







cos(2x) = sin(x) 
20181218 

From Liz: Determine all values of x in [0,2pi] that solve the equation Cos(2x)=sinx Answered by Penny Nom. 





The pointslope equation for a line 
20180923 

From Sally: The equation of the line in pointslope form for the line passing through the point ( 4, 6) and parallel to the line y = 6x + 2. Describe the steps. Answered by Penny Nom. 





Exponential form 
20180914 

From Saquanna: What is 25 in exponential form Answered by Penny Nom. 





Exponential form 
20180912 

From Grace: hi, I can't figure out how to do 735 in exponential form. note that im only in 5th grade and its not supposed to be in the scientific notation or whatever. okay, thanks! Answered by Penny Nom. 





Form a cone from a circle sector 
20180812 

From Tinashe: A 216 sector of a circle of radius 5cm is bent to form a cone. Find the radius of the base of the cone and its vertical angle. Answered by Penny Nom. 





The square root 3 in exponential form 
20180509 

From Paige: how do you write the square root 3 in exponential form Answered by Penny Nom. 





Simplify 1/2^i 
20180128 

From Deepak: How do I simplify this complex equation:
z=1/(2^i) Answered by Penny Nom. 





Exponential form 
20171125 

From Sherry: What is the exponential form of 3sqrt 15? 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. 





Exponential form 
20170706 

From estela: what is exponential form of 9×1000 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. 





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. 





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. 





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. 





sin 2x  sin x = 0 
20160424 

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





Exponential form 
20160126 

From Jufe: What is the exponential form of ³√11x² 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. 





Exponential form 
20151017 

From Will: What is exponential form of 8? 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 
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. 





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. 





Solve for theta 
20140425 

From ALASTAIR: Hi, The question asks Solve for 'theta' cos2theta=sintheta x costheta.
Substituting for cos2th either 12sin^2th or 2cos^2th does not give an equation in either sine or cosine alone how do I solve this please? Answered by Penny Nom. 





What is the exponential form of 1/square root of 6v? 
20140216 

From Prince: What is the exponential form of 1/square root of 6v Answered by Penny Nom. 





Prime factorization 
20140206 

From Kadeejah: Write the prime factorization of 37 in exponential form Answered by Penny Nom. 





Exponential form 
20131201 

From Alina: My question says to express each number in exponent form in as many different ways as I can; 16, 81 and 64. How do I do this? Answered by Penny Nom. 





Two teams of 4 playing 4 rounds of golf 
20130929 

From Tom: We would like to play a ryder cup format with two teams of 4 playing 4 rounds of golf. Three of the rounds would be pairs playing each other and one round would be singles. How can we set up the foursomes so we balance the number of times we play with every other golfer. Answered by Victoria West. 





An equation in slopeintercept form 
20130812 

From Brittney: write an equation in slopeintercept form of the line that is parallel to the grapg of y=3/4x+6 passes through 8,5 Answered by Penny Nom. 





Compound interest 
20130510 

From Kyla: I am doing correspondents and cannot figure out how to explain the solution to this question, I do not understand how they came to this answer and need it explained step by step so I can complete the following questions in this unit, please help!!!
Calculating compound Interest
Johnny invest $800 that pays 8% compounded quarterly for 5 years. How much is the investment worth at the end of the 5th year? Answered by Penny Nom. 





How do i reverse this formula? 
20130420 

From MK: I have 22,000,000 worth of gold and wants to want to resell the gold back with a profit.
Each transaction of gold will have a transaction fee of 15%, so if i resell the gold back at 22,000,000, I will only get back 18,700,000 after 15% transaction cut.
The current formula is X15%X = Y where X = 22,000,000 and Y = 18,700,000
Will u be able to come up with a new formula if we don't know the value of X but we know the value of Y
Something like this X15%X = 22,000,000.
How do i reverse this formula to find the value of X
Thanks Answered by Penny Nom. 





How do i write log_8(P) =7 in exponential form? 
20130414 

From nancy: How do i write this in exponential form log8P =7 Answered by Penny Nom. 





Row echelon form 
20130315 

From Shawn: Please help me put matrix in row echelon form:
1 9 8 0
5 8 1 35
1 4 1 17 Answered by Penny Nom. 





Exponential form 
20130205 

From Sandra: What is 37,008 in exponential form? Help me please!!! Answered by Penny Nom. 





A trig identity 
20130104 

From Tehmas: Prove sinC+sinD=2sin(C+D/2)cos(CD/2) Answered by Harley Weston. 





The quadratic formula 
20130103 

From itsel: Find the discriminant ans use it to determine the use the quadratic formula to solve the equasion 2x^2+3x+2=0 Answered by Penny Nom. 





Row echelon form 
20120905 

From Jennifer: Hello, my name is Jennifer. I am a 12th grader in PreCalculus and I was wondering if you may help me with Row Echelon Form.
x + 2y  3z = 5
2x  4y  6z = 10
3x + 7y  2z = 13 Answered by Penny Nom. 





Exponential form 
20120904 

From angie: How do i write 9^5 in exponential form? Answered by Penny Nom. 





Exponntial form 
20120830 

From Robin: My math teacher has asked the question:
"Write mmmxxjmyy2 in exponential form"
How would you solve this problem? Answered by Penny Nom. 





Golf for 20, two teams of 10 
20120830 

From Mark: Hi
I have to teams of 10 people playing Ryder cup format(against each other)
Can I have all 20 people playing with someone different over 3rounds of golf while remaining on there respective team I.e. players 1 to 10 must team up with a player of that group against a pair for players 11 to 20
I hope you can solve this for me
Thanks a bunch Mark Answered by Victoria West. 





Expanded exponential form? 
20120612 

From Ramon: express the numbers 990 614 000 005 in expanded exponential form. Answered by Harley Weston. 





The area of a quadrilateral 
20120421 

From Rajat: calculate the area ABCD in which AB is 48'1'',BC is 98'4'',CD is 61'4'',DA is 102'10'',AC is 110'3'',BD is 116'9''. Answered by Penny Nom. 





A uniform probability density function 
20120326 

From Noeline: The label on a bottle of liquid detergent shows contents to be 12 ounces per bottle. The production operation fills the bottle uniformly according to the following probability density function:
f(x) = 8 for 11.975 ≤ x ≤12.10
and
f(x) = 0 elsewhere
a. What is the probability that a bottle will be filled with 12.02 or more ounces?
b. What is the probability that a bottle will be filled between 12 and 12.05 ounces?
c. Quality control accepts production that is within .002 ounces of number of ounces shown on the container label. What is the probability that a bottle of this liquid detergent will fail to meet the quality control standard? Answered by Penny Nom. 





Exponential form 
20120115 

From Helen: How do you write (1/x) in exponential form? Answered by Penny Nom. 





Three sides of a triangle 
20111224 

From saba: the three sides of a triangular lot have lengths 10,11and 13cm,respectively.
find the measure of its largest angle and the area of the lot? Answered by Penny Nom. 





Exponential form 
20111212 

From Zoey: What is the exponential form of 1/8?? Answered by Penny Nom. 





Uniform acceleration 
20111206 

From Android: At a certain instant, two cars A and B are 2000 ft apart. At this instant, car A is traveling at 15 miles/hr. and accelerating at 3 ft/s^2 while B is moving towards A at 30 miles/hr. and an acceleration of 2 ft/s^2.
Find the ff:
a.) The possible time of their collusion in minutes.
b.) The distance in ft. each has traveled before collusion. Answered by Penny Nom. 





2 + f(x) and f(x) + 2 
20111121 

From Beth: Do you do y=2+f(x) the same way as if the 2 came after the equation such as y=f(x) +2 when graphing? Answered by Penny Nom. 





A log equation in exponential form 
20111111 

From Sarah: Express the equation in Exponential form
log2 to the 16th power=4 Answered by Penny Nom. 





A mythical soccer ball 
20111027 

From Joel: We've been working on this problem diligently and can't seem to come up with the answer book's answer. We think it may be wrong, yet want to check it with an expert. Here goes.
The school's new soccer balls are covered with 64 regular hexagonal panels. Each hexagon measures 2 inches between opposite corners and 1.5 inches between opposite sides. What is the total surface area of the soccer ball? Answered by Robert Dawson and Lorraine Dame. 





Expanded form 
20111012 

From Chris: Write this number in expanded form
4 326 180 501
Thanks!!! Answered by Penny Nom. 





Exponential form? 
20110830 

From Emily: I have a 6th grader that needs to find out what is the exponential form of 461,885,811 Answered by Penny Nom. 





Exponential form 
20110823 

From kiara: The African bush elephant is the largest land animal and
weighs about 8 tons . Write the amount in exponential form . Answered by Robert Dawson. 





Exponential form 
20110518 

From Kara: How do I write this in exponential form?
log 1/8 = 3 Answered by Penny Nom. 





Solve x(x3) = 5 (x+4) 
20110419 

From Ashley: I have to solve using the quadratic formula. And my answer should be in simplest exact form. And I can't approximate.
I really need help to prepare for a test ....
x(x3) = 5 (x+4) Answered by Penny Nom. 





If 25 items are evenly spread over 7 days 
20110323 

From michael: What is the formula to calculate:
If 25 items are evenly spread over 7 days, but one day has 3 items less than the other days, what is the number if items for each of the remaining 6 days? Answered by Penny Nom. 





Vertices and sides of a polygon 
20110304 

From RINA: My questions is : would a vertices and sides of a polygon be the same number. For example, a octagon it has 8 points and 8 sides. Am i correct? Answered by Robert Dawson. 





The equation of a circle 
20110214 

From Cristela: find the equation and all the information in General Form and Standard Form of the Circle that will passed trough the point (2,3) (6,1) (4,3) Answered by Stephen La Rocque. 





(7cubed * 8(exponent6))exponent 6 
20110129 

From Shalaine: What is the exponential form of (7cubed•8(exponent6))exponent 6? Answered by Penny Nom. 





The intercept form 
20110104 

From sussie: How do you find the intercept form of y=X^22x3? Answered by Penny Nom. 





Exponential form 
20110102 

From jumana: find any five examples of exponential form from real life situation Answered by Penny Nom. 





Can determine if it is scalene, isosceles, or equilateral 
20101201 

From Jessie: find the measures of the sides of triangle KPL and classify each triangle by its sides. my first problem would be K(3,2) P(2,1) L(2,3) ...The three points they give you are the vertices of the triangle and you need to match them up. Draw the triangle and write in the vertices and the related point with the vertex. You will then do the distance formula three times to find the distance of all three sides. Once you have the three sides you can determine if it is scalene, isosceles, or equilateral...using the distance formula how do i solve this? Answered by Penny Nom. 





Two girls agree to mow a lawn 
20101123 

From Milorad: Two girls agree to mow a lawn 60m by 80m so that the first girl cuts one half by
cutting a uniform strip around the lawn. How wide a strip should the first girl cut?
I've been struggling with the question above, mainly with the equation and I have
set it up as 2400=(602x)(802x), if this is incorrect I would like to know where I've
gone wrong and also would like a full answer to see it properly done. I need an algebraic
answer and not one with a diagram. Answered by Penny Nom. 





i^i 
20101121 

From trale: Can we use e^ix=cosx+isinx for finding i^i like that: x= pi/2 =>
e^(ipi/2)=0+i then [e^(ipi/2)]^i=i^i.then we find i^i= 0,207879576....
is it true? can we give value for x for free?thank you. Answered by Harley Weston. 





Powers 
20101020 

From dylan: how do you write 20736 in exponential form .same for 1728 and 50625.
is there a formula to figure out how to express large know numbers in exponential form. Answered by Penny Nom. 





Exponential form 
20101006 

From celina: what is the exponential form of 4x*4x Answered by Penny Nom. 





Decimal form 
20100908 

From Tracy: What is the decimal form of 0.14 x 10 the the first power? Answered by Penny Nom. 





Exponential form 
20100824 

From Courtney: What the Exponential form? For Ex. X2*X5*X4?? Answered by Penny Nom. 





Reflection in the line y = x 
20100721 

From tousif: Find the 2 x 2 matrix which represents a reflection in the line y = x?
Please help.... Answered by Penny Nom. 





Exponential form 
20100616 

From charlotte: what is the exponential form of 6x6x6x5x5x5x5= Answered by Robert Dawson. 





Compound interest 
20100601 

From Kenneth: Hello:
I have a question regarding the following compound interest and future value
calculation.
Year 1 P + rP equals balance after the first year.
Year 2 (P + rP) + r(P + rP) equals balance after the second year.
Year 3 ? equals balance after the third year.
This question is in two parts.
1. What would follow for year three?
2. I know that a pattern will develop. What will it be so that I can determine
the extended pattern for following years ? Answered by Penny Nom. 





A trig equation 
20100428 

From Steve: 2cos^2(X)2sin^2(x)+1=0 Answered by Harley Weston. 





cos(x) = sin(x  1) 
20100428 

From alex: In the equation cos x = sin x1 for pi/2
A: solve for x graphically
B: solve algebraically and prove the solution is correct.
Alex Answered by Penny Nom. 





If (x, 4) is equidistant from (5, 2) and (3, 4), find x. 
20100421 

From abeth: If (x, 4) is equidistant from (5, 2) and (3, 4), find x.
Find the point on the y  axis that is equidistant from (4, 2) and (3, 1). Answered by Penny Nom. 





A model for the population of a Canadian city 
20100407 

From jess: Let t^2 represent tsquared. The population of a Canadian City is modelled by: f(t) = 12t^2 + 800t + 40,000, where t is the time in years. When t= 0, the year is 2007.
a) According to the model, what will the population be in 2010?
B) In what year is the population predicted to be 300,000? Answered by Penny Nom. 





Standard form 
20100305 

From Laura: How do I change 3y=4x+1 into standard Ax+By=C standard form. This is my son's schoolwork. I homeschool him. I got the answer to the problem as 3y=4x+1, but it needs to be written in standard form and I know it needs to read 4x3y=1, but how do I get that answer into standard form. I need to know how to explain it to him. Can you show me? Thank you so much. Answered by Penny Nom. 





Trigonometry and picture hanging 
20100113 

From george: The top of a picture 1m high 0.8m from the ceiling. At a point on the ceiling directly in front of the picture, we wish to install a light so that the angle subtended by the picture equals to the angle of depression of the top of the picture. How far out from the wall should the light be installed? Answered by Penny Nom. 





The graph of f(x)=1/x 2 
20091129 

From Kapilan: Please answer the following question:
Sketch the graph of f(x)=1/x 2 Answered by Harley Weston. 





A linear equation 
20091022 

From Ryan: How do you convert the equation 2x6y=7? This is on my homework and I am really stuck!!! Answered by Penny Nom. 





Exponential form 
20090918 

From karen: Q: Write the following in exponent from: a * a * a * a * * * a, where there are n 1 a's
note: *asterisk means times. Answered by Penny Nom. 





The slopeintercept form 
20090911 

From Shelby: Write an equation in slopeintercept form of the line that is parallel to the graph of 3y4x=1 and passes through (0,6) Answered by Penny Nom. 





Exponential form 
20090908 

From hanna: hi,
well i am really bad in math and i have a math paper and i was just
wondering what 3x3x3x3x3 was in exponential form and what is
exponential in a way a person like me would understand? Answered by Penny Nom. 





What is 8 tons in exponential form? 
20090901 

From Tyler: what is 8 tons in exponential form Answered by Penny Nom. 





Exponential form 
20090831 

From cecil: what is the exponent form 564000? Answered by Stephen La Rocque and Harley Weston. 





Exponential form 
20090805 

From motaz: Let x = log_2 1/8 Write the exponential form of the equation and solve the equation for x Answered by Stephen La Rocque. 





The Pythagorean theorem 
20090624 

From supreet: What are some realworld applications of the Pythagorean theorem?
and
How are the Pythagorean theorem and the distance formula related? Answered by Harley Weston. 





Completing the square 
20090427 

From Daniel: I tried following an example of yours but I still couldn't figure it out.
Here is my question,
2x^2  6x + 1 = 0.
Any help would be greatly appreciated. Answered by Stephen La Rocque. 





The center of an ellipse 
20090421 

From Nae: what is the ellipse center of 5x^2+3y^2=15 Answered by Stephen La Rocque. 





A perpendicular line in standard form 
20090421 

From Kristy: Can you help me with this equation?
Find the equation, in standard form of the line perpendicular to 2x3y=5 and passing through
(3,2) With the equation in standard form with all integer coefficient. Answered by Stephen La Rocque. 





Exponential form 
20090416 

From Pete: Hi,
How do you express ³√h^4 in exponential form. I am having a lot of
trouble with this one.
thanks
Pete Answered by Stephen La Rocque. 





2sinB=3tanA 
20090410 

From Xanathax: ABC is a rightangled triangle. 2sinB=3tanA.
Calculate the measure of angle A. Answered by Penny Nom. 





Winding paper after a break 
20090410 

From Olen: Question from Olen:
I work in a paper mill and have been handed the task to search for a formula to determine how much paper needs to be added to a parent roll to make up the difference at the winder. (Ex. The spool diameter at the reel is 18.25" we measure roughly 33.5" to make two 58" rolls in the winder. If the is a paper break and the roll diameter in the winder is 30" how much do I add to a single parent roll (22" roughly) to make one 58 " and the 28" needed at the winder. I would appreciate any help to complete this task. I would like to be able to build a chart that operators can refer to based on what is needed. Thank you. Answered by Harley Weston. 





A fraction in its simplest form 
20090402 

From Michael: I'm in 4th grade and need to express decimals as a fraction in its simplest
form. Is there a step by step method to figure out?
ex 0.64 = 64/100 = ? Answered by Robert Dawson. 





A linear system 
20090313 

From Rasanga: Use the row echelon form of the augmented matrix to solve the following linear system.
X1+2X2+X4=6
X3+6X4=7
X5=1 Answered by Harley Weston. 





Time in a Swing 
20090222 

From Barb: I looked at the questions concerning a pendulum as I know I need to use this formula but I am stiil not able to figure this problem out. Can you help?
If a child is on a swing with a 10 foot chain, then how long des it take to complete one cycle of the swing?
I know I am suppose to use the formula 8T^2 = pi^2 L but I do not understand how to do this.
Thanks Answered by Janice Cotcher. 





0/0 
20090215 

From Justin: Hello, I was just wondering, what is the difference between 0/0 being represented as nullity or as an indeterminate form?
Justin Answered by Harley Weston. 





The height of a triangle 
20090214 

From GARIMA: IF THE SIDES OF TRIANGLE ARE GIVEN . HOW WE WILL
CALCULATE THE HEIGHT OF TRIANGLE. Answered by Penny Nom. 





Faces, edges and vertices 
20090204 

From sheila: what is the relationship between the number of faces and the number of edges of a triangular pyramid ? Answered by Penny Nom. 





Transformations 
20090204 

From Vickie: Hello,
My daughter had a question on her
Week By Week about transformations and I can't remember what transformations
will result in proportional figures. If a transformation looks like it is smaller
what is that called? Also if the figure looks bigger what is that called?
Vickie Answered by Robert Dawson. 





What is 301 million in word form? 
20090130 

From chyamber: What is 301 million in word form? Answered by Penny Nom. 





Archimedes' formula for parabolic arches 
20090123 

From La: Use calculus to verify Archimedes' formula for y=9x^2. Prove Archimedes' formula for a general parabolic arch. Answered by Harley Weston. 





Segments of a sphere 
20090116 

From Herman: How do I solve for a segment of a sphere so that the orange peel or pie shaped section is converted to a flat surface with dimensions. I form large diameter domes, elliptical and sphere heads on a press. I enter the diameter say 30 feet with two segments above and below the equator and the total number of segment around the circumference at say 18 so the widest part of the pie shaped section will fit my press. How do I take the upper or lower course above or below the equator and figure the height of the orange peel shape, the chord length at top and bottom, and solve for the right angle at 2 degree increments down the arc length of the pieces so I can layout the flat plates prior to pressing. Thanks for your help. Answered by Robert Dawson. 





The slope intercept form 
20090111 

From Norma: write equation in slope intercept form and then find the slope and yintercpet of the corresponding line.
please show step by step
1). 2x3y9=0 and 2). 3x4y+8=0 Answered by Penny Nom. 





What is i^i? 
20081227 

From randomness: i have learnt that 'i' is square root of 1. What is then i^i ? It baffles my maths teacher... Answered by Robert Dawson and Penny Nom. 





A line in slope intercept form 
20081208 

From laurie: the question: Write and equation of the line that passes through the point
and has the give slope. Then rewrite the equation in slope intercept form.
(2, 5 ) m= 3 Answered by Penny Nom. 





Gravity's Effect at a Distance 
20081206 

From ROHAN: AT WHAT HEIGHT FROM THE SURFACE OF EARTH,THE WEIGHT OF THE BODY BECOMES HALF? (RADIUS OF THE EARTH = 6400) Answered by Stephen La Rocque. 





The height of an equilateral triangle 
20081106 

From touqeer: My question is that how can we find the height of an equilateral triangle without using pythagoras theorem? Answered by Penny Nom. 





Exponential form 
20081021 

From layla: how we wite 256 in exponential form Answered by Harley Weston. 





I have 6 vertices and 10 edges 
20081020 

From Jacquelin: I have 6 vertices and 10 edges. One of my faces is a regular polygon. Answered by Chris Fisher. 





3,6,10,15,and 21 
20080928 

From jarred: i am currently stumped on a math project that requires me to find out the recursive formula for a sequence of numbers. the numbers in the sequence are 3,6,10,15,and 21. Thank you for your time. Answered by Walter Whiteley. 





The standard form Ax+By=C 
20080926 

From Susan: I am having difficulty changing the pointslope form of the equation of the line yy1=m(xx1) to the standard form Ax+By=C. You must express A,B,C in terms of the constants m,x1,y1. I have been able to insert numbers and switch easily from the general to the point slope equation, but I am stumped on how to convert it this way. Answered by Penny Nom. 





Exponential form 
20080925 

From Pat: The African bush elephant is the largest land animal and weighs about 8 tons. Write this amount in exponential form. Answered by Penny Nom. 





Exponential form 
20080916 

From shawn: Write the product in exponential form: 5.5.5.2 Answered by Penny Nom. 





A line through two points 
20080910 

From Conor: Find the equation of the straight line which passes through the points (2,14) and (8,1) Answered by Penny Nom. 





1,679,616 as a power of 6 
20080903 

From Denise: express 1,679,616 in exponential form as a power of 6. Answered by Penny Nom. 





A linear system 
20080823 

From dipesh: consider the system of equations
x6y+2z=5
2x9yz=14
4x+12y3z=19 by reducing the augm matrix to row echelon form, find
the solution to the equation.
leaving the first two equations the third is changed to 3x+6y+14z=31
show the equations have infinitely many solutions and give a general
formula for them Answered by Penny Nom. 





A linear function 
20080807 

From Warren: What are the conditions of the numerical coefficients of the standard form Ax+By=C in Linear Function?
How will you transform y=square root of 3 x + 1 in standard form Ax+By=C? Answered by Penny Nom. 





Time with NonUniform Motion 
20080721 

From jenina: An unmarked police car, travelling a constant 95km/h, is passed by a speeder travelling 145km/h. precisely 1.00s after the speed passes, the policeman steps on the accelerator. If the police car’s acceleration is 2.00m/s², how much time elapses after the police car is passed until it overtakes the speeder (assumed moving at constant speed)? Answered by Janice Cotcher. 





A Falling Rock 
20080711 

From Rita: This question has 3 parts.
If a rock falls from a height of 20 meters on the planet Jupiter, its height H
(in meters) after x seconds is about H(x) = 20  13x^2
(a) What is the height of the rock when x = 1.2 seconds?
(b) When is the height of the rock 15 meters?
(c) When does the rock strike the ground?
Thank you Answered by Janice Cotcher. 





Exponential form 
20080703 

From Kent: How to write 8 365 005 106 in expanded and exponential form? May I request you also to explane how does it solve. Answered by Stephen La Rocque. 





Write log_2 (1/8) = 3 in exponential form 
20080627 

From Jaime: how do you write log2 (1/8) = 3 in exponential form?
the 1/8 is a fraction and the 2 is a base of 2 Answered by Penny Nom. 





Percent difference? 
20080614 

From Cathy: I am trying to verify a "percent of difference" as stated on a tax form. I cannot seem to come up with the equation to do so.
Here are a few examples on the form:
Last year $62.91 this year $66.05 tax difference $3.14 percent difference 5.64%
Last year $ 2014.97 this year $1982.93 tax difference $32.04 percent difference 57.56%
Last year $97.66 this year $79.58 tax difference $18.08 percent difference 32.48%
I have tried several different ways and per some of Q&A's already on your site I still have a problem and would appreciate some assistance.
ThanksCathy Answered by Penny Nom. 





2(x  1)^2 + 8 
20080612 

From kasondra: y=2(x1)2[thats a square] +8 that need to be put in standard form
the answer is y= 2x2 4x + 6
i got y= 2x2 4x 4
i just don't get how my teacher got that answer Answered by Penny Nom. 





A recursive formula for 9, 18, 36, 27, ... 
20080605 

From Rita: I am having trouble understanding how to write formulas (I should say create formulas) from a given sequence.
It does not matter what sort of sequence it is. The confusion remains.
I have not found a textbook or easy math book that explains this process for the average Joe to grasp.
Here are the two questions:
(1) Write a recursive formula for the sequence
9, 18, 36, 72, ...
(2) Write a recursive formula for the sequence
3, 3(sqrt{3}), 9, 9(sqrt{3}) Answered by Penny Nom. 





The cube of 2y in exponential form 
20080519 

From Xiu: I dont get this question..
Write "the cube of 2y" in exponential form. I know the answer is (2y)^2 but i really don't understand why. Can you explain how to do this whole problem for me? Answered by Leeanne Boehm. 





The standard form of an ellipse 
20080430 

From Rebecca: I have to write the following equation into standard form of an ellipse:
9(X1)^2 + (Y+1)^2 = 1 Answered by Stephen La Rocque and Harley Weston. 





The slope intercept form 
20080411 

From Dave: Hi, why is there a yintercept in the slope intercept form?What does the yintecept have to do with the equation? Answered by Penny Nom. 





A shape 
20080403 

From Joshua: what shape has 4 faces, 4 corners and 9 edges. Answered by Penny Nom. 





The exponential form of x radical y to the third power 
20080330 

From Jennifer: what is the exponential for of x radical y to the third power Answered by Penny Nom. 





A linear system 
20080310 

From sandhiya: one group of people purchased 10 hotdogs and 5 soft drinks at a cost of
$12.50. a second group bought 7 hotdogs and 4 soft drinks a ta cost of $9.00
find the cost of a single hot and a single soft drink.(using the row echelon form to solve) Answered by Penny Nom. 





Row echelon form 
20080221 

From cOCO: USE ELEMENTARY ROW OPERATIONS TO WRITE THE MATRIX BELOW IN ROW
ECHELON FORM.
1 1 8  2
2 1 1 11
2 1 14 11 Answered by Penny Nom. 





The equation of a line 
20080217 

From Jennifer: Given the point A(3,2)B(5,8) find the equation of the line AB ( in standard form ) Answered by Penny Nom. 





Exponential form 
20080216 

From annna: i already got the answer for what is the prime factorization of 648 which is 2x2x2x3x3x3x3
but how do i write that answer in exponential form? Answered by Penny Nom. 





The standard form of a line 
20080130 

From Thomas: I'm attempting to get this in standard form
slope=3;(1,5) Answered by Penny Nom. 





The standard form of a line 
20080124 

From James: I need to put it in Standard from ax+by=c the problem is
(4,0); parallel to y=2+1 how can I put this in Standard from Answered by Stephen La Rocque. 





The equation of a line 
20080120 

From Sara: The question is:
Write the equation of a line that is parallel to y=3x2 through the point (5,9).
I think the correct equation for this is y=3x+24.
But I have to write it in standard form, and I can't seem to figure out how to do that. Please answer soon! Thanks! Answered by Stephen La Rocque and Penny Nom. 





How do I write the following in exponential form? 
20080109 

From Mandy: How do I write the following in exponential form?
( square root of a^2 b)^5 Answered by Penny Nom. 





Exponential form 
20080108 

From liam: i was wondering if anyone could help me with this question and tell me how and what the did; exponetial form of 4 326 180 501 Answered by Stephen La Rocque. 





The area of a piece of property 
20080105 

From Greg: I need to know the area of a six sided piece of property. I sent a map by regular mail. Answered by Harley Weston. 





Multiplying exponentials 
20080102 

From jessie: Can you please explain how to put x^3 y^2 times x^1 y^3 in simplest exponential form? Answered by Penny Nom. 





Radicals in exponential form 
20080102 

From Andre: The title of the section in my textbook is to write each of the following
radicals in exponential form.
My question is how do u write the squareroot of 10 in exponential form? Answered by Penny Nom. 





Shooting an arrow over a wall 
20071211 

From Amy: The path of a large arrow fired from a non
torsion catapult can be modeled by y=0.0044x^2 + 1.68x, where x is the distance the
arrow travelled (in yards) and y is the height of the arrow (in yards). Given the height of
a castle wall, find the safest distance from the wall to launch an arrow over a 120 yardhigh wall. Answered by Victoria West and Stephen La Rocque. 





Exponential form 
20071130 

From Sasha: How do I write the number 127398 in exponential for? Answered by Penny Nom. 





Transformations and compositions 
20071129 

From mary: Is there any possible relationship between composite functions and the concept of function transformations? Answered by Harley Weston. 





Area of a 17sided lot 
20071121 

From Lynda: My uncle is wanting to buy this piece of land [a 17sided polygon] but we are questioning the acerage total. the measurements are [on the attached diagram]. Answered by Stephen La Rocque. 





Exponential form 
20071116 

From ashley: write a sentence for exponential form. Answered by Penny Nom. 





The height of a triangle 
20071103 

From William: I need to find the height of a triangle if the base is 15, one side is 14 and the other side is 13. Answered by Stephen La Rocque and Penny Nom. 





How to solve related rates problems 
20071027 

From David: Can you plz explain how and where you come up with an equation to solve this?
Find the rate of change of the distance between the origin and a moving point on the graph of y = sin x if dx/dt = 2 centimeters per second. Answered by Stephen La Rocque. 





Area of a triangle formed by three points on a graph 
20071026 

From Betty: My question is 'find the are of a triangle whose vertices have
coordinates (3,5),(6,5), and (4,10) Answered by Stephen La Rocque. 





A triangular lot 
20071017 

From Brian: Seeking the square footage of a triangular property lot, dimensions are: 620 X 620X 720. Answered by Penny Nom and Melanie Tyrer. 





Four triangles in a square 
20071015 

From Kristina: A square with side lengths of 6 cm is divided into 3 right triangles and a larger isosceles triangle. If the three right triangles have equal area, find the exact area of the isosceles triangle. Answered by Stephen La Rocque. 





Triangle perimeter and area 
20071005 

From divakar: The sides of the triangle are integers. The perimeter is 8. What is the area? Answered by Stephen La Rocque. 





Find the equation of a line given two points 
20071005 

From Tiffany: The equation for the line through the points (11,2) and (18,12) can be written in the form Ax+By=C.
Find A and B. Answered by Victoria West. 





Exponents 
20070926 

From Calvin: Exponential form
5 3exponent x 5 4exponent divide 5 2exponent Answered by Stephen La Rocque. 





Exponential form 
20070912 

From Ericha: How do I express 1,679,616 in exponential form as a power of 6 using a calculator? Answered by Stepehe La Rocque and Penny Nom. 





Prime factors in exponential form 
20070906 

From Michelle: how would you write this: factor 48 as a product of primes written in exponential form Answered by Stephen La Rocque. 





Exponential form 
20070905 

From jeanette: the African bush elephant is the largest animal and weighs 8 tons. write this amount in exponential form. Answered by Stephen la Rocque and Penny Nom. 





Exponential form 
20070831 

From Victoria: The cost of each space shuttle is about $10,000,000.
Write this amount in exponential form. Answered by Stephen La Rocque. 





Exponential form 
20070829 

From Emily: Write the Exponential Form of 125 x 25 and 81 x 27. Answered by Stephen La Rocque. 





Pointslope form 
20070816 

From jenny: write an equation in the pointslope form and the intercept form
slope=4,passing through (1,3)
slope=8,passing through (4,1)
slope= 5,passing through (4,2)
slope= 2,passing through(0,3) Answered by Leeanne Boehm. 





Can you solve this by factoring? 10r^2  35r = 10 
20070812 

From Aranxa: how do u solve this equation by factoring:
10r^2  35r = 10 Answered by Stephen La Rocque. 





A statistics example 
20070802 

From Claudia: A particular employee arrives to work some time between 8:00 am  8:30 am. Based on past experience the Company has determined that the employee is equally likely to arrive at any time between 8:00 am  8:30 am.
On average, what time does the employee arrive?
What is the standard deviation of the time at which the employee arrives?
Find the probability that the employee arrives exactly at 8:12 am?
Find the probability that the employee arrives between 8:20 am  8:25 am? Answered by Har. 





A complex number in polar form 
20070723 

From roland: write the given complex number z in polar form lzl(p+qi) where lp + qil=1 for 3  4i. Answered by Harley Weston. 





Calculating the area (acreage) of a four sided lot 
20070718 

From A property owner: I have a real estate property and the lot size is something I need to find out. I know the lengths of the four sides, but it isn't a rectangle, it is an odd shape. How do I find the acreage? Answered by Stephen La Rocque. 





Algebraic EquationsAx+By=C 
20070702 

From Juan: The general "Standard" form of an equation is Ax+By=C.
ReWrite this equation in slopeintercept (y=mx+b) form. Answered by Harley Weston. 





Using Heron's Formula to help maximize the area of a triangle 
20070627 

From Claire: Given one side of a triangle is 4 cm and the ratio 1:3 for the other 2 sides. What is the largest area of the triangle? Answered by Stephen La Rocque and Harley Weston. 





Exponential form: x^y 
20070622 

From Kishor: whats the easy way to calculate X raised to Y where y is much greater than x. Answered by Stephen La Rocque. 





Rewrite 2x+4y+2=3y+5 in general form 
20070621 

From dawn: how do you rewrite 2x+4y+2=3y+5 in general form? Answered by Stephen La Rocque. 





Circumscribing a golden cuboid with a sphere: surface areas 
20070614 

From Ainslie: A golden cuboid is defined as a rectangular prism whose length, width and height are in the ratio of phi : 1 : 1/phi.
Prove that the ratio of the Surface Areas of the golden cuboid to that of the sphere that circumscribes it is Phi : Pi. Answered by Stephen La Rocque. 





Angles of depression 
20070613 

From Phonda: The pilot of a small private plane can look forward and see the control tower for a small airstrip. Beyond that is a large factory that is 3 milies from the airstrip. The angles of depression are 12.5 degrees and 4.8 degrees respectively.
Find the airplane's altitude, to the nearest ten feet. Answered by Stephen La Rocque. 





Solving a quadratic equation using the Quadratic Formula 
20070605 

From Stuart: Solve the following quadratic equation:
3xsquared5x4=0 Answered by Stephen La Rocque. 





Finding the area of a lot without knowing the angles 
20070605 

From Cristin: I have a landlocked piece of land. I need to know the square
footage in order to determine the acreage. My deed only gives the lengths of its five sides. Answered by Stephen La Rocque. 





Radical form 
20070418 

From Cassia: Hi
Um, I had a question for algebra, I'm just curious of how to put x^3/8y^1/4 in
radical form. Can you help me? Answered by Stephen La Rocque. 





Exponential form 
20070416 

From Cassia: I was just wondering, how do you write the squared root of 7x(to the 5th) in
exponential form? If you could help explain that I'd be grateful. Thanks Answered by Brennan Yaremko. 





A rotated rectangle 
20070416 

From Graham: There is a circle inside which from the centre to the top is a rectangle. Size is unimportant.
If I the rectangle is at 0 degrees and I know the coordinates of the 4 corners I can do a check to see
whether a given point x,y is inside the rectangle or not.
Question : If the rectangle is rotated by 50 degrees how do I check then as the lines of the rectangle are not
perfectly straight with regards to x and y ie at 0 degrees x changes but y is constant and vice versa.
At 50 degrees x and y change together. Answered by Penny Nom. 





The area of a parcel of land 
20070403 

From Ricky: I need the attached land parcel (#0436) converted to acreage.
This would be of great help to me.
Thanks,
Ricky Answered by Penny Nom. 





The area of an irregular pentagon 
20070326 

From grace: hi I am doing graphics and need to find the area of the section given to us (it is just drawn). the sides measure 15m, 35.4m, 5m, 17.8m, 35.7m. the angle between the 15m side and the 35.4m side is 17degrees, the angle between the 35.4m side and the 5m side is 73degrees. the angle between the 5m side and the 17.8m side is 151degrees, the angle between the 17.8m side and the 35.7m side is 90degrees and the angle between the 35.7m side and the 15m side is 95degrees. if you could tell me the area i would be extremely grateful. thanks very much. Answered by Penny Nom. 





yintercept form 
20070316 

From Ken: Simple way on how to convert to & from yintercept form & Std. form.
Eg: Convert into yintercept form: 3x+4y+7=0,
Eg.: Convert into Std. Form: y=1/2x +3, y=50x +300. I would appreciate your
help in this matter, as I find it hard to understand.
Kind Regards: Ken Answered by Penny Nom. 





Triple angle tangent formula 
20070315 

From sam: Hi I am trying to derive a triple angle formulae for tan. I know i need to use compound and double angle formulae but am finding it difficult to "clean" up my fraction to get the triple angle formulae can you show me a worked derivation?! thanks Answered by Penny Nom. 





The area of a property 
20070314 

From Greg: Hi my name is Greg. I have a piece of property I am trying to buy,
but need to find out the square feet of it first.
The four sides are unequal lengths and none at a right angle or
parallel. Here are the measurement in feet.
The base of the square is 29.12 feet in width.
The right side of the square is 44.33 feet high.
The top of the square is 28.80 feet in width.
The left side of the square is 46.20 feet high.
I have not done this math in ages and really need your help. Answered by Harley Weston. 





Finding the xintercept 
20070302 

From Ash: Y = 1/100X^2 =27/10X +0 = 0 THE Y INTERCEPT IS 50 HOW DO I FIND THE X INTERCEPT Answered by Gabriel Potter. 





sin(3a), cos(3a) and tan(3a) 
20070228 

From mailene: hi, i...indeed,to..need..your..help how..cn..i..prove..this,formula??? sin3a=3sina4sin^3a cos3a=4cos^33cosa tan3a=3tantan^3a /13tan^2a the..symbol...^is..the..expOnent Answered by Haley Ess and Penny Nom. 





Find the area of the triangle 
20070220 

From Christina: Graph the function f(X)= x+1/x1 and graph the tangent line to the function at the points A:(2,3) and B:(1,0). The point of intersection of the two tangent lines is C. Find the area of the triangle ABC. Answered by Stephen La Rocque. 





What constitutes a face for a geometric solid? 
20070214 

From Erica: What constitutes a face for a geometric solid? We have been getting conflicting answers from different textbooks. Some teachers are saying that cylinders and cones do not have faces. I'm thinking that cylinders have 2 and cones have 1. Please enlighten me. Thanks! Answered by Walter Whiteley. 





Exponential form of complex numbers 
20070212 

From Austin: When dealing with imaginary numbers in engineering, I am having trouble getting things into the exponential form. The equation is 1+i now I do know that re^(theta)i = r*cos(theta) + r*i*sin(theta). Just not quite understanding the order of operations. Thanks Answered by Penny Nom. 





Irregular multi sided polygon 
20070120 

From Graham: I have an irregular polygon. I know the length of all the sides and know approximately all the internal angles. Is there a formula or table that can calculate the area for me? Answered by Steve La Rocque, Chris Fisher and Penny Nom. 





The slopeintercept form 
20070104 

From Earnestine: Given a line containing the points (1,4), (2,7), and (3,10) determine the slopeintercept form of the equation, provide one additional point on this line, and graph the function. Answered by Penny Nom. 





The slopeintercept form 
20061217 

From Anthony: I'm really confused with this, tried to figure it out on my own but i can't seem to grasp it here's the problem: Two points are given a. Write an equation in slopeintercept form for the line containing the two points. b. Graph the line from Part a and check that both points are on the line. Answered by Penny Nom. 





The slopeintercept form 
20061108 

From Kilihea: I need to graph this equation but first need to turn it into a slopeintercept form. 6x  3y = 3 I would really appreciate it if you could help me turn it into a slopeintercept form. Answered by Penny Nom. 





Putting things in exponent form 
20061018 

From Sheila: Write in exponential form 2 sq. root a with an exponent 5. I do not understand on how to do it. Answered by Stephen La Rocque. 





Convert a standard form to a slope intercept form 
20060914 

From Maiko: I need to know step by step procedures to convert a standard form to a slope intercept form? Answered by Penny Nom. 





The area of an irregular octagon 
20060823 

From Billy: How do you figure the area of an irregular octagon? Measurements are 4 equal sides of =BD", and 4 equal sides of =BE". It measures 1 1/2" = from flat to flat. Answered by Penny Nom. 





How old is y = mx + b? 
20060705 

From Beckie: I am taking intermediate algebra this summer (Math 95), and have a question for you. My instructor will award extra credit points to any of us who find out how old the formula
y = mx+b is. Would you happen to know the answer? Answered by Penny Nom. 





The area of a triangle 
20060521 

From A student: how do you find the area of a triangle? Answered by Penny Nom. 





10^100 in binary form 
20060510 

From Headmaster: How many digits has the number 10^{100} if we write it in binary form? Answered by Chris Fisher, Paul Betts and Steve La Rocque. 





A hallway in an old house 
20060506 

From Sabrina: I am trying to determine how many square feet is in a room that is not square or rectangular. It has basically 5 walls of different lengths, it is acutely considered a hallway in an old house, how can I figure out the footage, the Length times Width requires to much wasted materials Answered by Penny Nom. 





The perimeter of a regular octagon 
20060420 

From Martin: I would like to make an octagon out of 2x4 lumber. I know that the lumber needs to be cut at 67.5 degree angles, but how do I determine the length of each piece if I want to make, say, a 2.5 ft diameter octagon? Answered by Stephen La Rocque. 





cos(3X) 
20060329 

From Joshua: I'm having trouble proving that cos(3X)=cos^{3}X (cosX)(sin^{2} X) Answered by Penny Nom. 





The area of a block of land 
20060326 

From Ronald:
I have a building block of land with four unequal sides and only one right angle. I want to know the total area (in metres) and how the calculations were carried out.
The four sides are: Rear of property: 9.14 metres
left side: 36.9 metres
Right side: 32.61 Metres
front to street: 27.43 Metres
The front to street and right side constitute a right angle. but there are no others. Answered by Penny Nom. 





The quadratic formula 
20060303 

From Miriam: Please show work and indicate "answer", using the quadratic formula 
(x+2) (2x+3) = 6 Answered by penny Nom. 





Is there a solid shape with 5 faces, 8 edges, and 4 vertices? 
20060211 

From Annie: Is there a solid shape with 5 faces, 8 edges, and 4 vertices? Answered by Penny Nom. 





y  y1 = m(x  x1) 
20060108 

From Greg: How do you change 2x + 3y = 7 into y  y1 = m(xx1)?
Answered by Penny Nom. 





Area of a lot 
20051203 

From Ben:
How do you calculate the area of the following Lot?
I figured the following angles from the deed, which read:
N 86 degrees, 45 minutes E, for 322 feet.
S 10 degrees, 30 minutes W for 113 feet.
N 84 degrees, 30 minutes W for 368 feet.
N 50 degrees, 42 minutes E for 76 feet.
N 40 degrees, 40 minutes E for 15 feet.
There is a discrepancy between two surveyors and I'd like to figure out how to calculate the Area of such a shape. Answered by Harley Weston. 





I = PRT 
20051116 

From Ryan: Use the formula to find the value of the variable that is not given:
I=PRT;I=$2880, R=0.08, P=$12,000 Answered by Penny Nom. 





Prove that a rhombus' diagonals are perpendicular 
20051002 

From Tania: How do you prove that a rhombus' diagonals are perpendicular using the 2 column proof method? Answered by Walter Whiteley. 





The area of a lot 
20050829 

From Richard: My wife and I are interested in buying property in Idaho but the owner can't give us a square footage of the lot. The dimensions are as follows:
121.0 on the left side
157.0 on the right side
135.0 on the bottom
162.0 on the top
The bottom right corner of the lot is a true right angle, the rest are not. Answered by Penny Nom. 





The area of a lot 
20050717 

From John: A plot of land has the following dimensions: 391 ft. x 757 ft. x 208 ft. x 788 ft. Q: How many acres is this? Answered by Harley Weston. 





sin x + sin 2x + sin 3x + sin 4x = 0 
20050510 

From Elia: I tried many times, but can't get to solve the following question:
sin x + sin 2x + sin 3x + sin 4x = 0 Answered by Chris Fisher. 





Some triangle problems 
20050506 

From A student: 1.use the
heron's formula to find area of triangle ABC to nerest tenth
A.a=21 b=28 c=11
B.a=23 b=28 c=12
2.Find the nearest tenth the altitude of the longest side if a=3 b=3 c=5
3.the length of each side of a rhombus is 10 cm the length of one diagonal
is 12 cm find the area to the nearest square centermeter Answered by Penny Nom. 





Bayes Theorem 
20050403 

From wei:
In the January 11,1988,issue of the Oil&Gas Journal, R.A.Baker
describes how the Bayesian approach can be used to revise probabilities
that a prospect field will produce oil. In one case he describes,
geological assessment indicates a 25% chance the field will produce
oil. Further,there is an 80% chance that a particular well will strike
oil given that oil is present on the prospect field.
 Suppose that one well is drilled on the field and
it comes up dry. What is the probability the prospect field will
produce oil?
 If two wells come up dry, what is the probability
the field will produce oil?
 The oil company would like to keep looking as long
as the chances of finding oil are greater than 1%. How many dry wells
must be drilled before the field will be abandoned
 If the first well produces oil,what is the chance
the field will produce oil?
Answered by Andrei Volodin and Penny Nom. 





A torus and a sphere 
20050327 

From Tony: Is it possible to shrink a torus into a sphere? Answered by Andrei Volodin and Penny Nom. 





The area of a quadrilateral 
20050227 

From Jonathan: I want to know how to find the area of a quadrilateral. Answered by Penny Nom. 





Finding the missing side of a triangle 
20050120 

From Jason: I found a geometry problem that reads as follows:In triangle ABC, Answered by Penny Nom. 





A sequence of transformations 
20050103 

From Abraham: Please go to this web site and look at number 31.
http://www.nysedregents.org/testing/mathre/matharch/mathbtestau02.pdf
That is the New York state education web site.
Can you tell me if my answer would be marked correct? My answer was Transformation of 4,3 (T 4,3) followed by a reflection in the xaxis.If I graphed the question and wrote that, would I get full credit Answered by Harley Weston. 





The area of a triangle 
20041230 

From Perry: What is the area of a triangle with dimensions 3"X5"X7"? Could you provide the formula? Answered by Penny Nom. 





The point slope form of a line 
20041026 

From Jack: Given a set of ordered pairs, ie (1,1) (2,4) (3,7), how does one determine the rule f(n) other than by trial and error Answered by Penny Nom. 





sin(3A) 
20041020 

From A student: Express sin3A in terms of sinA and cosA. Answered by Penny Nom. 





Finding the height of a triangle 
20040914 

From A student: I have to calculate the height of a triangle.
The base is 6 (units)say ab
One of the top sides is 4 (units)say ca
The other side is 2 (units) say cb
I don't know the angles.
How to find the height? Answered by Chris Fisher and Penny Nom. 





The distance formula 
20040904 

From Joe: Why do we use square roots and squares in the distance formula Wholdnt they cancel each other out? Answered by Claude Tardif. 





Row echelon form 
20040724 

From Michael: My name is Michael and I'm in the 11th grade. I have a Math question that I can't solve. The problem is system of equations that I need to do in augmented matrix form, find the row echelon form, and solve it by using back substitution.
2x + 3y + 7z =13
3x + 2y  5z = 22
5x+ 7y  3z = 28 Answered by Penny Nom. 





Some trig expressions 
20040523 

From A student: Prove:
sin A + sin B = 2sin(A+B/2)cos(AB/2)
cos A  cos B = 2sin(A+B/2)sin(AB/2)
cos A + cos B = 2cos(A+B/2)cos(AB/2)
sin A  sin B = 2cos(A+B/2)sin(A+B/2) Answered by Penny Nom. 





An oildrilling platform 
20040427 

From Alie: An oildrilling platform is located in the Gulf of Mexico 3.25 miles from the nearest point on shore. From a point B on the shore due east of A the bearing of the platform is S51.2W. How far is it from B to the platform? Answered by Penny Nom. 





Dividing zero by infinity 
20040108 

From Jason: What do you get when dividing zero by infinity? Our Calculus teacher was pretty sure that the expression was indeterminate from. However, if this is so...Why? Zero divded by any number (except zero) is zero, true. Any number (except infinite) over infinite is zero. So, why isn't Zero divided by infinite zero. A simpler way if I had 4 potatoes and was to split them among 2 friends, each friend would get 2 potatoes. However, if I had 0 potatoes and split them a infinite number of ways, each person would still have 0. Explain please! Answered by Penny Nom. 





The area of a plot of land 
20031219 

From David: I have a plot of land that I cannot find the square footage of. Actually my home sits on a large lot. Local building codes require that a home is seated on no less than 7500 square feet of land and have no less than 50ft of road frontage (the rear of the lot has 65ft of frontage on another road). I need to know if I have enough square footage to build a second home on the rear lot. The lot has five sides. Only one angle is a 90 deg. angle. The others I cannot determine. Of the 4 remaining angles, all 4 angles are obtuse, or greater than 90 deg. The dementions are 89.19' x 130' x 118.52' x 65' x 170.94'. The two legs that make the 90 deg angle are 89.19' and 170.94'. The measurements fall in order using the 90 deg angle as the point of origin and proceeding clockwise, 89.19', 130', 118.52', 65', 170.94'. I have used all the skill I can muster, however, it has been a long time since school and regretably I cannot find an answer. Answered by Penny Nom. 





The area of a triangle 
20031201 

From A student: Find the Area of Triangle ABC
A(3,2)
B(4,0)
C(0,8) Answered by Penny Nom. 





The volume of an irregular tetrahedron 
20031124 

From Peter: How do I calculate the volume of an irregular shaped tetrahedron where: side a = 1.4 m side b = 1.4 m side c = 1.2 m and height = 0.75 m at the junction of sides a and b. Answered by Penny Nom. 





Indeterminate forms 
20031006 

From A teacher: Is it possible for me to find any geometrical interpretation without using calculus to explain indeterminate forms? Answered by Chris Fisher. 





Notation 
20030915 

From Kim:
Question: i have a couple of questions 1. write in standard form a)4x2x8 b) 5 to the power of 4 . . . Answered by Penny Nom. 





The quadratic formula 
20030831 

From Alex: I am using Houghton Mifflin's Precalculus with Limits book, 2nd edition. However, the first chapter encompasses Algebra review, and I am stuck on a problem. All that's required is to solve the following and verify using a calculator: 3y2+6y+2=0 I have solved the problem using the quadratic formula, but from what I remember, the quadratic formula is used in the case of equations following the AX2+BX+C=0 pattern. As the problem I am attempting uses a yvariable, can I still use the quadratic formula? Since I am not sure what route to take in solving this problem, I am hoping you can assist me. Answered by Harley Weston. 





A rule with a variable 
20030824 

From Crystal: what is a rule with a variable Answered by Penny Nom. 





Write sin(3x) in terms of sin(x) 
20030505 

From A student: Write sin 2x in terms of sin x Answered by Penny Nom. 





Finite differences 
20030210 

From Jenny:
I need to find a formula that will work with any number. I am finding the volume of a 3d cross shape. Here are my results so far:
Term Number 0 1 2 3 4 5
nth term 1 7 25 63 129 231
1rst diff 6 18 38 66 102
2nd diff 12 20 28 36
3rd diff 8 8 8
I can't seem to find a formula that will work with any number. Any help would be much appreciated. Answered by Penny Nom. 





Transformations of pattern blocks 
20030206 

From Cheryl: I am trying to help my 8th grade son with Transformations  use of patttern blocks. He has to trace a figure and reflect it across the xaxis, which I can do, but then it indicates include ordered pairs  that confuses me. Answered by Penny Nom. 





Augmented matrix 
20021231 

From Michelle: I am trying to augment a matrix so that i can find the values of the variables a, b, and c. For the life of me i can't find a solution to the matrix: 3 5 2 ' 22 2 3 1 ' 9 4 3 3 ' 1 I thank you for your help, Michelle Answered by Penny Nom. 





Performance reviews 
20021121 

From Lara: Perhaps you can help. He's doing performance reviews at work. The average performance review is 3.92 on a 5.0 scale. This person would receive a 3.5% raise for next year. The highest performance review is 4.9 and this person would recieve a 6.0% raise for next year. How do I solve for the other performance review numbers. Answered by Penny Nom. 





Formulating equtions 
20020914 

From Theresa: Hello. In math class we have to formulate equations for certin questions for extra credit. We are allowed to ask anyone and anyone can do it for us and explain it to us. Could you please do that? Here are the questions  Jordan has 3 times as much money as Reva. Together they have $44. How much money does each have?
 The Tigers played 48 games. They won twice as many as they lost. How many did they win?
 There are 900 students in Sewickley Academy. There are 20 more girls than boys. How many girls are there?
 A board 400 cm long is cut into 2 pieces. One piece is 66 cm longer than the other. Find the lenght of the shorter piece.
Answered by Penny Nom. 





The quadratic formula 
20020911 

From Kathleen: im having a problem trying to understand quadratic formulas can u please help me i have problems like 3x^{2}  4x  11 = 0 how do i work out that problem? i have the formula written down but it doesnt seem to register for me. Answered by Penny Nom. 





The area of a triangle 
20020907 

From Phill: How do you find the area of a equilateral and other triangles? Answered by Penny Nom. 





1/8 in decimal form 
20020904 

From A student: explain how you put 1/8 in a decimal form Answered by Penny Nom. 





Distance in 3space 
20020816 

From David: The question is: how do I figure out the distance of one object in 3D space to another object in 3D space? I have an object at say x = 5.872, y = 2.876, and z = 7.290; and the other object is at x = 1.129, y = 8.213, and z = 11.127. I have been suggested to use the pythagorean theory on this, but since there are three variables, I don't understand how. Answered by Penny Nom. 





The area of a circle 
20020603 

From Jessica: I am doing a maths assigment for university, which is aimed towrds primary school students(k6). I was wondering if you could give me some information as to how I could describe to students the rule for finding the area of circle, using a circle cut up into equal sectors (like a pizza). I know it has something to do with the fact that you can make these shapes into a parallelogram, but I am a bit uncertain as to how I can express this idea clearly and articulately to students. Answered by Penny Nom. 





A triangular prism 
20020428 

From A student: Need the formula for the surface area of a triangular prisim? Answered by Penny Nom. 





Area of a triangle 
20020407 

From Puzzled: What is the surface area of a triangle 13 ft x 13 ft x 18 ft? Answered by Penny Nom. 





sin 2x = cos 3x 
20020225 

From Allan: solve: sin 2x = cos 3x Primary question: how do you handle the cos 3x? Answered by Paul Betts and Chris Fisher. 





Rolling 5 sevens before rolling a six or an eight 
20020120 

From Tony: When rolling 2 dice, what is the probability of rolling 5 sevens before rolling a six or an eight? Answered by Andrei Volodin and Penny Nom. 





Exponential form 
20011211 

From Crystal: Hi, I am asking a question on behalf of a homeschooling grade 11 student. She is having trouble with changing something like (3^{4})^{2} into a exponential form. First of all she needs to know what the term means "exponential form" and then the process of it. Answered by Penny Nom. 





Slope intercept form 
20011127 

From A student: what is slope intercept form? Answered by Penny Nom. 





Rewriting and evaluating formulas 
20011119 

From A conserned mother: Due to the wide range of temperatures experienced in Canada, engineers who construct roads must allow for expansion and contraction of the road surface. The following formula is used to calculate the amount of expansion E to allow for: E= kL(Tt), where k is the constant of expansion for the road surface. L is the length of the section of highway in metres. T is the temperature of the air in degrees Celsius. t is the temperature, in degress Celsius, at which the section of the highway was constructed. Answered by Walter Whiteley. 





Fourier transform 
20010807 

From Adbul:
 Sir, we have the Dirichlet's condition for the Fourier transform : " The function should be integral over the real line " But why we are we neglecting this for example when we take the Fourier transform of an impulse train?
 Suppose we want to travel from one corner of a square of side 'a' to the diagonally opposite corner. We can travel along the sides which gives a pah length of '2a'. We can also do it in steps as shown below:
_  _PATH  _ _____
Suppose The step size =DELTA x Then the path length will be again '2a'. Now in the limit DELTA x >0 again we get '2a' But when we take the limit we get the straight line diagonal whose length is 'SQRT(2)X a' Where did I go wrong? Answered by Chris Fisher. 





Conformable matrices 
20010805 

From Wayne: Can someone explain the concept of conformable matrices in a way that is easy to understand ? One definition says to multiply matrices rows and columns must conform, ie, 5 x 3 matrix times a 3 x 5 matrix. In the next example, however a 8 x 1 matrix and a 8 x 3 matrix are said to be conformable! Answered by Steve Kirkland. 





Exponential form 
20010606 

From A student: Hello can u please answer my question what is the exponent form of 8x8x8x8 Answered by Penny Nom. 





New Quebec reform 
20010524 

From MarieAndrée: I am a middle school teacher beginning to adapt to the new Quebec reform. I am regularely doing projects in écologie and géographie in French immersion based on the international schools way of thinking (What form does it have? How does it work? What is its history? How does it change? How is it linking to our lives? What is our responsibility about that fact or that thing?) and I have real difficulty to make it work for math. So now, I am looking for math concepts (8) which would link to the same way of thinking. What are your suggestions? Answered by Claude Tardif. 





Faces 
20010221 

From Sandy: How many faces are there on a sphere? What are the faces of a cone? What is the definition of a "face" of a 3D object? Answered by Walter Whiteley. 





An irregular polygon 
20010209 

From Jason: I have a 5 sided irregular polygon I am trying to figure out the area of. There are no right angles in the polygon as far as I can tell. I do not know any angles. Answered by Chris Fisher. 





A problem with distance 
20010116 

From A student: For what values of a is the distance between P(a, 3) and Q(5, 2a) greater than the square root of 26. Answered by Penny Nom. 





Euler's Formula 
20001111 

From Denise Roberts: I'm trying to design a unit (possibly involving a Webquest) on Polyhedra and I cannot find a formula I once used. The formula involved the number of vertices (V), edges (E), and faces (F) of the polyhedra. Answered by Walter Whiteley. 





A cycloid in Cartesian form 
20000920 

From Billy: The parametric equation of cycloid is given: x=r(tsint) y=r(1cost) How to eliminate t? Answered by Harley Weston. 





A conic in standard form 
20000518 

From Tara McConkey: Im havign trouble converting the following conic to standard form, i know that the conic is a hyperbola but that is all 16x^{2}9y^{2}160x18y+247=0 Answered by Harley Weston. 





A system of equations in five unknowns 
20000320 

From Will: I have been having some problem with the following question for some time. I would appreciate any help on solving the problem or a solution. Q: Assume that a system of equations in the unknowns x1, x2, x3, x4 and x5 when converted to row echelon form gives . . . Answered by Penny Nom. 





Polar coordinates 
20000224 

From Tran Trung: How do I convert r = 2/(2sin(theta)  3cos(theta)) to rectangular and x^{2} + y^{2} 2y = 0 to polar form? Answered by Harley Weston. 





Triple angle formula 
20000223 

From Sara: Can one derive a triple angle formula for sine and cosine? If so, how? Answered by Chris Fisher. 





Derive the quadratic equation 
20000101 

From Thuy: My teacher asked us this question in which i can't understand when she asked to derive the quadratic equation. What does this mean? Answered by Penny Nom. 





Bases other than 10 
19991206 

From Garret Magin: We are doing a lesson on numbers of other bases than 10. We are working with binary, octal, and Hexadecimal. I was wondering what is used to represent number of different bases other then 16? Does it just continue on with the alphabet and if so what happens when you get to Z. It would be a help if you could answer this because it is really bugging me. And none of the math teachers at my school could let me know. Answered by Claude Tardif and Patrick Maidorn. 





A Trigonometry Question 
19990828 

From Diane Simms: My question is can the following be factored. I am a teacher who needs the factors to this right away. 2 Sin^{2}X + 2 SinX CosX  1= 0 Answered by Harley Weston. 





Shapepreserving transformations 
19990504 

From J McAndrew: A shape preserves its shape if a rotation, translation or scaling is performed on it. Are these the only continuous transformations which have this property? These transformations if performed on the parts and then summed have the same effect as the transformation being applied to the whole; are these linear transformations? Who, and what area of mathematics has classified all transformations of this type completely? Answered by Chris Fisher. 





Standard Form 
19990330 

From Pam: How do you put this equation into standard form? y=3.572x+5.409 Would you please put this equation in this form Ax+Dy+C=0 Answered by Penny Nom. 





The Quadratic Formula 
19990122 

From Eric Morgan: Hi my name is Eric Morgan and I m in 8th Grade honors math (middle) and I'd like to know how to prove the quadratic formula b±sqrt of b(a)(c)over 2(a) Answered by Penny Nom. 





Complex numbers and the quadratic formula 
19981225 

From Richard Peter: My age is 16, and my name is Richard. My question relates to the topic complex numbers & the quadratic formula. I would like to know how to solve quadratic equations in which the discriminant is less than 0 (i.e. we get two complex solutions to the quadratic) 3x^{2}+2x+5 = 0 and how mathematicians like euler contributed to this field. If it would be possible I would also like to know how this type of quadratic equations can be graphed? Answered by Harley Weston. 





Indeterminate forms 
19981211 

From R. Dixon: What is the correct evaluation of infinity/0 ? I've checked three different math sites. One says definitively, that infinity/0 is "not" possible. Another states that infinity/0 is one of the indeterminate forms having a large range of different values. The last reasons that infinity/0 "is" equal to infinity. Answered by Walter Whiteley and Harley Weston. 





The bricklayers formula 
19981124 

From Rachel Kaplan: I have to do a report on the bricklayers formula N = 7LH. Can you give me any information on this. Answered by Harley Weston. 





Area of a triangle. 
19980201 

From Jodi Blucher: Is there a formula for the area of an equilateral triangle knowing the length of the sides? Answered by Chris Fisher and Harley Weston. 





Equivalent Expressions 
19970226 

From Karyn Jones: Josie says that s=n/(n+1) and s/(1s)=n are two ways to write the same formula. Describe whether or not you agree with Joise. Explain how you made your decision. Answered by Walter Whiteley and Penny Nom. 





Deriving the Quadratic Formula 
19970204 

From James: How do you derive the quadratic formula? I know what it is, but the textbook doesn't say how to derive it. Answered by Penny Nom. 





Why is lbs the abbreviation for pounds? 
19961003 

From Nancy Mutdosch: What does lbs stand for? Why is it the abbreviation for pounds? Answered by Chris Fisher. 





Avec les chiffres 1,5,6,7, vous devez arriver a un total de 21 
20060928 

From Danny: J'ai un problème qui est le suivant: Avec les chiffres 1,5,6,7, vous devez arriver a un total de 21 en les utilisant qu'une seule fois et en utilisant la multiplication, l'addition, la division et la soustraction... Answered by Claude Tardif. 





problème de trigonométrie 
20051101 

From Manon: Soit un triangle ABC, de cotes a , b et c, avec A=45° et B=60°.
Apres avoir demontre que 3a²2b²=0 (que jai fais en utilisant la regle du sinus) et a²2c²+2ac=0 (que jai fait en utilisant la regle du cosinus), vous montrerez que laire du triangle ABC peut sexprimer: { [ 3 + racine carre 3 ] / 12 } b² unites.
Je ne sais pas comment arriver a cette expression de laire. Je narrive pas a exprimer c² et ac en fonction de b².. et je pense que ca pourrait vraiment aider..
puisque je suis arrive a letape:
ac[(racine carre 3) / 4]
avec ac = a² + c²  b²
et a² = 2/3 b²
ms c²= 1/3 b² + ac Answered by Claude Tardif. 





La longueur des segments formant un triangle 
19991005 

From Michel Provencher: Connaissant la longueur des segments formant un triangle,comment détermineton chacun de ses angles si:  il S'agit d'un triangle rectangle
Sachant que la somme des angles d'un triangle est de 180 degrés et sachant par conséquant qu'un des angle est de 90 degrés (triangle rectangle) il reste donc, 90 degrés à partager entre les 2 angles restant. Si les 2 segments formant l'angle droit sont de même longueur on obtient un angle de 45 degrés pour les angles restant soit 1/2 angle droit ce qui ne me pose évidement aucun problème. Quel relation, S'il y en a une, y a til entre la longueur de ces 2 segments et les angles restants.  il S'agit d'un triangle quelconque
Answered by Claude Tardif. 

