. Find (to the nearest square centimetre) the total surface
area of the vase. Answered by Penny Nom. 





Doubling the dimensions of a cone 
20141121 

From Hannah: If the volume of a cone of height 10 cm is 261.8 cm3, show that this
volume is increased by a factor of 8 if the dimensions of the cone are doubled. Answered by Penny Nom. 





Two quadratic equations 
20141120 

From rajesh: Sir,
I would like to discuss on question
Find the value of variable X and Y, equations are
X2+Y2+2XY=25
X2+Y22XY=1
Sir, my point is equation looks not so easy.My opinion is there many
(more than 4)value possible for both X and Y.
Kindly help me.
Waiting for your response.
regards,
rajesh Answered by Penny Nom. 





Factorise 15x + 15y 
20141120 

From Jordan: hi i saw a question in class today that i didn't understand and i didn't really understand what my teacher was going on about so how do you factorise 15x + 15y Answered by Robert Dawson and Penny Nom. 





An arithmetic progression 
20141119 

From Gbenga: In an A.P the difference between 8th and 4th term is 20. The 8th term is 1\2 times the 4th term . Find arithmetic progression.. Answered by Penny Nom. 





Two ships 
20141118 

From Laura: 7. A ship leaves its home port and sails on a bearing of N28.17°E. Another ship leaves the same port at the same time and sails on a bearing of S61.83E. If the first ship sails at 24 mph and the second at 28 mph find the distance between the two ships after 4 hours. Answered by Robert Dawson. 





An age related word problem 
20141118 

From Cole: Susan and Russell are brother and sister. Susan says that in two years she will be twice Russell's current age. Russell says that he's only three years younger than Susan. How old is each of the siblings? Answered by Penny Nom. 





How many square feet in 10 gallons of liquid at 1/4 in thick? 
20141114 

From Rich: How many square feet in 10 gallons of liquid at 1/4 in thick Answered by Penny Nom. 





(x3)^2(x+3)^2 
20141113 

From Bernice: (x3)^2(x+3)^2 Answered by Penny Nom. 





1/6k=11 
20141113 

From Marty: Using the balance method, what is the answer to 1/6k=11, trying to find what k equals. Thanks Answered by Penny Nom. 





An irregular convex octagon 
20141113 

From james: I have an irregular convex octagon, alternating between 4 large edges, say 'a' mm long and 4 small edges, say 'b' mm long, is there a formula available so that I can work out the minimum size sit a circle with a radius of 34.25mm inside it thank you Answered by Chris Fisher. 





The cube root of 729 
20141112 

From Alexis: What would be the square root of 729 to the third power and could you
explain how to get the answer? Answered by Penny Nom. 





What is 3 squared? 
20141112 

From Christine: On a math test, it said "What is 3 squared?" It did NOT say "What's is (3)squared"
The teacher's explanation is that if there are no brackets or parenthesis, you ALWAYS square the number first then do the negative, so the answer should be 9, but I can't find anywhere that confirms this.
Help please. Answered by Robert Dawson. 





Some geometry problems 
20141107 

From Maria: Hi there,
My name is Maria and I'm a student in Ireland.
Can you pleeeease help me with questions 1 to 4 on the attached file. I'm really stuck: Answered by Penny Nom. 





The area of a pentagon 
20141104 

From Gracie: i really need help with this problem in my math book, will you help?
"Derrick drew regular pentagon with side lengths of 8 centimeters.
He divided the pentagon into 5 identical triangles, and measured the
height of one of the triangles to be 5.5 centimeters. Find the area of
the pentagon."
this really makes no sense to me. Can you help me with anything
to make it easier?
THANKS!!!!! Answered by Penny Nom. 





The area of a circle in terms of the circumference 
20141104 

From Sarah: How do you find the area of a circle if you already have the circumference?
There was one answer to this question already but it didn't make sense to
me, because they rounded up pi which you can't do so the answer is
incorrect. thanks Answered by Penny Nom. 





A quadratic function modelling the heightof a flea jump 
20141102 

From Hannah: A flea jumps from the ground to a height of 30 cm and travels 15 cm horizontally from where it started. Suppose the origin is located at the point from which the flea jumped. Determine a quadratic function in vertex form to model the height of
the flea compared to the horizontal distance travelled Answered by Penny Nom. 





The density of sea sand 
20141102 

From Lenny: Hi There,
I need to find out the the density of sea sand to convert one metric ton to cubic
meter as I am submitting for a tender which is in cubic meter but the requirement
is in metric ton. I searched through the web site but no density of sea sand is given
though there is specific Gravity of dry sand is available. I was given a density of
1.6 to work with. If that is true am I right to say that 1 cubic meter of sea sand is
equivalent to 1.6 metric ton? Please help as I am getting confused with what I am
able to find out on the web.
Thanks much in advance
Rgds
Lenny Answered by Penny Nom. 





4 card hands 
20141102 

From Ronaldo: How many Mus hands (combination of 4 cards allowing repetitions)
can be made from a deck containing 8 types of cards?
RRRR, RRRC, RRRS, RRR7, RRR6, RRR5, RRR4, RRRA,
RRCC, RRCS, RRC7, RRC^, RRC5, RRC4, RRCA,
RRSS, RRS7, etc.
I think 330. If so, what is the formula? Answered by Penny Nom. 





Jason's speed 
20141031 

From jason: the speed of Jason is 12 times faster than everyone. The speed of Jason is 108mph. Write the equation and solve to find the speed of everyone else. Answered by Penny Nom. 





Prime factorization in exponent form 
20141031 

From Emma: I need to find out how to make a prime factorization of 120 in exponential form. Answered by Penny Nom. 





What is the speed of the boat in still water? 
20141030 

From Adam: The current in a stream moves at a speed of 2 km/h. A boat travels 38 km upstream and 38 km downstream in a total time of 3 hr. What is the speed of the boat in still water? Answered by Penny Nom. 





Two quadratic polynomials 
20141028 

From khushboo: The zeroes of a quadratic polynomial x^2+ax+b are 'c' and 'd'
and the zeroes of a quadratic polynomial x^2+cx+d=0 are 'a' and 'b'.
find the numerical value of a+b+c+d where a, b, c and d are non zero integers. Answered by Penny Nom. 





The region between two concentric circles 
20141027 

From Ray: two circles, concentric; Given the length of chord of outer circle that is tangent to inner circle. what are the areas of both? how to calculate? Answered by Penny Nom. 





logbase4 (sin x) = 0.5 
20141026 

From Susan: Solve for x: logbase4 (sin x) = 0.5 Answered by Penny Nom. 





6 bolt holes around a circle 
20141026 

From Bobby: What Is The Cord Dimension For 6 Holes On A 24" Bolt Circule Answered by Penny Nom. 





Find the nth term 
20141026 

From Kenneth: According to the pattern of the following sequence. Find it's nth term:
3,9,27,81,243,.......... Answered by Penny Nom. 





Revolutions per minute 
20141024 

From Edward: Hello; I have a 28.2 inch diameter tire; do not worry about engine RPM or gear ratios, please tell me what the RPM
of that tire is at 8 MPH and 64 MPH. Thank you.
Sincerely; Edward Answered by Penny Nom. 





A truncated squarebased pyramid 
20141022 

From Beth: How do you find the height of the original squarebased pyramid when given the sides (12cm) of the base and height (6cm) of the truncated pyramid, as well as the sides (3cm) of the base of the chopped off top (chopped off parallel to the base)? Answered by Penny Nom. 





A 10foot piece of PVC pipe 
20141021 

From David: A plumber has a 10foot piece of PVC pipe. How many 9/5foot pieces can be cut from the 10foot piece ? Answered by Penny Nom. 





Three consecutive odd integers 
20141017 

From Maddy: 3 times the largest of three consecutive odd integers is 13 more than the sum of the other two. What are the integers? Answered by Penny Nom. 





Water in a spherical container 
20141017 

From Natalie: A spherical container with radius 10cm being filled with water such that the water level, h cm, in the container increase at a rate of 0.5 cm s^(1). Show that the area of the horizontal surface of water, A cm^(2), in the container is given by A = π(20h  h^(2) ). Answered by Penny Nom. 





A poorly worded question 
20141014 

From Marjorie: How do I figure out the following? Dylan's dog weights 12 times more than his pet rabbit. The dog and the rabbit weight 104 pounds. How much does Dylan's dog weigh? Would you explain in detail how I would arrive at the answer so I can convey same to my grandson who is in the 5th grade.
Thanks. Answered by Penny Nom. 





A linear system 
20141014 

From pheter: 4/x  1/y = 3 .... equation (1)
6/x  2/y = 5 .... equation (2) Answered by Penny Nom. 





A fact family containing 4, 4 and 16 
20141014 

From Leslie: I am helping my son and the question is 4,4,16 in fact family what does that mean Answered by Penny Nom. 





How does pir^2 = 1/4pid^2? 
20141014 

From al: Hi I cant work out the algebra. How does pir^2 = 1/4pid^2 Thanx Answered by Penny Nom. 





Building an 8 sided box 
20141014 

From Michael: I want to build an 8 sided box. The North, East, South, and West sides I want them to be 4 feet in length.
The NE, SE, SW, and NW sides I want to be 2 feet in length. What angles do I need to cut my angles.
Thanks Michael Answered by Penny Nom. 





15  (5x)/ x = 30 
20141013 

From AMANDA: 15  (5x)/ x = 30
I thought you had to multiply both sides by x in order to remove the fraction?
15x  5x  x2 = 30x
then combine 10x  x2 = 30x
x2 =20x
then take the sqrt of each side...
what am I doing wrong?? Answered by Penny Nom. 





Pre algebra 
20141012 

From mohamed: i want to know the meaning of pre algebra Answered by Penny Nom. 





A quarter mile row of trees 
20141009 

From junna: a farmer would like to plant trees on one side
of his lot which is 1/4 of a mile in a length
His friend advised him that if he would plant
the trees 5 feet farther apart,he would need 44
fewer trees.If the farmer would take the advice,
how many trees would he plant? Answered by Penny Nom. 





Why express fractions in lowest terms? 
20141009 

From John: I teach in a Faculty of Education. A colleague in the university asked me about fractions and lowest terms. I am quoting the person below, and would appreciate your insights into the question/thought.
"One I'm struggling with is why (for example) 6/18 is not considered as good an answer to a fraction question as 1/3. The traditional response is that 6/18 is not in lowest terms so the question has not been finished until the fraction is reduced, but what actually makes the lowest terms answer the better one? Is it convention? Is there a way to explain why simplest form answers in fractions are right and and anything else is considered incorrect without alluding to some need for this 'good habit' elsewhere in math or science? Is there a reallife reason?"
Thank you for any insights and if you have nothing to offer to this query, that is fine too. I appreciate your consideration.
John Answered by Robert Dawson. 





A 20% markup 
20141009 

From Fatima: What is the 20% markup price of $1.50 Answered by Penny Nom. 





Maximizing the ticket revenue 
20141007 

From Allen: An airplane whose capacity is 100 passengers is to be chartered for a flight to Europe. The fare is to be $150 per person, if 60 people buy tickets. However, the airline agrees to reduce the fare for every passenger by $1 for each additional ticket sold. How many tickets should be sold to maximize the ticket revenue for this flight? Answered by Chris Fisher. 





One zero to a quadratic expression 
20141006 

From Kevin: Find a value of n such that f(x) = 3^x2 + nx + 6 only has one zero, is this the only solution to the question? Answered by Penny Nom. 





A tennis ball in a triangular prism 
20141006 

From Anna: Hi, I need to find the the base and the height of a triangular prism, but I only know the diameter of a tennis ball that fits exactly in the triangular container.. The diameter for the ball is 8.50cm.
Can you help me find the formula?
Thank you! Answered by Penny Nom. 





A factoring problem 
20141005 

From Gina: 3x^2+6x+3 Answered by Penny Nom. 





Sieve of Eratosthenes 
20141003 

From Hope: using Sieve of Eratosthenes to determine for in instance prime numbers between 1 to 200, to what nth number should i stop?, 4th, which is 11 or what? Answered by Robert Dawson. 





Percentages in a mixture 
20141002 

From viola: Hi there
can you help me convert the below so it makes 100% (individual %)
400 gr =
100 gr =
50 gr =
50 gr =
20 gr =
2 gr =
1 gr =
1 gr =
Be great to hear back from you
Thank you
V Answered by Penny Nom. 





Trig functions and the unit circle 
20141002 

From Jake: I was wondering what conclusions can be drawn about the trigonometric functions and how they work about the circle. Can you also please give me an explanation for it? Thank you. Answered by Penny Nom. 





Division in base 3 
20140930 

From Nnubia: 1021 in base 3 divided by 2 in base 3 Answered by Penny Nom. 





A lost combination 
20140928 

From Kim: I cannot remember my combo to this simple lockbox. It is 3 digits from 09. They can be used more than once . I thought it was 117..but no joy. I am fairly sure it was using those digits 1, and 7. can you give me a list of all possible combinations, using 1s and 7s, for the 3 number code? Thank you and I am in awe of people who have math skills, for I certainly do not. Answered by Penny Nom. 





A rectangle and a triangle 
20140927 

From rajesh: The perimeter of a rectangle is equal to the perimeter of a rightangled triangle of height 12 cm if the base of the triangle is equal to the breadth of the rectangle, what is the length of the rectangle? Answered by Penny Nom. 





A man a ship and a wharf 
20140926 

From Ralph: A man om wharf 12 meters above the level of water is pulling a rope tide to a boat at the rate of 2 meters per minute. How fast is the boat approaching the wharf when there are 20 meters of the rope our. (with solution) Answered by Penny Nom. 





A wire is bent to form a right triangle 
20140925 

From Lorena: A wire 24 dm is bent to form a right triangle. The ratio of the shorter leg to the hypotenuse is 3:5. Find the length of the longer leg? Answered by Penny Nom. 





Two equations in x and y 
20140925 

From seyilogo: solve y=2x  3 and (4x  2y) / x + y = 1 simultaneously Answered by Harley Weston. 





Continuity on a closed interval 
20140921 

From Pragya: The trouble I'm having is as follows :
a continuous function is most of the times defined on a closed interval,
but how is it possible to define it on a closed interval ,because to be continuous at endpoints of the interval the function's
limit must exist at that endpoint,for which it has to be defined in its neighborhood,but we don't know anything about whether the function is always defined in the neighborhood.
Please help... Answered by Penny Nom. 





A quadratic equation 
20140920 

From Najah: (E): (m2_1)x2 _ (m+3)x+4_m2=0
A) for what values of m is the equation (E) quadratic?
B) for what value of m is the real number 1 a root of (E) Answered by Penny Nom. 





The perimeter of a parcel of land 
20140918 

From Shirley: What is the perimeter of a parcel of land that is 564 acres square Answered by Penny Nom. 





Meetings for 77 students 
20140918 

From Adam: We have a new group of students starting, and would like to set up a series of small group meetings so each student meets each other, hopefully without meeting the same people twice.
We have 77 students. In theory I would like to have 11 meeting slots, with 10 groups in each slot, with up to 8 students in each group. Is there a way to do this?
I have wondered if it might be easier to do 9 meeting slots, with 9 groups per slot, with 9 students per group.
Thanks! Answered by Victoria West. 





Two equations in two variables 
20140918 

From Susan: (28x + 36y)  [20000  .75(28x + 36y) + 60000] = 5000
x + y = 10000
solving two equations involving variables Answered by Penny Nom. 





How much did each dog weigh? 
20140916 

From Fred: LJ owned two dogs that weighed a total of 140 pounds. If one dog weighed 10 pounds more than the other, how much did each dog weigh Answered by Penny Nom. 





A tangent to a curve passing through a point not on the graph 
20140915 

From Aquilah: For the curve y = x2 + 3x, find the equations of all tangent lines for this graph
that also go through the point (3, 14). Answered by Penny Nom. 





A six team track schedule 
20140915 

From Paul: I need to make a six (6) team track schedule. It needs to be five (5) triangular (3 team) meets with each team playing each team twice Answered by Victoria West. 





Grandpa had an apple tree 
20140914 

From Emma: Grandpa had an apple tree. On the first day half of the apples plus one fell to the ground. On the second day, half of the remaining apples plus one fell to the ground. On the third day, half of what was left plus one fell to the ground. The tree was left with only one apple now. How many apples did the tree produce originally? Answered by Penny Nom. 





Two chords in a circle 
20140913 

From Carlos: Find the length of the radius of a circle in which a
chord of length 6 units is twice as far from the
center as a chord of length 12 units Answered by Penny Nom. 





The average of 9 numbers is 45 
20140912 

From rizza: The average of 9 numbers is 45. If 90 and 88 are added to the set of numbers. What will be the resulting average? Answered by Penny Nom. 





The average age of a group of 10 students 
20140911 

From sujan: The average age of a group of 10 students was 20. The average age increased by 2 years when two new students joined the group . What is the average age of the two new students who joined the group? Answered by Robert Dawson and Penny Nom. 





The perimeter and diagonal of a rectangle 
20140910 

From niniha: the perimeter of a rectangle is 68cm.if the diagonal is 26, find its dimensions Answered by Penny Nom. 





Base 6 
20140910 

From Amanda: using base 6, what is the next number after 25? 35? 55? and 455?
I need to be able to show the base 6 material. Answered by Penny Nom. 





35 base 6 
20140910 

From Amanda: Sorry I am having trouble understanding base,
35 in base 6 means 3 10's and 5 ones, which is the same ____ in base 10? Answered by Penny Nom. 





211(base x)=152(base 8) 
20140909 

From Vaidehi: Find the base value (i.e. x):
211(base x)=152(base 8) Answered by Penny Nom. 





A second grade word problem 
20140909 

From Beth: How do I explain to my second grader how to find the answer to the problem:
My tens digit is 8 more than my ones digit. My ones digit can not be zero. Answered by Penny Nom. 





Problem solving 
20140908 

From hubert: a car left the house and travelled at an average speed of 60 kph.how many minutes will it take for the car to reach the school which is 8 km away from the house Answered by Penny Nom. 





A secret number 
20140908 

From jai: it is smaller than half of 100, it is more than 4 tens and less than 5 tens, the tens digit is two more than the ones digit , together the digits have a sum of 6..... What is my secret number? Answered by Penny Nom. 





The diagonals of a cube 
20140904 

From Rukshanth: How many diagonals does a cube have? Answered by Harley Weston. 





The sum of two numbers is 52 
20140901 

From Blake: The sum of two numbers is 52 and the difference is 10. What are the numbers? i used to be real good at this stuff? Answered by Penny Nom. 





Interior angles in a parallelogram 
20140830 

From xavier: so, one of my math homework questions requires me to know how to find out how to find the interior angles in a parallelogram, the question is, "how many interior angles does a parallelogram have?" Answered by Penny Nom. 





Water usage in Ames 
20140829 

From Abigail: The City of Ames water treatment plant treats 7 million gallons of water per day on
average to meet water demands. Hypothetically, if water is withdrawn from a
groundwater system with an area of 51.6 square miles
(approximate area of Ames and surrounding area),
what is the depth of water in inches that would have to be added to
the groundwater system annually to replace the water that is withdrawn by the city? Answered by Penny Nom. 





Three collinear points 
20140828 

From jhanavi: p,q,r are three collinear points.p and q are(3,4) and (7,7) respectively and PR is equal to 10 units.find coordinates of R Answered by Penny Nom. 





Logarithms 
20140828 

From effaryna: how logarithms is applied in everyday life? Answered by Penny Nom. 





Using a bucket to fill a tub 
20140827 

From Charlotte: A bathtub needs to be filled with water. To fill the tub, a bucket needs to be filled then dumped into the tub. If the bucket is a cylinder with a radius of 6 in. and a height of 12 in, how many buckets will it take to fill the 5 ft x 3 ft x 3 ft tub. Answered by Penny Nom. 





Cutting a round cake so that it doesn't dry out 
20140826 

From James: I'm wondering if there's a simple way to calculate the area between two parallel chords of a circle equidistant from its diameter, or if I have the area, to find the distance between the two chords.
Here's my "problem". You may have heard of the way of cutting a round cake so that it doesn't dry out  make two parallel cuts (chords) the length of the cake, take the middle piece, then push the two pieces together.
So I know the area of a 12" cake, and I want say, exactly an eighth of the cake. How wide do I cut the centre piece?
Now to get even more difficult, the next day I want another eighth from the centre. How wide do I cut the next pieces, and so on...?
Thanks,
James Answered by Harley Weston. 





A car passing a bus 
20140824 

From Athish: the driver of the car is travelling at 36 km/hr and spots a bus 80 m ahead of him after 1 hr the bus is 120 m behind the car what is the speed of the bus Answered by Penny Nom. 





The inverse of f(x) = x^2  x 
20140822 

From Tyler: Find the Inverse function of:
f(x) = x^2  x Answered by Robert Dawson. 





The perimeter of a triangle 
20140821 

From Phyllis: What is the perimeter of a five acre triangle with one side being 250 feet and the second side would be at a 90 degree angle.
Thank you. Answered by Penny Nom. 





Filling three holes with stones 
20140820 

From mark: how many tonnes of hardcore/crushed stone would it take to fill
1 hole 9ft diameter 5ft deep
and 2 holes both 3ft diameter and 5ft deep Answered by Penny Nom. 




