







A barrel on its side 
20081113 

From Dave: Question from Dave:
How many gallons are left in a 36x60 in. barrel (laying on its side) and has 16 in. of gasoline left. I have attached a diagram. Answered by Harley Weston. 





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 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. 





Two equations in x and y 
20140925 

From seyilogo: solve y=2x  3 and (4x  2y) / x + y = 1 simultaneously Answered by Harley Weston. 





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. 





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. 





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. 





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 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. 





Distance, speed and time 
20140813 

From abdel: Mac walked to a park from the college at 5 km/h. 10 minutes later, Steve started
riding his bike at 15 km/h to the same park to meet Mac. They arrive at the same
time at the park. How far is the park from the college? Answered by Tyler Wood. 





Speed, distance, time 
20140813 

From Aarti: a theif running at 8 km/hr is chased by a policeman whose speed is 10km/hr.if the thief is 100 m ahead the policeman then what will b time required for the policeman to catch the thief? Answered by Tyler Wood. 





The dimensions of a rectangle 
20140803 

From Jamaica: if the perimeter of a rectangle is 30m and its area is 56 m2.find its length and width? Answered by Penny Nom. 





The method of elimination 
20140705 

From leo: please explain how can i solve this problem
3x6y=38
6x9y=44
using elimination and simultaneous method thank you :) Answered by Penny Nom. 





The width of a rectangle 
20140702 

From john: if the area of a rectangular field is 90 sq. m and its length its is 19 m find its width Answered by Penny Nom. 





Simultaneous equations 
20140620 

From rana: solve the simultaneous equations
a)3x=7y
12y=5x1 Answered by Penny Nom. 





The number of standard deviations 
20140615 

From Dawn: Suppose that, at a certain college, the average weight of all male students is 160 pounds with a standard deviation of 30 pounds. A certain male student weighs 145 pounds. Determine how many SD's his weight is above or below average. Answered by Penny Nom. 





A model of the sun and the Earth 
20140614 

From Lynn: There is a model of the sun that is 2 1/2 inches in diameter. This is the only clue we have! How far away is the earth from this model? Answered by Penny Nom. 





What is the speed of the buses? 
20140518 

From musliu: Two buses leave a bus station and travel in opposite direction from that same starting point.if the speed of one is twice the speed of the other and they are 240km apart at the end of 1h, what is the speed of the buses? Answered by Penny Nom. 





A circle a square and a rectngle 
20140512 

From mazhar: suppose the length and breadth of the rectangle are 5 cm and 10 cm respectively and M is a point along the corner of the circle. what is the radius of the circle?(diagram is given..but i didn't mention it..actually the diagram looks like a circle inscribed in a square and the right bottom corner one rectangle will be given ,it is touches to circle at a point M that I've already mentioned and the dimensions of that rectangle also I've mentioned) please help me out.. Answered by Penny Nom. 





Travelling upstream and downstream 
20140512 

From Mohanad: Howie Sorkin can travel 8 miles upstream in the same time it takes him to go 12 miles downstream. His boat goes 15 mph in still water. What is the rate of the current? Answered by Penny Nom. 





2 cars driving towards each other 
20140427 

From Joakim: 2 cars driving towards eachother , the distance between them is 162km. they meet after 2 hours. car A is driving with 4/5 of car B´s speed. what is the speed of each car... Answered by Penny Nom. 





What time was it when joe's brother passed him? 
20140425 

From Nathan: joe left home in his bike at 10:00 am, traveling 21 km/h. At noon, his brother set out after him on his motorcycle, following the same route. if the motorcycle traveled at 63 km/h, what time was it when joe's brother passed him? Answered by Penny Nom. 





Simultaneous equations with fractions 
20140419 

From Maryam: I looked at your example of simultaneous equations with fractions and applied it to my question from an educate exam papers but I couldn't get it to work. The question is:
x/8  y = 5/2
3x + y/3 = 13 Answered by Penny Nom. 





A tangent of the curve (x/a)^n+(y/b)^n =2 
20140415 

From sudhir: the equation of tangent of the curve (x/a)^n+(y/b)^n =2. at(a,b) is Answered by Penny Nom. 





Two rectangular prisms 
20140410 

From hannah: two rectangular prisms have a combined volume of 432 cubic feet Prism A has half the volume prism b has what are the volumes of prism a and prism Answered by Penny Nom. 





Two circles that touch each other externally 
20140408 

From Ameya: Two circles of radii a and b (a > b) touch each other externally. ST is a common tangent touching the circles at S and T respectively, then ST^2 is equal to Answered by Chris Fisher. 





The surface area of a rectangular prism 
20140408 

From Manraj: Find the surface area of a rectangular prism with dimensions 4, 5, and 7 units. Answered by Penny Nom. 





A cubical tank 
20140401 

From renzo: A cubical tank contains 2048 cubic ft of water when HALFFULL. Find the total area of the tank and the length of its diagonal Answered by Penny Nom. 





A circle which is tangent to two perpendicular lines 
20140309 

From MJ: I'm a College Student taking up Bachelor of Secondary Education on Math Subject.
And I'm struggling for my research about Circles. I done solving the said topic particularly on this question:
"What are the possible equations of a circle being tangent to a pair of perpendicular lines, having the origin as the Point of Intersection and the C (h, k), where h, k ∈ℤ"
But I can't get what would be the process that I must do in order to jive to my idea/goal for that problem.
Please check my idea that the numerical coefficients of the equation is equal to the radius of the circle.
Thanks in advance! :) Answered by Penny Nom. 





A speed word problem 
20140224 

From kiss: Hank bicycles 5 km/h slower than Kelly. In the time that it takes Hank to bicycle 42 km, Kelly can bicycle 57 km. How fast does each bicyclist travel? Answered by Penny Nom. 





Simultaneous fractional equations 
20140215 

From benjamin: hi math central. benjamin here. during class, i had problem with this topic. normally i wont have problems with math but this topic i just too hard for me. please help i am having exam and test next week on this topic
here is the question:
using substitution method, solve the simultaneous equation.
(x+1)/(y+2)=0.5
(x2)/(y1)=1/3 Answered by Penny Nom. 





Two bicyclists traveled in opposite directions 
20140207 

From Susan: Two bicyclists traveled in opposite directions, one at a rate of 8 km/hour and the other at a rate of 7 km per hour. In how many hours were they 45 km apart? Answered by Penny Nom. 





Walking up and down a hill 
20140206 

From flo: michelle walks 4 km to the top of a hill at 3 km/h then immediately walks back down at an average speed of 5 km/h what is her average speed for the 8km walk Answered by Penny Nom. 





Related rates 
20140130 

From Veronica: A container is the shape of an inverted right circular cone has a radius of 1.00 inches at the top and a height of 5.00 inches. At the instant when the water in the container is 1.00 inches deep, the surface level is falling at the rate of 2.00 inches/second. Find the rate at which the water is being drained. Answered by Penny Nom. 





Two nonlinear equations 
20140126 

From Naryn: (1÷x) + (1÷y) = (7÷12)
xy = 12 Answered by Penny Nom. 





A rectangular shaped property 
20140117 

From Donna: If I I have property that is rectangle shaped. I I know the ends are 100 feet how many feet would the sides be to make 5.4 acres Answered by Penny Nom. 





A rectangle inscribed in a circle 
20140110 

From Marian: A 16 cm by 12 cm rectangle is inscribed in a circle. Find the radius of the circle. Answered by Penny Nom. 





Radio direction finders 
20140109 

From Nathan: Radio direction finders set up two points A and B, which are 2.5 miles
apart on an eastwest line. From A, it is found that the bearing of a
signal from a radio transmitter is N36.33 degress E, while from B the
bearing of the same signal is N53.67 degrees W. Find the distance of
the transmitter from B. Answered by Penny Nom. 





Two tuna boats 
20140109 

From amanda: Two tuna boats start from the same port at the same time, but they head in opposite directions. The faster boat travels 10 knots per hour faster than the slower boat. At the end of 8 hours, they were 272 nautical miles had each boat traveled by the end of the 8 hour period? Answered by Penny Nom. 





Distance from a point to a line 
20131228 

From Sue: I need to find the distances from the west line on 1st Take Point and 2nd
Take Point.
Thanks,
Sue Answered by Penny Nom. 





Analytic Geometry 
20131218 

From fRitz: if (x,4) is equidistant from (5,2) and (3,4), find x. Answered by Penny Nom. 





The area of an irregular octagon 
20131118 

From zafar: if i have a rectangular octagon then how i can find its area
1. The length of rectangle is 42 and the width is 21 and and the base length is 4212 =30 i mean the
length of base =30 Answered by Penny Nom. 





One train overtaking another 
20131111 

From kiran: two trains of equal length are running in parallel tracks in the same direction with the speed of 60km/hr and 90km/hr respectively the latter completely crosses the former in 30 seconds the length of each train is in mtr Answered by Penny Nom. 





The average time per mile for a marathoner 
20131104 

From Peter: a runner ran a 26.2 mile marathon in 2hours 8minutes and 24secounds. the question is, what was his average time for each mile that he ran? Answered by Penny Nom. 





Substitution type simultaneous equations 
20131103 

From Kayla: I am having problems with substitution type simultaneous equations, when the variable you are substituting is a algebraic one:
y=x^23x+4 and 3x2y=1
I have rearranged 3x2y=1 to get x=(1+2y)/3 but when I substitute this x value into the other equation, I get the wrong answers!
Would appreciate any help! Thank you. Answered by Penny Nom. 





The perimeter of a rectangle 
20131024 

From sana: if the length is given 70 m and the breadth is given as 40 m find the perimeter of the rectangle Answered by Penny Nom. 





Four tangent circles 
20131009 

From Nilesh: Four circular cardboard pieces, each of radius 7cm are placed in such a way that each piece touches two other pieces. How to find the area of the space enclosed by the four pieces?
Please let me know. Answered by Robert Dawson. 





A pool, a school, a park and home 
20130924 

From Selena: The distance from the park to the pool is the same distance as the distance from your house to school. The school is between the pool and your house. Prove that the distance from the park to the school is the same distance from the pool to your house. Answered by Robert Dawson. 





A rectangular hyperbola 
20130919 

From Soumya: Is the graph of an inverse variation a RECTANGULAR HYPERBOLA? If it is, then how can be the equation of a rectangular hyperbola be xy=constant , whereas in the books it is written that the graph of a rectangular hyperbola is x^2y^2=a^2? Answered by Chris Fisher. 





Similar rectangles 
20130817 

From Mattie: The dimensions of a rectangularshaped picture frame are 14 inches long and four inches wide. Which dimensions below represent another frame that i geometrically similar>
a. l=49 in. and w=14in.
b. l=7in and w=3in
c. l=21in and w=8in
d. l=24in and w=14in
thanks Answered by Penny Nom. 





Equal ordinate and abscissa 
20130815 

From sonit: the slope of tangent to the curve y=(4x^2)^1/2 at the point, where the ordinate and abscissa are equal, is Answered by Penny Nom. 





What is the original speed? 
20130810 

From MJ: If a truck increases its average speed by 10 km/h it can cover 60 km at the original speed in the same time that it can cover 80 km at the faster speed. What is the original speed? Answered by Penny Nom. 





Simultaneous equations 
20130710 

From Warren: solve this simultaneous equation: xy=4
2x+3y=14 Answered by Penny Nom. 





Distance as a function of acceleration 
20130710 

From Tom: If you start at a stoplight and your acceleration is 16t  t^2, how far have you gone after 8 seconds? Answered by Penny Nom. 





Diego and his dog 
20130709 

From William: john went hunting and walked at a speed of 4 km/h. one hour later, Diego and his dog went to meet john with a speed of 6 km/h and the dog was running between john and diego until they meet up with a speed of 18 km/h. After Diego meets john, how much distance did the dog run? Answered by Penny Nom. 





Water use in a rectangular flush tank 
20130510 

From milo: A rectangular flush tank 22" by 71/4 contains water to depth of 17" how many gallons of water will be saved if a conservation device reduces the capacity to 3/5 of this amount? And reduced to the nearest tenth Answered by Penny Nom. 





A triangle and an incircle 
20130509 

From Max: On my Geometry Test about tangent, chord, and secant lengths, my teacher gave an extremely difficult problem.
It was a Circle inscribed in a Triangle with all triangle sides being tangents and lengths were given. My class was told to find the length of each segment of the line.
The points on each line were the vertexes of the triangle, and the point where the line hits the circle.
Please explain how someone could do this. Answered by Chris Fisher. 





4 linear equations with 3 unknowns 
20130412 

From Marian: how to solve for 3 unknowns in 4 simultaneous equations Answered by Penny Nom. 





The distance between 2 lines in 4D 
20130401 

From samane: how can i measure the distance between 2 lines in 4D?? Answered by Chris Fisher. 





Simultaneous equations with fractions 
20130331 

From Terence: 5/x6/y=1
17/x+30/y=16
I been spending whole day to solve this question. Would be very grateful if you can help I try
The denominator value is a equations term which make is simultaneous equations so hard. Answered by Penny Nom. 





A shortest distance problem 
20130328 

From LYNDELL: I have a right triangle and know the length of all sides. How do I calculate the shortest distance from the vertex of the 90 degree angle to the hypotenuse? Answered by Penny Nom. 





Tangents to the curve y = x^3 
20130324 

From Ethan: How many tangent lines to the curve y = x^33 pass through the
point (2, 4)? For each such line, and the exact coordinates of the point of
tangency on the curve. Answered by Penny Nom. 





Trigonometry 
20130323 

From Tizoc: I am in a trig class and I have a conflict. When solving the length of a side, I know what trig function to use, but I do not know what angle to use in a calculator. To make this a little more understandable, if I have all the angles available in a right triangle and I use the tangent function, how do I know what to use?
Heres what I do not know what to put in my calculator: Tan(?)
Thanks in Advance! Answered by Penny Nom. 





The dimensions of a rectangle 
20130319 

From stephanie: the length of a rectangle is 5m more than twice its width, and the area of the rectangle is 88m^2 find the demensions of the rectangle Answered by Penny Nom. 





Fencing a parcel of land 
20130311 

From Koleen: How much fencing do I need for an 56,850 parcel of land for a 15 stable horse barn Answered by Penny Nom. 





6 miles in 28 minutes what's my average speed? 
20130305 

From lynda: 6 miles in 28 minutes what's my average speed? Answered by Penny Nom. 





The tangent to a circle at a point on the circle 
20130222 

From Andrew: What is the equation of the line tangent to the circle with equation x^2+y^2=25 at the point (4,3) Answered by Penny Nom. 





An electron in a TV tube 
20130215 

From anu: an electron in a TV tube is beamed horizontally at a speed of (50^6) m/sec. towards the face of a tube 40 cm away
about how far will the electron drop before it hits? no information has been provided of initial height from where it is beamed. Answered by Robert Dawson. 





A word problem involving toys 
20130214 

From sandy: Each boy gets 5 toys.Each girl gets 3 toys.There are 150 pupils.
The boys had 74 more toys than girls.
How many boys?
How many girls? Answered by Penny Nom. 





Simultaneous equations 
20130210 

From Michael: 2P + 1/3V =8
3P  2/V=5 Answered by Penny Nom. 





A journey of two parts 
20130206 

From Natalie: Mr Lim drove at 70 km per hour for 1 hour and 30 minutes. He then drove another 55 km. if his average speed for the whole journey was 80km per hour, what was his speed for the 55 km journey? Answered by Penny Nom. 





The area of a rectangle 
20130129 

From Bali: if the length of the
rectangular field is decreased by 5m,
its area is decreased by 70 sqm. if the
width is increased by 6m, the area is
increased by 180 sqm. determine the
length and width of the rectangular
field? Answered by Penny Nom. 





How fast are we approaching each other? 
20130111 

From Heather: If I am skating at 7 mph, and a car drives towards me at 15 mph, how fast are we approaching each other? Answered by Penny Nom. 





How fast is the distance between the aircraft and the car increasing? 
20121024 

From Steven: At a certain instant an aircraft flying due east at 240 miles per hour passes directly over a car traveling due southeast at 60 miles per hour on a straight, level road. If the aircraft is flying at an altitude of .5mile, how fast is the distance between the aircraft and the car increasing 36 seconds after the aircraft passes directly over the car? Answered by Penny Nom. 





Two swimmers 
20121022 

From Emily: Two swimmers start from opposite sides of the pool. Each swimmer swims the length of the pool and back at a constant rate. They pass each other for the first time 40 feet from one side of the pool and for the second time 45 feet from the other side of the pool. What is the length of the pool? Answered by Penny Nom. 





Two congruent circles in a rectangle 
20121020 

From Alexander: Have you ever solved a problem, in which you have a rectangle, from which you need to cut the largest two circles of equivalent diameter? I bisected a rectangle diagonally, but the circles, while tangent to two of the sides, are not tangent to eachother. Can you devise a method for two equivalent circles, that are tangent to two sides, are also to eachother?
Take for example a piece of paper, Each if the two largest circles has a diameter that is greater than the distance to the midpoint of the diagonal bisector of the rectangle. Answered by Chris Fisher. 





A tank with an inner walled compartment 
20121012 

From don: I have a tank 20 feet diameter, 19' 8" tall with an inner walled compartment that has a 7' 6" radius arc with in the tank. I need to figure out the volume of the inner area and the volume of the larger area. Answered by Harley Weston. 





A word problem involving a fraction 
20121012 

From Derrick: If the numerator and denominator of a fraction are both decreased by 1 the fraction becomes 2/3. If the numerator and denominator are both increased by 1 the fraction will be 3/4. Find the original fraction. How to do? Answered by Penny Nom. 





Four tangent circles 
20121004 

From renu: inside of a circle K of radius length measure R,three circular discs A,Band C each of radius r are placed so that each touches the other two and K . express R in terms of r. in the space between K, A and B , another circular disc D is placed which just touches K, A and B. if the radius is s, show that (6+root3)s=(2+root3)r Answered by Penny Nom. 





The perimeter of a rectangle 
20120919 

From aretha: calculate the perimeter of a rectangle with the long side 462ft x 9inches and the short side 50% less. Answered by Penny Nom. 





The dimensions of a rectangle 
20120912 

From Becky: A rectangle has an area of 48 square inches and perimeter of 32 inches. Find the dimensions of the rectangle. Answered by Penny Nom. 





The volume of fluid in a tank 
20120906 

From Dave: I have vertical round flat bottom tanks of various dimensions. It is easy to find total volume but I would like to know how to figure out the coversion factor to go from how many centimeters of liquid is in the tank to the number of total cubic meters of volume. So if my float gauge on the tank says there is 50 cm of fluid in the tank, how many cubic meter of total volume is there? Answered by Harley Weston. 





A tangent to f(x) = 1/x 
20120904 

From Steven: Consider the graph of the function f(x) = 1/x in the first quadrant, and a line tangent to f at a point P where x = k. Find the slop of the line tangent to f at x = k in terms of k and write an equation for the tangent line l in terms of k. Answered by Penny Nom. 





The area of a rectangle 
20120831 

From mario: The area of a triangle when on side is x and the other is x+6 Answered by Harley Weston. 





Problem solving 
20120815 

From Sugavanas: If length of a rectangle exceeds its width by 5 m. if the width is increased by 1m and the length is decreased by 2 m, the area of the new rectangle is4 sq m less than the area of the original rectangle. Find the dimensions of the original rectangle. Answered by Penny Nom. 





A plane travelling with the wind and against the wind 
20120803 

From Gwen: The time of a plane trip of 450 miles, with the wind is 3/5 the time of the return trip against the wind. If the plane travels 120 mph in still air, what is the wind speed? Answered by Penny Nom. 





The area of a rectangle 
20120724 

From michael: the dimension of the rectangle are (x+5) and (x3) find its area Answered by Penny Nom. 





A cubical tank 
20120707 

From jake: a storage tank is in the form of a cube. when it is full of water,the volume of water is 15.625 m cube. if the present depth of water is 1.3m, find the volume of water already used from tank Answered by Penny Nom. 





A cyclist a jogger and a fly 
20120604 

From Emd: A cyclist & a jogger are 20 miles apart.
Cyclist goes 20 mph & jogger 7mph towards each other.
A fly starts on nose of cyclist & flies at 20 mph from cyclist to jogger &
back & forth until they meet.
How far has the fly travelled? Answered by Penny Nom. 





Romeo and Juliet live 40 miles apart 
20120518 

From Abigaíl: Romeo and Juliet live 40 miles apart. Romeo jogs 8mph, while Juliet “fast walks” at 4mph. They leave their houses at the same time and journey toward each other.
a) How many hours after they start will they meet?
b) Approximately how many miles from Romeo’s house is their meeting point? Answered by Penny Nom. 





Math, time and rate 
20120518 

From Abigaíl: Romeo and Juliet live 40 miles apart. Romeo jogs 8mph, while Juliet “fast walks” at 4mph. They leave their houses at the same time and journey toward each other.
a) How many hours after they start will they meet?
b) Approximately how many miles from Romeo’s house is their meeting point? Answered by Penny Nom. 





Cycling and running 
20120507 

From liz: a biathlete travels 20 miles in 2.25 hours. She cycles part of the way at 12 mph and runs the rest at 5 mph. How far did she run? Answered by Penny Nom. 





The maximum distance from the vertex of a triangle 
20120502 

From David: There are three towns A,B,and C, equidistant apart.
A car is 3 miles from town A, and 4 miles from town B.
(ie, somehwere outside of the triangle which the three towns form)
What is the maximum distance that the car can be from town A?
This was asked as quiz question in my local pub last Sunday.
The answer is 7. How do I prove it?
Best regards. David in Denton. Answered by Robert Dawson and Chris Fisher. 





The dimensions of a rectangle 
20120430 

From Nikki: Name the dimensions of a rectangle that has the same area as this triangle?
I found the area of the triangle, which is 30. What do I have to do in order to complete this math problem? Answered by Penny Nom. 





A tangent line to a circle 
20120414 

From Novelyn: find an equation of the line tangent to a circle with equation x^2+y^2+6x8y27=0 at the point P(1,2) Answered by Penny Nom. 





Two cars approach a rightangled intersection 
20120410 

From Michael: Two cars approach a rightangled intersection, one traveling south a 40km/h and the other west at 70km/h.
When the faster car is 4km from the intersection and the other case if 3km from the intersection,
how fast is the distance between the car cars changing? Answered by Penny Nom. 





A rectangular prism 
20120405 

From Tori: How do you find the base height if the base width is 10ft. The height is 7ft. And the volume is105ft. Answered by Penny Nom. 





How long will it take lee to catch up with jodie? 
20120321 

From kirsten: for example, if jodie is on the bus travelling at 10 m.p.h and lee is walking at 4 m.p.h how long will it take lee to catch up with jodie?? what is this mathematical name for this Answered by Harley Weston. 





The dimensions of a rectangle 
20120313 

From irvyn: if you are only given the area and the perimeter how do you find the dimension? Answered by Penny Nom. 





A water tank is in the shape of a truncated cone 
20120308 

From Victoria: Suppose you have a water tank in the shape of a truncated cone. The larger diameter is K, the smaller diameter is K/2, and the height is also K (all measured in meters). The force of gravity on an object of mass, m, is F=9.8m (measured in Newtons). The density of the water is 1000 kilograms per cubic meter. What is the volume of the tank and how much mass will the tank have when it is full? Answered by Penny Nom. 





The area and perimeter of a rectangle 
20120301 

From RAJIB: PEREMETER OF A RECTANGLE IS 24. FIND THE AREA ? Answered by Penny Nom. 





Measuring the liquid in a horizontal tank 
20120228 

From Philip: I have a steel gas tank that is 3' dia X 5' length. The total volume is 1000 litres.
But how much is left when I use a stick and measure 6" from the bottom or 12" or 24" ??
Is there a formula to use for this task?
Thanks. Answered by Harley Weston. 





Margie threw a ball 
20120216 

From mary: at 9:45 Margie threw a ball upwards while standing on a platform 35ft above the ground. The height after t seconds follows the equation:
h(t)= 0.6t^2 +72t+35
a) what will be the maximum height of the ball?
b)how long will it take the ball reach its maximum height?? Answered by Harley Weston. 





Jack and Kate set off in their cars ... 
20120213 

From akiri: Jack and Kate set off in their cars from the same point to travel the same journey. Jack has a start of eight minutes before Katie sets off. If Jack travels at 50mph and Katie travels at 75mph, how many miles will be travelled when the two cars are level? Answered by Penny Nom. 





A road around a garden 
20120207 

From Manu: Inside a square garden of side 158m, a road 4m wide is built all around. What is the area of the remaining part of the garden? Answered by Penny Nom. 





There is a police officer in pursuit of suspect 
20120201 

From Jay: There is a police officer in pursuit of suspect. They suspect is driving on a straight road traveling at 79 mph, the officer is 233 yds away, traveling at 92 mph, the suspects car 5 ft long and the officers car is 5.3 ft long, how long will it take to have the front of the officers car, equal to the front of the suspects car down to the tenth of a second. Answered by Harley Weston. 





The dimensions of a rectangle 
20120131 

From Dazz: Hi I was wondering how to find the length of a rectangle if you know the area is 484 square inches And the length is 10 square inches or 22 square inches?
Thanks~Dazz Answered by Penny Nom. 





Two cars in a race 
20120130 

From Christine: In a car race, the speed of one car is 120kph and the other car is 105 kph. If the faster car finished the race 20 mins before the slower one, what was the distance of the race? Thanks for the answer and the previous answer to my question. Answered by Penny Nom. 





Tangent of theta 
20120117 

From stahl: explain what the 'tangent of theta' means. Draw and label a diagram to help with your explanation. Answered by Harley Weston. 





Brian on his bike 
20120116 

From tiffany: Brian rides his bike 0.29 miles per minute. If it takes him 22 minutes to ride his bike to his friend's house, how far away does his friend live? Answered by Penny Nom. 





Running 5 km 
20120112 

From Fayeann: What amount of time will it take a person running 7 m/s to travel a distance of 5 km? Answered by Penny Nom. 





An equilateral triangle and some circles 
20120110 

From tushar: draw an equilateral triangle with side 6cm.draw 3circles with radii 3cm on each angular point of triangle.draw common tangent on each of two circles Answered by Penny Nom. 





The dimensions of a rectangle 
20120106 

From joseph: The perimeter of a rectangle is 72 inches. The length of the rectangle
is three more than 2 times the width of the rectangle. What is the
length of the rectangle? Write and solve an equation to determine the
dimension of the rectangle. Answered by Penny Nom. 





A straight line distance 
20120106 

From Margaret: If you traveled 300 miles east and 275 miles north, how many miles would you save by going in a straight line? Answered by Penny Nom. 





Jennifer wants to fence in her backyard 
20111209 

From Val: Jennifer wants to fence in her backyard. A yard is rectangular and is 15 feet by 12 feet. One 12foot side is against the house so it does not need fencing. How many feet of fencing does Jennifer need? Answered by Penny Nom. 





A 3000 gallon tank 
20111208 

From Delores: I need to know what size to build a tank to hold 3000 gallons of water
one side needs to be 8 ft width X 6 ft height how long does it need to
be? Answered by Penny Nom. 





Two trains passing each other 
20111207 

From Tamkeen: two trains 245m and 315m long are travelling toward each other at 90km/h and 54km/h respectively on parallel lines . how long do the train take to pass one another train the time they meet each other? 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. 





Two boats 
20111130 

From Shayan: A boat is traveling 20 miles per hour when it passes a lighthouse.
another boat is traveling at 15 miles per hour when it passes a point.
the lighthouse and the point are 175 miles apart.
when will the boats pass each other? Answered by Penny Nom. 





Water pouring into a conical tank 
20111121 

From Patience: Hi my name is patience and I'm having a problem with this question.
Water pours into a conical tank of semi vertical angle 30 degrees at the rate of 4 cm^3/s, where h is the depth of the water at time t. At what rate is the water rising in the tank when h = 10 cm?
Thank you Answered by Penny Nom. 





Lines tangent to y^2=4x 
20111111 

From Reuchen: Find equations of the lines tangent to y^2=4x and containing (2,1). Answered by Penny Nom. 





The average speed for the whole journey 
20111030 

From Shahzad: a train travels 68 Km at an average speed of 51Km/h. It then travels another 20Km at an average speed of 40Km/h before reaching its destination. Calculate the average speed for the whole journey? Answered by Penny Nom. 





One central circle and three tangent circles 
20111016 

From Margaret: You have one central circle and three or more circles tangent to the outside of the circle of varying radii. You know the x,y coordinates of the centers of the other circles. If you now remove that central circle (and pretend you never knew where it was), can you calculate its center in x,y coordinates? Answered by Chris Fisher. 





What is the speed of the boat in still water? 
20111007 

From Hannah: The speed of a stream is 3 mph. A boat travels 10 miles upstream in the same time it takes to travel 16 miles downstream. What is the speed of the boat in still water Answered by Penny Nom. 





Chuong and Hassan drive to work 
20111004 

From Dilshad: Chuong and Hassan both drive 40 km from home to work each day. One day Chuong said to Hasssan, "If you drive home at your usual speed, I will average 40 kmph faster than you and arrive home in 20 minutes less time." Find Hassan's speed. Answered by Penny Nom. 





A rectangle of largest possible area 
20110916 

From mary: Steven has 100 feet of fencing and wants to build a fence in a shape of a rectangle to enclose the largest possible area what should be the dimensions of the rectangle Answered by Penny Nom. 





A tangent to the earth 
20110903 

From Vickram: I have a math problem regarding tangent and circle. My example is as
follows: if a long flat ruler measuring 1500 miles is placed on top of earth
which has a radius of 3960 miles what part (length) of the tangential ruler
will actually be touching the earth and what two parts will not? Answered by Chris Fisher. 





Driving to meet Mary 
20110824 

From Denise: mary leaves St Paul traveling 2000 miles @ 55 MPH; John leaves LA traveling 2000 miles @ 45 MPH how many miles will John had traveled to meet mary? Answered by Penny Nom. 





Three tangent circles 
20110821 

From maribie: three discs are tangent externally distances between their centers are 23cm, 15cm, and 20cm. find their radii.t Answered by Penny Nom. 





Three tangent circles 
20110819 

From hanniel: two coin are tangent to a third coin internally and are tangent to each other
externally. The distance between their centers are 14 mm, 17mm, and 5mm.
find their radii Answered by Penny Nom. 





The height of a fluid in a horizontal tank 
20110724 

From jason: Same set up as many others, cylindrical tank on its side, but I am interested in defining the change in volume and/or fluid level as a function of time at a constant volumetric outflow. I plan on hooking a pump to the tank so "gpms' will be constant. I have a couple different sized tanks and pumps so I want a general equation. Thanks for your help. Answered by Harley Weston. 





A rectangle is inscribed in a circle 
20110717 

From Alexea: A rectangle is inscribed in a circle of diameter 15in. Express the perimeter as a function of the width x. Answered by Penny Nom. 





Achilles and a turtle 
20110701 

From Jean: Achilles and a turtle are having a race. The turtle starts 45m ahead of Achilles and Achilles is twice as fast as the turtle. If turtle runs at 1m/s,how far would the turtle have run before he is outrun by Achilles? Answered by Penny Nom. 





Two trains 
20110607 

From Lynn: If the 1st train goes 60 mph and the 2nd train leaves 10 minutes later =
at a speed of 70 mph, how long does it take to catch up with the 1st =
train. Answered by Penny Nom. 





A line tangent to f(x)=1/x 
20110605 

From Michael: A line tangent to f(x)=1/x in the first quadrant creates a right triangle
with legs the xaxis and the yaxis. Prove that this triangle is always
2 square units regardless of where the point of tangency is. Answered by Penny Nom. 





How many meters long should the race be? 
20110526 

From Lee: Nathan can walk at a rate of two meters per second while David can
easily go threeandahalf meters per second. David offers Nathan
a 45 meter head start. How many meters long should the race be in
order for Nathan to win by a nose Answered by Penny Nom. 





The dimensions of a rectangle 
20110508 

From yolanda: If the length of a rectangle is 3ft less than twice its width and the area of the rectangle is 54ft^2,what are the dimensions of the rectangle? Answered by Penny Nom. 





Three tangent circles 
20110501 

From mark: Three circles of radii 24 cm, 32 cm, and 42 cm are externally tangent to each
other (each is tangent to the other two). Draw a diagram and using the Law of
Cosines find the largest angle of the triangle formed by joining their centres. Answered by Penny Nom. 





The area of a rectangle 
20110430 

From Hayley: A rectangles width is exactly twice its length. The area of the rectangle is 450 square feet. What are the length
and width of the rectangle? Answered by Penny Nom. 





The quadratic with two given roots and a constant term 
20110419 

From Lindah: how do I food quadratic with two given roots and a constant term? Answered by Penny Nom. 





A concrete walk around a pool 
20110415 

From Skipper: I want to know the answer if you were to want a pool to be 20 ft by 30 ft and wanted a 5 ft border around it what would be the dimension of the whole area plus concrete walk Answered by Penny Nom. 





How far is it from the control tower? 
20110411 

From Varun: An aircraft is vertically above a point which is 10 kms west and 5 kms north of a control tower. if the aircraft is 4000 mts above the ground,how far is it from the control tower? Answered by Penny Nom. 





Eliminate y 
20110407 

From Lynn: 2x + y = 8
y + 3z =5
z + 2w =1
5w + 3x = 9
Form three equations with y eliminated Answered by Penny Nom. 





Two ships 
20110405 

From Gevork: Ship A is sailing due south at 16 mph. At the same time, a second ship B, 32 miles south of A, is sailing due east at 12 mph.
(a) at what rate are they approaching or separating at the end of one hour?
(b) At what rate are they approaching or separating at the end of two hours?
(c) When do they cease to approach each other and how far apart are they at that instant. Answered by Penny Nom. 





The perimeter of a rectangle 
20110404 

From aspen: the perimeter of a rectangle is twice the sum of its length and its width. the perimeter is 40 meters and its length is 2 meters more then twice its width. what is the length? Answered by Penny Nom. 





The rectangle is reduced to 90% of its original size 
20110331 

From stephon: A rectangle has a length of 4cm and a width of 8cm.
If this rectangle is reduced to 90% of its original size what will be the new length Answered by Penny Nom. 





Two boats 
20110329 

From Mamie: Two speed boats leave the port of San Francisco traveling in opposite directions
at the same time.One boat travels 8 knots per hour faster than the other.After
one day's travel they are 1,920 nautical miles apart.What are the speeds of the
two boats. Answered by Penny Nom. 





Sample Standard deviation 
20110316 

From Iris: Help please: me on this type of math problem I can get through step one after that I get lost. Maybe you can explain it to me in a easier way to get the correct results. I have read the examples, but I am still lost cannot move on until the next practice until I get this one
Sample standard deviation
The following are distances (in miles) traveled to the workplace by employees of a certain computer company.
15,29,32 28 18 28
Find the standard deviation of this sample of distances. Round your answer to at least two decimal places. Answered by Penny Nom. 





A family of circles 
20110301 

From steffi: Find the equation of the family of the circle passing through the the point of intersection of x^2+ y^2 4x28=0 and x^2 +y^2 4x20+52=0; the member tangent to x=7. Answered by Penny Nom. 





Find the dimension of the original rectangle 
20110228 

From sandra: the perimeter of a rectangle is 40 cm. if the length were doubled and the width halved, the perimeter would be increased by 16cm. Find the dimension of the original rectangle Answered by Robert Dawson. 





Slicing a rectangular parallelepiped 
20110223 

From tom: a) Pass a plane containing a vertex of a rectangular parallelepiped and a
diagonal of a face not containing that vertex to cut a pyramid from the
parallelepiped. What fraction of the volume of the parallelepiped is the
volume of the pyramid thus cut off?
b)Pass a plane through a cube of edge 8 in so that the section formed
will be a regular hexagon. Through each side of the hexagon pass two
planes, one plane containing one of the two vertices of the cube
which are farthest away from the plane of the hexagon, the other
plane containing the diagonally opposite vertex of the cube. Find the
volume of the solid bounded by these planes.
c)three of the edges of a rectangular parallelepiped that meet in a point
are also the lateral edges of a pyramid. What fraction of the parallelepiped
is this pyramid...?
you know the my only problem is how to illustrate this one...if only i
could ...can you help me....all I need is the drawing and I can do the rest
..it's fine if you'll only answer any of these but I'll be thankful if you
will do the three :).... Answered by Penny Nom. 





Two conical tanks 
20110217 

From rustom: Two vertical conical tanks (both inverted) have their vertices connected by a short horizontal pipe.
One tank, initially full of water, has an altitude of 6 ft. and a diameter of base 7 ft.
The other tank, initially empty, has an altitude of 9 ft., and a diameter of base 8 ft.
If the water is allowed to flow through the connecting pipe, find the level to which
the water will ultimately rise in the empty tank (Neglect the water in the pipe.) Answered by Penny Nom. 





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. 





Two tangent circles 
20110209 

From xhesika(jessica): Two circles of radius 10 are tangent to each other.A tangent is drawn
from the centre of one of the circles to the second circle.To the nearest
integer find the area of the shaded region. Answered by Penny Nom. 





A tangent to a circle 
20110206 

From debz: what is the formulae of the tangent to a circle.... our teacher gave us a lot of homework.. and she ask us to find the formulae by ourselves.. Answered by Penny Nom. 





Calibrating a conical tank 
20110205 

From Bill: Hi, I have a round tank with tapered sides where I know the diameter at the top and bottom. Is there a formula I can use to calculate the volume by measuring from the bottom up the side (at the angle of the side) to any given point? Thanks, Bill Answered by Stephen La Rocque and Penny Nom. 





A fence around a water tank 
20110201 

From Heath: I am building a fence around a water tank. the fence is to be in the shape of a normal octagon. The tank has a circumference of 57 ' 6''. I would like the fence to be 3 ft from the tank at the skinny point . How would I calculate(for the simple guy) where to set each of my 4x4 posts at the 8 corners. Any help would be greatly appreciated. Answered by Harley Weston. 





The area of a rectangle 
20110131 

From T.S.: for which value of w does the rectangle below have an area of 864 square units if sides are width=w+15 and length=w15 Answered by Penny Nom. 





Points with distance 5 from the point (2, 1) 
20110119 

From Alexa: Find all points having a xcoordinate of 2 whose distance from the point (2, 1) is 5. Answered by Penny Nom. 





A rectangle 
20110116 

From meg: if a rectangle has a length that is 3cm less than 4 times its width and its perimeter is 19cm, what are the dimension? Answered by Penny Nom. 





A cylindrical tank 
20110116 

From tom: A cylindrical tank, 1 ft in diameter, length 6 ft , is placed so that its axis
is horizontal. How many pounds of water will be used in filling it to a depth
of 9in. , if water weighs 62.4 lbs. per cu. ft.? Answered by Penny Nom. 





Tan(x+pi)tan(pix)=2tan(x). 
20110109 

From Steven: Verify the identity:
Tan(x+pi)tan(pix)=2tan(x) Answered by Penny Nom. 





A 400 gallon oil tank 
20110108 

From theresa: we have a oil tank that holds 400 gallons of oil currently there is 11/16 volume in the tank how many gallons are there? Answered by Harley Weston. 





What is its speed in miles per hour? 
20110106 

From Miriam: An airliner travels 125miles in 15minutes. What is its speed in miles per hour? Answered by Penny Nom. 





A tangent line 
20110103 

From Amanda:
Question from Amanda, a student:
an equation of the line tangent to y=x^3+3x^2+2 at its point of inflection is
(A) y=6x6
(B) y= 3x+1
(C) y= 2x+10
(D) y=3x1
(E) y=4x+1 Answered by Penny Nom. 





The length is twice its breadth 
20101209 

From jenu: The length of the rectangular field is twice its breadth. A man jogged around it 5 times and covered a distance of 3 km. what is the length of the field? Answered by Penny Nom. 





80 miles in 40 minutes 
20101208 

From james: i travel 8o miles in 40 minutes. how fast am i going in mph Answered by Penny Nom. 





A rectangular solid 
20101208 

From ryan: Good day!
Have a question on rectangular solids. We were asked to find the dimensions of a rectangular solid, we were only given the volume of the rectangular solid, the total area, and the altitude. I tried using the volume of the rectangular solid and was able to get the area of the base, but I don't know how to get its length and its width. Hope you could help me again. Thanks! Answered by Penny Nom. 





Simultaneous equations 
20101205 

From ryan:
Question from ryan, a student:
3 4
   = 1 (1)
x y
7 2 11
   =  (2)
x y 12 Answered by Chris Fisher and Stephen La Rocque. 





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. 





A rectangular piece of plywood 
20101130 

From Austin: A rectangular piece of plywood is trimmed to make it square by cutting a 4cm strip off the top and a 2cm strip off one side. If the area of the original piece is 74cm2 greater than the area of the square, find the dimensions of the rectangle. Answered by Penny Nom. 





What is its speed in still air? 
20101128 

From Shelby: An Airplane flies a certain distance in 3 hours going WITH a 40km/hr wind. It travels the same distance in 5 hours when going against the wind. What is it's speed and how long would it take to travel the same distance in still air? Distance = speed x time Answered by Penny Nom. 





The perimeter of a rectangle 
20101124 

From shericka: a rectangle has a perimeter of 60cm. its length is 5 times greater than its width. what is its length? Answered by Penny Nom. 





How long will you and your friend be able to talk? 
20101123 

From beket: you and your friend leave your home town at the same time your friend travels by train 45 mph directly east while you travel by train 50 mph going directly south you are talking on cell phone but you plan charges extra if the phones are 100 miles apart. How long will you and your friend be able to talk before the charges increase? Answered by Penny Nom. 





A 400 gallon drum 
20101104 

From Jerry: Question from Jerry:
I want to build A tank. able to hold 400 gallons of asphalt sealer it will be round . basically like A old fuel oil drum but made with heavy material . math ? was I want tank to hold 400 gallons I think the length of 60" would be perfect. I don't know what diameter or radius of tank needs to be . to make it A 400 Gallon tank Answered by Harley Weston. 





A train passes a car 
20101024 

From Mary: A train, whose speed is 75 mph, takes 3 minutes to pass a car that is going 60 mph in the same direction. How long is the train? Answered by Stephen La Rocque. 





A rectangle with rounded corners 
20101021 

From Connie: How do you find surface area if the rectangle is 100ft. by 200ft. with quarter circles in the corners with a radius of 20ft. ? Answered by Penny Nom. 





What are the speeds of the boats? 
20101021 

From Adori: Two boats leave the port of San Francisco traveling in opposite directions at the same time. One boat travels 8 knots per hour faster than
the other. After one day's travel they are 1920 nautical miles apart. What are the speeds of the boats? Answered by Penny Nom. 





John and Mary are 200 miles apart 
20101020 

From Sarah: two people, john and mary, are 200 miles apart and leave at the same time to meet.
They are driving toward each other at constant rate on the same straight road.
John is traveling at 45 mph and Mary is traveling at 35 mph.
When they meet, how many miles will they be from john's house? Answered by Penny Nom. 





A commuter airline between two cities 
20101019 

From Adori: An airline runs a commuter between two cities that are 720 miles apart. If the average speed of the planes is increased by 40 miles per hour, the travel time is decreased An airline runs a commuter between two cities that are 720 miles apart. If the average speed of the planes is increased by 40 miles per hour, the travel time is decreased by 12 minutes. What airspeed is required to obtain this decrease in travel time? Answered by Penny Nom. 





Two jets leave denver at 9 am. 
20101015 

From Carl: two jets leave denver at 9 am. One flying east at a speed of 50 km per hour greater than the other which is traveling west. At 11 am the planes are 2500 km apart. Find their speeds. Answered by Stephen La Rocque. 





Electronic cars around a circular track 
20101011 

From Taylor: Cory and Melissa are racing electronic cars around a circular track. They begin at the same time going in the same direction. Cory's car completes a revolution in 35 secs, while Melissa's car completes a revolution in 30 secs. How long will it take them before both cars reach the starting point again simultaneously? Answered by Stephen La Rocque and Penny Nom. 





Two cars 
20100930 

From Amanda: Two cars, 142 miles apart, start moving towards each other at the same
time. One is moving 3 times as fast as the other. If they meet 1.7 hrs
later, find the average speed of the slower car in miles per hour? Answered by Penny Nom. 





Rectangular arrays 
20100929 

From Kim: My 4th grader has started working on rectangular array that shows 2 factors of a number.
The problem reads on centimeter grid paper draw as many arrays as you can for each of the #'s 2,3,4, 5,6,7,,11,12,15 and 16. That would be great except I have no idea what they are talking about and I cannot offer any help to my daughter. Answered by Penny Nom. 





The distance between the origin and a moving point 
20100924 

From Norma: I am having problems with this question
find the rate of change of the distance between the origin and a moving point on the graph of the function below if dx/dt=5 cm/sec
y=x^2+2 Answered by Penny Nom. 





Limiting Cases in Geometry 
20100922 

From Niki: Consider a rectangle inscribed in a circle with a radius or R. What are the possible perimeters for the rectangle? Answered by Stephen La Rocque. 





What is the average speed? 
20100921 

From Cindy: A boat travels downstream m nautical miles at d knots. It travels upstream m nautical miles at u knots. What is the average speed for the entire trip? Answered by Penny Nom. 





40 mph for 6 minutes 
20100920 

From Andy: If i was traveling at 40 mph for 6 minutes, what is my distance in miles? Answered by Penny Nom. 





How many cubic metres of water can safely be stored in the tank? 
20100910 

From susanna: This water tank is a perfect sphere with an inner radius of 12 metres. However, they used inferior materials to build the water tank, and the tank can only withstand a water pressure of 185 kiloPascals. Assume the density of water is exactly 1000 kg/m3, gravity is 9.8 metres/s2, and disregard atmospheric pressure.
How many cubic metres of water can safely be stored in the tank? Round DOWN to the nearest whole number (since rounding up could be catastrophic in this instance!), and please submit only a number with no other information. Answered by Robert Dawson. 





Driving north, east and west 
20100902 

From dane: suppose that you drive 27 miles north, 31 miles east, 45 miles west, and 14 miles east. how far are you from your starting point? Answered by Penny Nom. 





Three cars 
20100830 

From Anil: 3 cars are moving at speed of 4 kmph,5.5 kmph and 8 kmph in a circular track.The circular track has
a distance of 11 km. What is the time taken for all the 3 cars to meet at the starting point ? Answered by Stephen La Rocque. 





Running 100 km 
20100812 

From thomas: Another athlete runs 8 laps every day on the same 400m running track. How many days will it take him to run a total of 100 km? Answered by Robert Dawson. 





Two cars on a circular track 
20100812 

From david: If two cars starts to drive at point 1 and go in a circle when will they meet?
(one cars speed is faster the other ) all I need is a formula Answered by Tyler Wood. 





How fast is the second car taveling? 
20100726 

From Jeff: A car is traveling 75 mph. It takes 12 miles to overtake a second car that was .5 mile ahead. How fast is the second car taveling? Answered by Stephen La Rocque. 





How much longer will it take to reach Toronto 
20100722 

From Rachelle: We are taking a trip from Ottawa, ON to Toronto, ON. The total trip is 150 kms and will take us 4.5 hours. We have already driven 108 kms and there is still 42 kms left to go. If we are travelling 110 kms/hr, how much longer will it take to reach Toronto? Answered by Penny Nom. 





An 18ft round pool 
20100719 

From christine: will an 18ft round pool fit on a 12x16 ft rectangular cement slab? Answered by Tyler Wood. 





Pursuing Car 1 
20100713 

From Mark: Car 1 is traveling down the road at 50mph 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? Answered by Robert Dawson. 





Half a mile at 50 mph 
20100713 

From Mark: How long will it take a car to travel 1/2 mile at 50 mph? Answered by Robert Dawson. 





3 equidistant points on a circle 
20100621 

From Brian: We have to line up 3 pins on a lifting bridle to be 120 degrees apart from each other to connect into a lifting assembly.
I know pi*d. I know straight lines connecting these points to each other will result in an equilateral triangle.
How does one find these points without using a protractor? There must be a formula (formulae) to work this out mathematically.
r = 10.5 inches
pi*d = 65.9736
3 segments( arcs) = 21.9912 which is the distance along the circumference that the points are from each other. Answered by Penny Nom. 





How many gallons do I need to finish filling the tank? 
20100614 

From Bruce: I have a tank on it's side. 44" dia. by 72" long, I'm 6" from having tank full. How many gallons do I need to finish filling tank? Answered by Harley Weston. 





Standard Deviation from a Proportion 
20100608 

From silvestre: A large company finds that approximately 17% of all purchases are returned for credit. If the company sells 100,000 different items this year, about how many items will be returned. Find the Standard Deviation. Answered by Janice Cotcher. 





Going to the bike shop 
20100607 

From Omi: Marie rode her bicycle from her home to the bicycle shop in town and then walked back home. If she averaged 6 miles per hour riding and 3 miles per hour walking, how far is it from her home to the bicycle shop if her total travel time was 1 hour? Answered by Penny Nom. 





A fuel tank with a broken gage 
20100528 

From Kinsley: Hello, I have a fuel tank with a broken gage. It is a 2000 gallon tank. The dimensions are 64" dia. x 146" long. The fuel gage doesn't work, so the only measurement I can do is put a stick in it to see what is left. Currently it is at 19". PLEASE NOTE: the tank is laying on its side, meaning the long side is on the ground. So, how do I determine how much fuel is in the tank by the inches remaining? Thank you very much. Answered by Tyler Wood. 





Liquid in a horizontal tank 
20100526 

From Brian: I have a 50' long tank by 12' diameter it is lying down on it side with 12" of Liquid in the bottom i need to know how many gallons of fluid this is? Please Help, I was able to calculate out the Triangle but not the Sector! Answered by Harley Weston. 





How wide a strip has he cut when the lawn is half mowed? 
20100524 

From Arib: rectangular lawn has length 40 m and width 30 m. David starts cutting from the outside in. How wide a strip has he cut when the lawn is half mowed? Answered by Penny Nom. 





What is the distance from A to C via B? 
20100524 

From vivianne: The distance from A to B is d km and that from B to C is x km. if a bus maintains an average speed of 50km/hr between A and B and 60km/hr between B and C, it takes 3 hours to travel from A to C. If it maintains 60km/hr between A and B and 50km/hr between B and C, the journey takes 8 minutes less. What is the distance from A to C via B? Answered by Penny Nom. 





When will the second truck catch up to the first? 
20100522 

From Josie: At 9:00 a.m. a truck leaves the truck yard and travels west at a rate of 45 mi/hr. At 11:00 a.m., a second truck leaves along the same route, travelling at 60 mi/hr. When will the second truck catch up to the first? Answered by Tyler Wood. 





How far am I from the starting point? 
20100518 

From jilayna: if i walk 5 miles north, 7 miles east, and 3 miles north again.to the nearest tenth of a mile ,how far,in a straight line, am i from my starting point Answered by Penny Nom. 





Sammy and his motorboat 
20100511 

From Jordan: Sammy owns a motorboat that travels 4 miles/hour in still water. It goes 12 miles upstream and 12 miles back again (downstream) in a total of 8 hours. Find the speed of the current of the river. Answered by Penny Nom. 





Line of sight 
20100506 

From David: I live in St. Joseph, Michigan and there is an ongoing argument regarding lineofsight over the horizon.
Standing on a 200 foot high bluff here, people swear they can see the top of the Willis (nee Sears) Tower in Chicago, which is about 1653 feet high.
It is my contention that this is actually a "refracted reflection" and not directlineofsight.
So, to settle the argument, I'd sure like some simple explanation for this, even ifand I hope notI am incorrect.
David Answered by Harley Weston. 





The equation of a circle 
20100504 

From crystal: find the standard form of the circle with center (2,3) and tangent to the line y=1 Answered by Penny Nom. 





40 miles at 50mph 
20100502 

From gill: if a car travelled 40miles at 50mph, how long would it take? Answered by Penny Nom. 





When are the cars exactly 40 miles apart? 
20100501 

From Maryanne: A car traveling east at 45 mph passes a certain intersection at 3pm. Another car traveling north at 60mph passes the same intersection 25 minutes later. To the nearest minute, figure out when the cars are exactly 40 miles apart. Answered by Penny Nom. 





A rectangular prism 
20100427 

From Savannah: A rectangular prism is made of exactly 8 cubes. Find
the length, width, and height. 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 tangent line to a circle 
20100415 

From Rhonda: The Greek method for finding the equation of the tangent line to a circle used the fact that at any point on a circle the line containing the reauis and the tangent line are perpendicular. Use this method to find an equation of the tangent line to the circle x^2+y^2=9 at the point (1,2 square root of 2). Answered by Penny Nom. 





What are the dimensions of the box? 
20100413 

From Steven: The longest rod that will just fit inside a rectangular box,
if placed diagonally top to bottom, is 17 inches.
The box is 1 inch shorter and 3 inches longer than it is wide.
How much must you cut off the rod so that it will lie flat in the
bottom of the container? What are the dimensions of the box? Answered by Robert Dawson. 





A rectangle problem 
20100412 

From Charlene: The ratio of the width to the length of a certain rectangle is equal to the ratio of its length to the difference between its length and twice its width. If the area of the rectangle is 25cm^2, then what are its dimensions? Present a non algebraic solution? Answered by Tyler Wood. 





The perimeter of a rectangle 
20100412 

From Charlene: The area of a rectangle is 390m^2. If its length is increased by 10m and its width is decreased by 6m, then its area does not change. Find the perimeter of the original rectangle. Answered by Tyler Wood. 





The diagonals of a rectangle 
20100330 

From Tabatha: The diagonals of a rectangle are 8 units long and intersect at a 60 degree angle. Find the dimensions of the rectangle. Answered by Penny Nom. 





A rectangle inscribed in a circle 
20100324 

From sadiq: here is the question,
in my mathematics book there is equation of the area of the rectangle
inscribed in a circle having equation x^2+y^2=a^2
and the area of rectangle is 4xy=4x(a^2b^2)^1/2
i don't know what is b but a is surely the radius
(i want the derivation for the area of rectangle). Answered by Harley Weston. 





What is the speed of the current? 
20100317 

From Carl: If you can row 3 mph in still water and paddle 3 miles upstream and return in 3.6 hours then what is the speed of the current? Answered by Penny Nom. 





Constants and coefficients 
20100312 

From lourdes: identify the coefficients, constant term(s), and like terms of the expression.
8x + 9  3x
17  2a + 5a  1
7m  7 + 6m  6
10 15r 22r + 8 Answered by Penny Nom. 





The perimeter of a rectangle 
20100312 

From makiah: A rectangle has a perimeter of 12 meters.If each side is a whole number of meters,
what are the possible dimensions for the length and width? Answered by Penny Nom. 





The distance travelled by a minute hand 
20100306 

From Patric: How much distance will the minutes hand of length 14mm of a clock
cover in moving from 5 to 10? 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. 





The base area of rectangular prism 
20100305 

From Desiree: How do you find the base area of rectangular prism that has 4 cm by 4cm by 6cm ? Answered by Penny Nom. 





At what time would Joan catch Jo? 
20100304 

From Rusty: If Jo left his house at 6:30am traveling at 5mph and Joan left the same house 7:00am traveling at 8mph, at what time would Joan catch Jo? Answered by Penny Nom. 





The dimensions of a rectangle 
20100303 

From Kirsten: A rectangle is twice as long as it is wide. Its area is 128 square meters. What are the dimensions of the rectangle? Answered by Tyler Wood. 





The vertices of an equilateral triangle 
20100219 

From Emma: If two of the vertices of an equilateral triangle are (2,1) and (6,5), what
are the two possible coordinates of the third side of the triangle? Answer
in radical form. Answered by Tyler Wood. 





The equation of a circle 
20100218 

From AHMED: find the equation to the circle with centre at the point (1,1) and touching the straight line 5x+12y=7. Answered by Penny Nom. 





The center of a rectangular room 
20100216 

From Diana: Consider a rectangular room, 15 feet wide, 30 feet long and 12 feet high. What is the exact distance from any of the 8 corners of the room and its geometric center? Can you write a generic formula for such a distance? And if we keep the same proportions on all dimensions, can you write an expression for the same distance as a function of the floor perimeter? Answered by Penny Nom. 





The distance from a chord to an arc 
20100211 

From matt: hello, I have to layout a radius without being able to pull from the center my radius is 3819.53 feet and i have a chord length of 275.59 feet if i broke that up into 25.05 feet sections how would i calculate the lengths from my chord to that radius? Answered by Robert Dawson. 





Fencing a garden 
20100204 

From kris: How many meters of fencing do i need to enclose a garden if the yard is 26 meters long and half as wide? Answered by Penny Nom. 





A decrease in travel time 
20100130 

From Mike: if a 100 mile trip averages 50 miles per hour, how much distance does one need to travel at 90 miles per hour to decrease travel time by 10% Answered by Stephen La Rocque. 





The perimeter of a rectangle 
20100127 

From debbie: how many dimensions are there to get a perimeter of 400 feet for a rectangle? Answered by Penny Nom. 





A tunnel from Toronto to Montreal 
20100125 

From Dave: I want to make a tunnel from Toronto to Montreal (for example)
Something like this
http://mathcentral.uregina.ca/QQ/database/QQ.09.09/h/grant1.html

My coordinates are 45.442455,73.861340 (Montreal) and 43.442455, 79.861340 (Toronto)
I need to know how to find arc distance, chord distance and radius
What websites can i find for this subject
Google has many but they are useless (blah blah) websites
LOL
Thanks Answered by Chris Fisher and Robert Dawson. 





A triangle in a rectangle 
20100125 

From Sangya: The perimeter of the rectangle is 21 inches. The perimeter of the inscribed triangle is 21 inches. Find the dimensions of the rectangle Answered by Robert Dawson. 





Angle of incline 
20100120 

From Alan: how do I fnd the angle of an incline with a measurement of 0.042 with an adjacent of 1.2mtrs?. Thank You Answered by Penny Nom. 





How long will it take to go 1 mile at 80 mph? 
20100119 

From Susann: How long will it take to go 1 mile at 80 mph? Answered by Penny Nom. 





How fast am I walking? 
20100110 

From KEVIN: IF I WALK 3 MILES IN 28 MINUTES, HOW FAST AM I WALKING? Answered by Penny Nom. 





Gail and Bill drove to the beach 
20100110 

From Nicole: Gail and Bill drove to the beach at an average speed of 50mph. They return home over the same road at an average speed of 55mph. The tip took 30 min less time. How far is the beach from their house? Answered by Stephen La Rocque. 





A pair of simultaneous equations 
20100109 

From Yumiko: Solve the following pair of simultaneous equations.
x^2 4x = y^24
3y=2x  3 Answered by Penny Nom. 





The maximum area of a rectangle 
20100103 

From Mohammad: determine the maximum area of a rectangle with each perimeter to one decimal place?
a)100 cm b)72 m c)169 km d)143 mm Answered by Penny Nom. 





Write a function for the area in terms of x 
20100101 

From Almarie: Lauren has 40 feet of metal fencing material to fence three sides of a rectangular garden. A tall wooden fence serves as her fourth side. Write a function for the area of the garden A in terms of x, the width in feet. Answered by Penny Nom. 





A circle problem 
20091214 

From Fawad: AP is a tangent at P to a circle centre O, where AP=6cm. The straight line AQC is such that QC= 9cm.
Find the length, in cm of AQ. Answered by Chris Fisher. 





f(x)=x+2sinx 
20091212 

From amroziz: for which values of x does the graph of f(x)=x+2sinx have horizontal tangent Answered by Harley Weston. 





... the original speed of the car was? 
20091208 

From venkatesh: A car travels a distance of 840 miles at a uniform speed if the speed of the car is increased 10 m/h more ,it takes two hours less to cover the same distance ,the original speed of the car was?
options:75 mh,65 m/h,60 m/h,55 m/h,45 m/h . Answered by Claude Tardif. 





Walking at 4/5 of his usual speed 
20091205 

From venkatesh: walking at 4/5 of his usual speed a man is 10 minutes too late .find his usual time. Answered by Penny Nom. 





The dimensions of a rectangular room 
20091126 

From crystal: . The length of a rectangular room is 7 feet longer than its width. The area of the room is 60 feet. What are the dimensions of the room? Answered by Penny Nom. 





Solving two equations, one with a square root 
20091123 

From kacie: y = square root of x+3
x4y = 7
im having trouble with this problem...i have to find where they intersect. Answered by Harley Weston. 





The triangle formed by the tangent and the coordinates axes 
20091123 

From Nirmala: Given that y=1/x, x is not equal to zero. Prove that the area of the triangle formed by the tangent and the coordinates axes is 2. Answered by Harley Weston. 





The fourth vertex of a rectangle 
20091111 

From Ellena: The points A(2,1), B(5,3), and C(7,0) are the three vertices of a rectangle. Determine he coordinates of the fourth vertex. Answered by Penny Nom. 





At what rate are the people moving apart? 
20091101 

From saira: A man starts walking north at 4 ft/s from a point P. 5 minutes later a woman starts walking south at 5 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 minute after the woman starts walking ? Answered by Harley Weston. 





Is it a rectangle? 
20091029 

From sefora: The coordinates of the vertices of quadrilaterals are given.
Draw each quadrilateral on a grid.
Determine whether it is a rectangle (show your work)
P(5,1), Q(4,4), R(6,2), S(3,5) Answered by Penny Nom. 





Standard deviation 
20091027 

From Reggie: After you have computed the standard deviation of a set of 40 scores, you discover that the lowest score is in error and should be even lower. Will correcting this error affect the standard deviation? Answered by Penny Nom. 





How far will it travel in 45 mins? 
20091027 

From maison: I'm stuck on the formula i dont remeber what it is can you help me out
a car is traveling 80km/h how far will it travel in 45 mins Answered by Robert Dawson. 





The area of a rectangle 
20091010 

From Ann: given a rectangle with sides a and 2a and diagonal d, find the area of the rectangle as a function of the diagonal,d Answered by Penny Nom. 





Two rectangles 
20091008 

From Lillian: A rectangle is 5cm longer than twice its width.
The width of another rectangle is 3cm less
than the width of the first rectangle and its length is 6cm more than 3 times its
width. If the perimeters are equal, find the dimensions of both rectangles Answered by Penny Nom. 





Two jets are traveling towards each other 
20091005 

From jake: two jets are traveling towards each other and are 4000 km apart. the rate of one jet is 100 km/h faster than the rate of the other. if the jets pass each other after 2.5 hrs what is the rate of speed of the faster jet? Answered by Penny Nom. 





Three circles 
20091002 

From Brandon: There is a quarter circle with a radius of 1. along one eged of it,
there is a semicircl with a diameter of 1, and its center is on the
drawn line. there is another semicircle again with the center on the
other drawn line, and this one has an unknown diameter of X. both
circles are internally tangent, and are tangent to each other. Find X. Answered by Robert Dawson and Chris Fisher. 





A line tangent to a parabola 
20091001 

From kanchan: for what value of c a line y=mx+c touches a parabola y^2=4a(xa) Answered by Penny Nom. 





How long (distance)did it take to stop? 
20090930 

From mary: a car travelling at 50km/h stops in 4 seconds.how long (distance)did it take to stop? Answered by Harley Weston. 





How fast am i going? 
20090928 

From ron: how fast am i going if i drive 40 miles in 20 minutes...what is the formula for figuring this out. Answered by Leeanne Boehm. 





How long would it take the students to arrive at their campsite 
20090918 

From amanda: ..."A group of 5th grade student in New Zealand are going camping. They will hike from Wellingto to Ruapehu. Then they will follow a trail for another 1/2 mile to their campsite." Ok, 1 mile equals 5,280 feet. The class decided one step length is equal to 15 inches and there are 85 steps in 1 minute. Now for the question: About how long would it take the students to arrive at their campsite, if they don't make any stops??? Answered by Robert Dawson. 





Average speed 
20090911 

From john: Sally travels by car from one city to another. She drives for 20.0 min at 68.0 km/h, 40.0 min at 37.0 km/h, and 51.0 min at 77.0 km/h, and she spends 12.0 min eating lunch and buying gas.
What is the average speed for the trip? Answered by Penny Nom. 





Paddling downstream 
20090904 

From Nicole: You head downstream on a river in a canoe. You can paddle at 6 km/h and the river is flowing at 2.4 km/h. How far downstream will you be in 55 minutes? Answered by Penny Nom. 





Simultaneous equations 
20090828 

From onias: solve 3/a  2/b = 1/2 , 5/a + 3/b = 29/12 Answered by Robert Dawson. 





The distance traveled on a bike 
20090828 

From Dennis: I would like to calculate the distance traveled on a bike based on the size of the tire and on the number of revolutions per minute. This is based on the rider traveling at a constant speed. Answered by Stephen La Rocque. 





The area of a rectangle 
20090821 

From roxanne: the dimensions of the rectangle: 3x length and 4x width. What is the area of the rectangle in square units? Answered by Penny Nom. 





Two cars 
20090809 

From Jayna: If a car was traveling 20mph east and another car was traveling 30mph west,
assuming they were 300 miles apart, at what point would they collide at the center? Answered by Penny Nom. 





A degreaser for a fish tank 
20090723 

From charlie: I have a tank that is 10 feet in diameter that I want to put floating degreaser in.The rate for the degreaser is 1/2 gallon per square foot of surface water.How do I figure out how many gallons I need? Answered by Penny Nom. 





A tangent to a circle 
20090714 

From Eric: Hi I am trying to complete a packet that has a list of questions to brush up on precalculus skills. The question asks "For the circle x^2 +y^2 + 6x  4y + 3 = 0 find : the equation of the tangent at (2,5). I have already found the equation for the circle and standard form and the center and radius. However, i do not know how to find the slope or yintercept of the tangent line. Please help. Thanks. Answered by Stephen La Rocque. 





The surface area of a rectangular pyramid 
20090713 

From Shivani: What is the surface area of a rectangular pyramid with a length of 6 inches,
a width of 7 inches and a SLANT height of 4 inches. Answered by Penny Nom. 





Simultaneous Equations 
20090706 

From Mukulu: Solve the equation simultaneously X/5=(Y+2)/2= (Z1)/4 ……………….eqt 1
3X+4Y+2Z25=0 ………………eqt 2 Answered by Janice Cotcher. 





A diagonal of a rectangle 
20090701 

From Ruben: Please assist me with the following problem: A rectangle has a diagonal that is 3.6 feet longer than the length and 7.1 feet longer than the width. What are the dimensions of the rectangle? Thanks Answered by Harley Weston. 





A boat goes up stream 30 miles and ... 
20090629 

From Mohsin: A boat goes up stream 30 miles and down stream 44 miles in 10 hours. Again it goes up stream 40 miles and down stream
55 miles in 13 hours. Find the rates of the stream and of the boat.
I am confused and unable to get an answer. Please help.
Thanks Answered by Robert Dawson. 





The surface area of a tank 
20090625 

From Charles: I need to calculate the external wall and top sqft surface area of a tank 54ft od x 15ft high with a dome top 54ft od x 8ft high. Answered by Penny Nom. 





A train crosses a tunnel 
20090625 

From Sabrina: A goods train of length one and half kilometres, is moving at a speed of 27km/hr. find the time taken by it to cross a tunnel of length seven and half kilometres Answered by Penny Nom. 





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. 





Is one Infinity larger than another in the extended real number system? 
20090624 

From Justin: Hello there, I was wondering if one infinity is larger than another in the extended real number system (just like in the transfinite ordinals and cardinals with respect to infinite sets) or are all infinities the same size in the extended real number system? Thanks sooo much for answering my question! I greatly appreciate it!
All the Best,
Justin Answered by Robert Dawson. 





An aeroplane flying in a wind 
20090602 

From Maria: The aeroplane flies in a wind of speed 50 kph from the direction S80◦W. However, the direction in which it is pointed, and its speed in still air,
are such that its resultant speed and direction are 800 kph, and direction N71.6◦E
I need to find the size of the angle between v and vw, in degrees to one
decimal place, and find the speed at which the aeroplane would fly if the air were
still, to the nearest kph.
It would help me greatly if I could see a diagram illustrating the velocity va that the aeroplane
would have if the air were still, the velocity vw of the wind, and
the resultant velocity v of the aeroplane (diagram should be
in the form of a triangle illustrating how one velocity vector is the
sum of the other two)
Thanks Answered by Harley Weston. 





Stones around a pool 
20090601 

From Jessica: I am putting a yard pond in and I am trying to find out how many stones I would need for the perimeter.
The pond is 4ft (W) by ft (L) by 1.5ft (D)
Thank You,
Jessica Answered by Penny Nom. 





The dimensions of a rectangle 
20090530 

From Linda: A rectangle has a perimeter of 38 feet & an area of 48 square feet. What are the dimensions of the rectangle? Answered by Stephen La Rocque. 





The width of a rectangle 
20090519 

From Stacey: If the length of rectangle is fixed at 29 cm, what widths will make the perimeter greater than 82 cm? Answered by Penny Nom. 





4 tan(360/(2n)) 
20090518 

From molly: in the formula to find the area of any regular polygon how do you figure out 4tan part of the formula Answered by Penny Nom. 





Driving to school and back 
20090517 

From marylyne: suppose you are late for school and you drive from your house at a constant rate of 70 mph.when class is over, you drive home at a more leisurely 50mph. what is your average speed? Answered by Penny Nom. 





The dimensions of a toy chest 
20090507 

From charlotta: My son needs to find the 3 dimensions of a toy chest that has to have a volume of 24 cubic feet can you show how to get the answer Answered by Penny Nom. 





What was her rate of speed? 
20090506 

From Stephanie: beth paddled a canoe to a picnic spot in the river in 2 hours. she traveled up the stream back to the original spot in three hours. the current was two miles per hour.
What was her rate of speed? Answered by Robert Dawson and Stephen La Rocque. 





Rectangular prisms 
20090501 

From deborah: Could you please tell me some examples of different objects in the real world of rectangular prisms? Answered by Harley Weston. 





Two airplanes are 300 miles apart 
20090422 

From afzalsultan: Two airplanes are 300 miles apart and flying directly towards each other.One is flying at 200 miles per hour, and the other at 160 miles per hour.How long will it take for the two planes to meet Answered by Robert Dawson. 





The center of an ellipse 
20090421 

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





Volume of a prism 
20090421 

From David: The base of a rectangular prism has an area of 15.3 square inches and a volume of 185.13 cubic inches. Write an equation that can be used to find the height "h" of the prism Answered by Robert Dawson and 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. 





Two similar rectangles 
20090419 

From Alyssa: The ratio of the lengths of corresponding sides of two similar rectangles is 3:5. the small rectangle has an area of 36 square centimeters. What is the are of the large rectangle? Answered by Penny Nom. 





Passing three cars 
20090416 

From Larry: If 3 cars are going 50 mph, and a fourth car pass the first 3 cars in 200 feet, how fast is the fourth car going? Answered by Stephen La Rocque. 





A man travels a total of 8km in 6 hours 
20090410 

From Kieran: Hello!
I was wondering if you could help me with this question! Thank you
A man travels a total of 8km in 6 hours
if his speed was xkm/4hours in the first stage
then his speed was 8x/2hours in the second part.
If the average speed for the first leg of the journey
was 1.1km/h faster than the second part: find x Answered by Penny Nom. 





How many miles per hour was it traveling? 
20090404 

From Regina: a car traveled 16 miles in 30 minutes. How many miles per hour was it traveling? Answered by Penny Nom. 





310,000 cubic yards of concrete 
20090331 

From Mary: I am interested in getting a good, general analogy for 310,000 cubic yards of concrete 
ideally as a length (miles) or distance between two US cities. Thanks! Answered by Penny Nom. 





A trip at two different speeds 
20090328 

From A student: Good afternoon!
An automobile travels 4 hours at an average speed of 42MPH. How much
longer must the truck travel at an average speed of 55MPH so the
average speed for the total trip will be 50MPH?
Thank you for your assistance! Answered by Penny Nom. 





The speed of a tire in revolutions per minute 
20090328 

From Jules: Suppose that a tire on a car has an outer diameter of 2,5 feet. How many
revolutions per minute does that tire make when the car is travelling 60
miles per hour? (hint:first find the angular velocity in radians per minute.) Answered by Harley Weston. 





Subdividing a foursided lot 
20090327 

From kannan: i have a 1.5 acre land having four sides
AB=64.8 meters
BC=94.2 meters
CD=54.4 meters
DA=127.2 meters
angle at D is 90
the side AB (frontage)is road facing i want to split the plot in to two halves
having same almost area and almost equal frontage, kindly help me, if possible
explain with drawing.
Regards
Kannan Answered by Harley Weston. 





A 5 ounce object traveling at 60 mph 
20090327 

From James: if a 5 ounce object traveling at 60 mph at 100 feet above the ground, how far will it travel forward before hitting the ground. Answered by Robert Dawson. 





Depth to height ratio 
20090326 

From Janet: Is there a formula to determine how deep something (a cabinet) should be based on how tall it is? Answered by Robert Dawson. 





The rate of change of the volume of a sphere 
20090325 

From Kaylin: why the rate of change of volume of a sphere is not constant even though dr/dt is constant? Answered by Walter Whiteley. 





Zscore 
20090325 

From Barb: I am having trouble finding information on a z score and the conversion to the number of standard deviations a z value can be away from the mean.
What exactly does that mean and what am I looking for?
Help Please. Answered by Harley Weston. 





A 1.5:1 rectangle 
20090323 

From melody: I have an origami model that says to use a 1.5:1 rectangle. I don't understand how to calculate the size of paper I need to use. Surely there is a formula to calculate this ratio? Thanks for your help. Answered by Penny Nom. 





A rectangular open box 
20090321 

From tina: An open box is to be made from a rectangular piece of tin by cutting two inches squares out of the corners and folding up the sides. The volume of the box will be 100 cubic inches. Find the dimensions of the rectangular piece of tin. Answered by Stephen La Rocque. 





The perimeter of a rectangle 
20090318 

From marylyne: the perimeter of the rectangular is 70 meters. if the width is 40% of the length, find the dimensions? Answered by Penny Nom. 





Water drains from a conical tank 
20090311 

From Tyler: Water drains from a conical tank at the rate of 5ft/min^3. If the initial radius of the tank is 4' and the initial height is 10'.
a) What is the relation between the variables h and r? (height and radius)
b) How fast is the water level dropping when h=6'?
Thanks for the help, i'm stumped. Answered by Penny Nom. 





A common tangent to two curves 
20090302 

From Jay: For what values of a and b will the parabola y = x^2 + ax + b be tangent to the curve y = x^3 at (1,1)? Answered by Penny Nom. 





Two racers going around a track 
20090226 

From larisa: One racer makes a complete trip around the track every 28 seconds, while the other racer completes a trip around the track every minute. How many times will the first racer pass the second racer in 30 minutes? Answered by Robert Dawson. 





A rectangular prism 
20090225 

From Christina: I am trying to find the area of the base of a rectangular prism where one cube=_1 cu in. The Answer is given in square inches. I also need the volume of the prism in cu in. For example length=3, w=2, h=5 Answered by Penny Nom. 





Fred in his canoe 
20090221 

From Susan: Fred paddled for 4 hours with a 7 km/hr current to reach a campsite. The return trip against the same current took 9 hr. Find the speed of Fred's canoe in still water. (Remember to include correct units) Answered by Penny Nom. 





How long will it take Jake to catch up? 
20090220 

From Rebecca: John is walking 2 miles per hour. Jake leaves home 15 minutes later and is walking 5 miles per hour . How long will it take Jake to catch up ? Answered by Penny Nom. 





Joggong in opposite directions 
20090219 

From Mallory: Emma and her mother jog along a milelong circular path in opposite directions. They begin at the same place and time. Emma jogs at a pace of 4 mi/h, and her mother runs at 6 mi/h. In how many minutes will they meet? Answered by Robert Dawson. 





The surface area of a cube and rectangular prism 
20090216 

From Mhiko: how to derived the total surface area of a cube and rectangular prism using geoboard?? Answered by Robert Dawson. 





Solid figures 
20090210 

From Rebecca: I need to know the names of solid figures. I have several pictures that I need to answer what type they are.
Thanks, Rebecca 3rd grade Answered by Penny Nom. 





A rectangular park 
20090206 

From Debbie: A park named Writer's Rectangle opened in town. When asked about the dimensions of the rectangle, the city planner, responded with these clues: The diagonals of the rectangular park plus its longer sides together measure seven times one of the shorter sides. The length of one diagonal is 250 m longer than one of the shorter sides. Use this information to find the area of the park. Answered by Stephen La Rocque. 





Catching up to the car ahead 
20090206 

From Ashley: Car A passes Car B on a freeway. The driver of Car B decides to speed up to 75 mph and catch Car A, whose driver is maintaining a constant speed.
Looking ahead, the driver of Car B sees Car A go under an overpass oneqarter mile up the road. Exactly six minutes later, Car B catches Car A.
How fast was the car going? Answered by Penny Nom. 





A point on 8x^2+5xy+y^3=149 
20090204 

From Vivian: Consider the curve defined by 8x2+5xy+y3=149
a) find dy/dx
b) Write an equation for the line tangent to the curve at the point (4,1)
c) There is a number k so that the point (4.2,k) is on the curve. Using the tangent line found in part b), approximate the value of k.
d) write an equation that can be solved to find the actual value of k so that the point (4.2,k) is on the curve
e) Solve the equation found in part d) for the value of k Answered by Harley Weston. 





Simultaneous equations with an xy term 
20090201 

From angelee: xy+5x2y10=0
2x+y=1 Answered by Penny Nom. 





The amount of concrete in a football stand 
20090130 

From jacques: A football stand 150 yd long has 20 tiers of seats; each tier has a rise of 2ft and tread of 3ft.Its construction of reinforced concrete with a cross section as shown. Find the amount of the material used in its construction. Answered by Penny Nom. 





Find area of the rectangle in terms of L. 
20090127 

From Arlen: The length of a rectangle is L. The width is 8 less than the length. Find area of the rectangle in terms of L. Answered by Penny Nom. 





How long will it take to make 50 miles? 
20090126 

From Tamara: An object is traveling at a speed of 45 km/minute. How long will it take to make 50 miles? Answered by Robert Dawson and Stephen La Rocque. 





A cubical tank that is 8 m on a side 
20090125 

From gina: Suppose one edge of a cubic tank is 8m; Find the volume of the tank in cubic meters Answered by Penny Nom. 





Two tangent circles 
20090123 

From Murtaza: Two circles touch externally at T. A chord of the first circle XY is produced and touches the other at Z. The chord ZT of the second circle, when produced, cuts the first circle at W. Prove that angle XTW = angle YTZ. Answered by Robert Dawson and Chris Fisher. 





A cyclic quadrilateral 
20090123 

From Murtaza: Line ATB touches a circle at T and TC is a diameter. AC and BC cut the circle at D and E respectively.Prove that the quadrilateral ADEB is cyclic. Answered by Robert Dawson and Chris Fisher. 





1 foot drop every 25 feet 
20090122 

From jerry: 1 foot drop every 25 feet what is the angle of the degree Answered by Penny Nom. 





A tortoise and a hare 
20090120 

From jenna: A tortoise can run with a speed of 0.14 m/s, and a hare can run 20 times as fast. In a race, they both start at the same time, but the hare stops to rest for 1.0 minutes. The tortoise wins by a shell (25 cm).
(a) How long does the race take?
(b) What is the length of the race? Answered by Stephen La Rocque. 





The number of gallons in a tank 
20090119 

From Jim: Hi, i need to know how many gallons of water can fit into our tank, and how to do the calculations my self. The tank is 72" round by 72" long, i would like some help. Thanks Jim. Answered by Harley Weston. 





The dimensions of a pool 
20090118 

From denise: a rectangular swimming pool is three times as long as it is wide. if the perimeter of the pool is 320 feet, what are its dimensions Answered by Penny Nom. 





Fuel in a tank 
20090116 

From Steve: I am not a math expert and want help seeing how much fuel is in a tank at one given time the tank that i have is 27 inches round. It is 69 inches long. laying length ways. it holds 140 gallons of fuel at fill up. I do know that it would hold less at the bottom of the tank an more in the center. Is there anybody that could just give me the figures by the inch without a formula. thanks for your time Answered by Stephen La Rocque. 





Parallel distances from arc of circle to its chord 
20090116 

From Roger: Give the length of a chord of a circle and the height of the arc, how do I
find the lengths of equally spaced parallel lines drawn from the chord to
the arc. (Think of the lengths of vertical slats in an archtopped bed head
board.) Answered by Chris Fisher and Stephen La Rocque. 





A rectangular prism 
20090113 

From nika: How many bases does a rectangular prism have? What are they? Answered by Harley Weston. 





Two trains 
20090112 

From Shanise: If train A leaves the train station at noon traveling 45mph and train B leaves the train station at 1pm traveling 65mph, what time will the trains meet? Answered by Robert Dawson. 





A stack of rectangles 
20090111 

From ashwani: Could you please advise the area of a rectangles pyramid.
There are 5 rectangles placed one above the other. The top most rectangle has length 2 cm and height 2 cm. The subsequent rectangles length is increased by 1 cm on both the sides, while the height of the 2nd and 3rd rectangle is 2cm each, while the 4th & 5th has a height of 3 cm each. Could you please let me know the the area of the figure and the formula to calculate Answered by Penny Nom. 





Constants, and coeficiants 
20090110 

From Kelsey: I am having trouble trying to remember what like terms, constants, and coeficiants are. My math teacher
hasent been explaining it very well and i was wondering how to remember what they are, and what they are? I dont understand the concepts. Answered by Stephen La Rocque. 





Two rectangular plots have the same area 
20081223 

From Jason: Two rectangular plots have the same area. The first has a perimeter of 40m while the second has a length 2m less than the first and a width 1m greater. Find the length and breadth of the first rectangle Answered by Stephen La Rocque. 





A standard bill on a highway 
20081219 

From Stephanie: A standard bill on a highway has a perimeter of 14 feet. the length of the bill board is 6 feet greater than triple the width.
What is the length?
what is the width? Answered by Robert Dawson and Penny Nom. 





A rectangle with diagonal 8.5 inches 
20081214 

From nekasia: what is the area of a rectangle with a diagonal of 8.5 inches PLEASE SHOW WORK Answered by Penny Nom. 





The sides of a rectangle 
20081208 

From Mitchell: The perimeter of rectangle ABCD (represented on a Cartesian plane) is 52cm.
The equation associated with segment AD is 3x+4y60=0
Point C is at (18, 14).
What is the length of segment AD? Answered by Penny Nom. 





3 equidistant points 
20081201 

From Damien: How do you find 3 equidistant points (C,D,E) on a line between point A(Xa, Ya) and point B(Xb, Yb) so that AC, CD, DE and EB are all equal? Answered by Chris Fisher. 





Two tangent circles and common tangents 
20081201 

From Alan: Radius of big circle 30cm, radius of small circle 10 cm. From the diagram, the radius from the tangent do not form a semicircle but at an angle. Find the perimeter of the band around both the circle. May need to use trigonometry to find reflex angle AOB, CMD and get the major arc length AB and minor arc length CD Answered by Penny. 





Two tangents to a circle 
20081126 

From rogerson: The length of the tangent to a circle is 15 cm. If the angle between the two tangent lines to the circle is 28 degrees, what is the radius of the circle? Answered by Penny Nom. 





Tan(3x) 
20081123 

From Evan: Derive an expression for tan3x in terms of tanx Answered by Harley Weston. 





Sigma in a normal distribution 
20081118 

From Justin: Suppose the random variable Y can be described by a normal curve with
Mu=40. For what value of the standard deviation is
P(20 less than or equal to Y less than or equal to 60) = 0.50
Justin Answered by Harley Weston. 





How far are the boats apart? 
20081114 

From dom: Two boats leave port at the same time. They leave at 150 degree angle. One boat travels at 10mph and the other at 20mph. After two hours how far are the boats apart? Answered by Penny Nom. 





The dimensions of a rectangle 
20081107 

From laela: A rectangle is 8 feet long and 6 feet wide.If the dimension is increased by the same number of feet,the area of the new rectangle formed is 32 square feet more than the area of the original rectangle.By how many feet was the each dimension increased? Answered by Penny Nom. 





A circle tangent to a line and with its centre on another line 
20081101 

From liza: Find the equation of the circle of radius squareroot 26 tangent to the line 5x+y=13 and having its center on the line 3x+y+7=0. Answered by Chris Fisher. 





The speed of the boat and the river 
20081028 

From Jenn: On the Amazon River in Brazil, a boat goes 50 miles upstream in 3 hours, later the boat returns to the starting point in 2 hours. What is the speed of the boat in still water and what is the current speed in this part of the Amazon? Answered by Penny Nom. 





Three congruent rectangles 
20081027 

From Meagan: Here is my problem: Three congruent (nonsquare) rectangles are placed
to form a larger rectangle. [Two are oriented the same way and the
"stacked" while the third is rotated 90 degrees and placed next to the
other two.] The total area is 1350 square cetimeters. Square ABCD is
then created that has the same perimeter as the large rectangle that was
created. E is the midpoint of line CD and F is the midpoint of BC. Find the
area of triangle AEF. Answered by Penny Nom. 





Tangent line 
20081027 

From Maddie: Find a general equation for a line that touches, but does not pass through the function Y=X2(X squared) + BX+C. Answered by Stephen La Rocque and Victoria West. 





The length of a rectangle is 6 inches less than 3 times its width. 
20081026 

From Angela: The length of a rectangle is 6 inches less than 3 times its width. Find the
dimensions of the rectangle if its area is 45 square inches. Answered by Penny Nom. 





Two tangent lines to a parabola 
20081026 

From Marcus: Show that the tangent lines to the parabola y = ax^2 + bx + c at any two points with xcoordinates p and q must intersect at a point whose xcoordinate is halfway between p and q. Answered by Penny Nom. 





The height of a tank 
20081026 

From Kyle: If a water tank holds 750 cubic meters of water and it is 15 metres long and 10 metres wide how many meters tall is it ? Answered by Penny Nom. 





The amount of diesel fuel in a tank 
20081026 

From Mike: I have an cylinder shaped oil tank that holds approx. 283 gals of diesel fuel. The tank is laying on on its side, (like taking a garbage can and laying it down on its side). What is the formula to calculate how much oil is in the tank at any given time. If the tank was sitting on end it would be easy to figure out, but it is not. Answered by Stephen La Rocque. 





The slope of a tangent line 
20081018 

From Amanda: If f(x)=square root of (x+4), and the slope of the tangent line at x=21 was 1/n for some integer n, then what would you expect n to be? Answered by Stephen La Rocque. 





Travelling home o the train 
20081018 

From nadha: MELISSA reached the railway station at 9.30am.The distance between the railway station and her hometown was 720 km.At what time would she reach her hometown if the train travelled at an average speed of 120 km/h? Answered by Penny Nom. 





If you are driving 40mph, how long does it take to go 2.5 miles? 
20081018 

From Nathan: If you are driving 40mph, how long does it take to go 2.5 miles? Answered by Penny Nom. 





Two equations in two unknowns 
20081017 

From Dushayne: Please help me in solving this problem:
a. 3x4y=32
5x+2y=10
b. 2x+3y=11
4x+3y=10 Answered by Penny Nom. 





A tangent line to f(x) = 1/(x  1) 
20081016 

From Amanda: If f(x)=1/(x1) then what is the slope of the tangent line at x=2? Answered by Harley Weston. 





Two planes flying in opposite directions 
20081016 

From samantha: i don't understand how to do this problem.two jets leave denver at 9:00 am one flying at a speed 50 km/h greater than the other, which is traveling west. at 11:00 am the planes are 2500 km apart. find their speeds. Answered by Penny Nom. 





The dimensions of a rectangle 
20081016 

From cristine: the area of a rectangle is 675sq.cm.
if the width is 1/3 of the length.
find the dimensions of the rectangle.... Answered by Penny Nom. 





Finding the Raw Score for a Mean of 0 and Standard Deviation of 1 
20081002 

From Anita: A variable Y has a distribution of mean of Y =80 and standard deviation of Y=36. Find the values of A and B for transforming y*=A +BY so that mean of y* =0 and standard deviation of y*=1. Answered by Janice Cotcher. 





The length of a tank 
20081001 

From alex: I have a tank which I can only partly see. It is 70cms wide, 45 cm deep and hold 500litres. How long is it? Answered by Harley Weston. 





How many parallel tangents may a circle have? 
20080929 

From Manish: how many parallel tangents may a circle have? the text book shows two.but a circle can have infinite tangents.then why not parallel tangents coz
theoretically each tangent have a parallel tangnts then no. of parallel tangent a circle may have is equals to half of the infinity i.e. infinity.. Answered by Walter Whiteley. 





What is the perimeter of the rectangle? 
20080927 

From Pauline: A rectangle has an area of 27 squared inches. the height is 3 times the base
What is the perimeter of the rectangle? Answered by Penny Nom. 





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. 





5 units from (1,2) and 5 units from yaxis 
20080926 

From Shaun: Find the points (x,y) in the plane that are 5 units from (1,2) and 5 units from yaxis.
I am more interested in the approach, in general terms, than the numerical values. Answered by Penny Nom. 





Parallel Tangents 
20080924 

From manish: how many parallel tangents may a circle have? the text book shows two.but a crcle can have infinite tangents. Answered by Janice Cotcher. 





Limit as it Approaches a Constant 
20080916 

From Brooks: what is the limit as x approaches 10 for f(x) = sqrt(x1) = 3 pleeeeeaase help me out here Answered by Janice Cotcher. 





Distance, time and rate 
20080911 

From Pauline: During the first part of a trip, a canoeist travels 100 miles at a certain speed. The canoeist travels 25 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 5 hrs. What was the speed on each part of the trip? Answered by Penny Nom. 





A tangent to a circle 
20080906 

From Jake: Find an equation of the line that is tangent to the circle x^2 + y^2 = 3 at the point (1,√2) Answered by Penny Nom. 





Largest Inscribed Rectangle 
20080903 

From astrogirl: find the shape and area of the largest rectangle that can be inscribed in a circle of a diameter a=2 Answered by Janice Cotcher. 





A rectangular tank of water 
20080902 

From Angela: A rectangular tank is 80 ft long, 30 ft wide, and 20 ft deep. If 100,000 gallons of water were pumped into the tank, what would be the water rise? Answered by Penny Nom. 





The lengths of the sides of a rectangle are in ratio 5:3 
20080829 

From todd: the lengths of the sides of a rectangle are in ratio 5:3 the perimeter of the rectangle is 32 cm find the length of each side Answered by Stephen La Rocque. 





Two tangent circles 
20080822 

From Michele: A circle of radius 2 is externally tangent to a circle of radius 8,
How do you find the length of their common tangent. Answered by Penny Nom. 





Irregular polygon and Circle that Intersects All Sides 
20080820 

From Xetro: Hi,
Suppose you have an irregular polygon(convex or concave) with n > 3 sides.
The question is  Find some circle that will cut(in limiting case  touch) all the sides of that polygon.
It doesnt matter how many times it cuts the side(1 or 2), it just have to cut or touch it.
How to find such a circle? or how to decide if such circle even exists?
What if those segments do not form a polygon but are some arbitrary segments ?
Really want to know how to do it................
Thanks a lot..
Regards,
Xetro Answered by Janice Cotcher. 





Coefficients, Like Terms, and Constants 
20080814 

From Maddie: How Would I Answer This Problem?

Coefficients 
Like Terms 
Constants 
3x+7 



4m+(3n)+n 



6kp+9k+kp14 



8y+6ab+73ba 



c+2c+c5c+1 



I Would Really Appreciate It If You Could Help Me
Sincerely,
Maddie 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. 





The volume of a fuel tank 
20080801 

From G.: I have a fuel tank that is 70 inches by 48 inches and 24 inches deep, how many imperial gallons does it hold? Answered by Victoria West. 





Area of triangle formed by three tangent circles 
20080731 

From brian: Three circles with radii 3,4 and 5 touch each other. The circles are tangent to each other. What is the area of the triangle formed by the centers of the circles? Answered by Stephen La Rocque. 





Inscribed Rectangle 
20080730 

From Felicia: A rectangle whose base is twice its altitude is inscribed in a circle whose radius is 5 mm.
Find the area of the rectangle. Answered by Penny Nom. 





Running in opposite directions 
20080729 

From maame: if i run six miles per hour and my friend runs four miles per hour and we both run for two hours in opposite directions how many miles apart will we be after the two hours? Answered by Janice Cotcher and Penny Nom. 





Problems understanding math 
20080727 

From Cindy: why do so many people have problems understanding math.
is it because at some point along the way they didn't fully understand
a concept and they then lose confidence. Learning math is cummulative so what you
don't learn at one point just gets more confusing as you move along. how do
we correct this? how can i help students in junior and senior high who do poorly in math. Answered by Stephen La Rocque and Victoria West. 





Braking Distance Relationship 
20080723 

From Mr.Adjetey: you are travelling at 30km/h.According to the rule of thumb,the braking distance is 9 metres when braking normally.How long is the braking distance under the same conditions when travelling at 60km/h? Answered by Janice Cotcher. 





Simultaneous equations 
20080723 

From Franco: Solve
3 D + E  F = 10
2 D  F = 4
3 D  4 E  F = 25
Franco Answered by Penny Nom. 





A tangent to a curve through a point not on the curve 
20080723 

From Carter: How does one find the tangent points on a curve, given only the curve's function
and the xintercept of that tangent line?
i.e. Find the point(s) on the curve y = (x^2) + 1, where the tangent line passes
through the point (2, 0).
I know that there will be two such points, one where y is very close to 1, and the
other point where y is a large negative number. However, I do not recall how to
figure out the tangent line equation given a single intercept and solving to find the
tangent points. Answered by Penny Nom. 





A tangent line to a circle 
20080709 

From Rita: The tangent to a circle may be defined as the line that intersects the circle in a single point, called the point of tangency. If the equation of the circle is x^2 + y^2 = r^2 and the equation of the tangent line is y = mx + b, show
r^2(1 + m^2) = b^2 Answered by Harley Weston. 





Going from 45 mph to 35 mph 
20080709 

From Terry: How long (distance  feet AND time) will it take a car traveling at 45 mph to slow down to a speed of 35 mph? Answered by Harley Weston. 





Two trains 
20080707 

From Elisha: Trains at each end of the 50. km long Eurotunnel under the English Channel start at the same time into the tunnel. Find their speeds if the train from France travels 8. km/h faster than the train from England and they pass in 17 minutes. Answered by Janice Cotcher and Penny Nom. 





A boat travels 20 kms upstream in 6 hrs ... 
20080707 

From vidya: A boat travels 20 kms upstream in 6 hrs and 18 kms downstream in 4 hrs. Find the speed of the boat in still water and the speed of the water current? Answered by Penny Nom. 





Fit 7 different rectangles on grid paper 
20080702 

From anonomous: I need to fit 7 different rectangles on grid paper of 1cm squared.
Each squared centimetre equals 4 squared metres, and it needs to end up as area 64 square metres. Answered by Janice Cotcher. 





A rectangular room 
20080630 

From Peter: A rectangular room has a perimeter of 42 feet and an area of 108 square feet. What is the length, in feet, of the shorter side? Answered by Penny Nom. 





A rectangle 
20080626 

From SEBASTIAN: How to arrange quadrilateral in the form of a rectangle? Answered by Penny Nom. 





Two forces acting on a body 
20080621 

From Rita: Before answering the question below, what exactly is, in basic words, resultant force?
QUESTION:
Two forces of 50 and 68 pounds act on a body to produce a resultant force of 70 pounds.
Find, to the nearest 10 minutes or nearest tenth of a degree, the angle formed between the resultant force and the smaller force. Answered by Harley Weston. 





How far from each other will they be? 
20080618 

From kerstin: a women jogging at 6 mi/h passes a men biking in the opposite direction at 12 mi/h. if the maintain their speeds, how far from each other will they be 10 minutes after passing? Answered by Stephen La Rocque. 





A space camera circles the Earth 
20080616 

From Rita: A space camera circles the Earth at a height of h miles above the surface. Suppose that d distance, IN MILES, on the surface of the Earth can be seen from the camera.
(a) Find an equation that relates the central angle theta to the height h.
(b) Find an equation that relates the observable distance d and theta.
(c) Find an equation that relates d and h.
(d) If d is to be 3500 miles, how high must the camera orbit above Earth?
(e) If the camera orbits at a height of 400 miles, what distance d on the surface can be seen? Answered by Penny Nom. 





Escort cards on a rectangular table 
20080613 

From Susan: What size rectangular table will we need to put 230 2" X 3.5" escort cards on for my daughter's wedding reception with a spacing of .5 inch between them on all sides? Thanks so much for your help 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. 





tan(4a  b) 
20080612 

From A student: hi guys just a quick help on question needed thanx
if tan a = 1/5 and
tan b = 1/239
find value of tan(4ab)
thanks alot in advance Answered by Harley Weston. 





The length and width of a rectangle 
20080611 

From gregg: the perimeter of a rectangle is 70 feet. the ratio of length to width is 4:3. how would i calculate the length of the height and width? Answered by Penny Nom. 





What are the dimensions of the rectangle? 
20080611 

From Denise: A rectangle has a diagonal that is 3.6 feet longer than the length and 7.1 feet longer than the width. What are the dimensions of the rectangle? Answered by Claude Tardif and Victoria West. 





Three mutually tangent circles 
20080604 

From Jacob: If three circles are mutually tangent, does that mean that the two tangent lines are perpendicular? Answered by Chris Fisher. 





The area of a rectangle 
20080527 

From Becky: the area of a rectangular lot is represented by 6t^2+13t5. What are the length and the width of the rectangular lot? Answered by Harley Weston. 





The length of a shadow 
20080527 

From Simon: A figure skater is directly beneath a spotlight 10 m above the ice. IF she skates away from the light at a rate of 6m/s and the spot follows her, how fast is her shadow's head moving when she is 8m from her starting point? The skater is (almost) 1.6m tall with her skates on. Answered by Stephen La Rocque and Harley Weston. 





Gasoline in a cylindrical tank 
20080525 

From Simon: A cylindrical tank with height 15m and diameter 2m is being filled with gasoline at a rate of 500L/min. At what rate is the fluid level in the tank rising?(1L = 1000cm^3). About how long will it take to fill the tank? Answered by Penny Nom. 





How many bricks I can place around a 26inch circle? 
20080522 

From Jon: I want to know how many bricks I can place around a 26inch circle? There must be a formula other than trial and error. The length of the bricks is 6inches. [How many 6inch tangents can be in a 26inch circle?
Thank you very much.
Jon Answered by Harley Weston. 





55 mi/h for 4 h 
20080521 

From brenda: mary drove her car at 55 mi/h for 4 h. Use the formula d = rt (where d is the distance traveled, r is the rate of travel and t is the time traveled) to determine how far mary traveled. Answered by Penny Nom. 





The sides of a rectangle 
20080516 

From bill: The area of the rectangle is 170 sq.ft. the width is unknown and the length is the width plus 7 ft.
I set it up like this w(w+7)=170 and this is where I get lost. Thanks, Bill Answered by Penny Nom. 





Fencing around a playground 
20080515 

From Vanessa: If the playground is a rectangle with it's width 10ft shorter than it's length,
and it can be enclosed by exactly 140ft of fence,
what is the length and width of the playground? Answered by Penny Nom. 





A crate is launched from an airplane 
20080510 

From Michelle: A crate is launched from an airplane, 75 feet above the ocean, with an initial vertical velocity of 60 feet per second. How many seconds will it take for the crate to hit the water? Round to the nearest hundredth. Answered by Harley Weston. 





How far is it from the top to the bottom of the mountain? 
20080509 

From Matthew: A ski lift carries a skier up a slope at a rate of 2 miles per hour. Following the same path down the mountain, the hiker has a rate of 4 miles per hour. If the round trip took 3 hours, how far is it from the top to the bottom of the mountain? Answered by Penny Nom. 





The surface area of a tank 
20080509 

From jack: i'm looking for the square footage of a tank that is 10'diameter x 23'high,floor,ceiling and walls Answered by Penny Nom. 





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. 





5 miles per hour for 30 minutes 
20080429 

From Joshua: A boat travels at a constant rate of 5 miles per hour for 30 minutes. How far does the boat go in that time? Answered by Penny Nom. 





A rectangle inscribed in a circle 
20080427 

From sridhar: A rectangle with perimeter 28 cm inscribed in a circle of radius 5 cm
find the area ? Answered by Penny Nom. 





An octagonal prism 
20080427 

From Melanie: My son is identifying geometric shapes in the real world? We are stuck on octagonal prism, rectangular prism and square prism. Can you help me out with some examples. Thanks Answered by Penny Nom. 





Driving home from work 
20080425 

From brittanygrant: brittany house is 37 miles from his job. He leaves at 6:25pm, and drives 49 miles per hour. what time will he get beck home? Answered by Penny Nom. 





Find the length and the width of the rectangle 
20080424 

From Vickie: A rectangle is 2 times longer than it is wide. It has a diagonal length of 50 centimeters. Find the length and the width of the rectangle. Round your answers to the nearest tenth. Show your work. Answered by Penny Nom. 





The dimensions of a rectangle 
20080420 

From Brandy: Find the dimensions of a rectangle with a primeter of 54 cm if the length is 5 less than three times the width. Answered by Penny Nom. 





45 miles at 50 mph 
20080418 

From Willie: If you travel at 50 mph, how long does it take to go 45 miles? Answered by Penny Nom. 





A solid figure with 3 rectangular faces and 2 triangular faces 
20080417 

From Emily: I am in the 3rd grade and my teacher gave us a question. What is a
solid figure with 3 rectangular faces and 2 triangular faces? Answered by Penny Nom. 





A tangent to two circles 
20080413 

From erson: find the length of the tangent segment AB to two circles whose radii are a and b respectively, when the circles touch each other.
the illustration looks like this...hope you'll understand...
there are 2 circles  one is big one is small. they touch each other. and there is this irregular 4 sided polygon that connects them...there is a line that connects them from their center point and another from the tip of the circles...and that's it...i cannot explain very well
please bear with me Answered by Stephen La Rocque. 





A tangent to a circle 
20080413 

From rogerson: Line t from point P is tangent to circle O at T, the point of tangency. Find the length of PT when the radius of the circle is 5cm and the distance between points P and O is 8cm. Answered by Stephen La Rocque. 





Jill and Matt run on a 400 meter long oval track 
20080411 

From jamie: Jill and Matt run on a 400 meter long oval track. Jill and Matt each run 10 laps daily and both run in the same lane.
One day Jill and Matt began at the same point, but ran around the track in opposite directions. Jill ran at a constant speed that was 2 meters per second faster than matts constant speed. Jill passed Matt for the first time in 40 seconds. Jill ran at a constant rate of how many meters per second? Answered by Penny Nom. 





Two trains left the city at the same time 
20080411 

From J: Two trains left the city at the same time, traveling in opposite directions. The eastbound train travels for ten hours and the westbound train travels for 5 hours. They are now 1300 km apart. The westbound train's rate is 20 km/hr faster than the eastbound train. Find the speed of each train. Answered by Penny Nom. 





A rectangle word problem 
20080410 

From Nick: A rectangle is twice as long as it is wide. If the length and width are both increased by 5cm, the resulting rectangle has an area of 50cm^2. Find the dimensions of the original. Answered by Penny Nom. 





A river boat 
20080409 

From jessica: heres a crazy riddle a river boat that travels 12 mph in still water makes a
pleasure trip to a city upstream and back in 3 hours. If the city is 10 miles aways, what is the rate of the current Answered by Stephen La Rocque. 





The shortest distance from a point to a line 
20080403 

From Katherine: How do I find the shortest distance from the point (3,5) to the line x = 2 Answered by Stephen La Rocque. 





Perimeter, area and diagonals of a rectangle 
20080403 

From jenea: I have to find the perimeter as well as the area of a rectangle when given the diagonals are 12 units long and they intersect at a 60 degree angle. how do i find both the area and perimeter; do i use the 30 60 90 triangle rule? Answered by Stephen La Rocque and Penny Nom. 





The rectangle with smallest perimeter 
20080401 

From nicole: when given an area,squares are the rectangles with the smallest perimeter write the length and width of the rectangle with the smallest perimeter Answered by Penny Nom. 





A rectangular prism 
20080331 

From Chanlie: i need need to find a rectangular prism with a total surface area of 210 units. Answered by Penny Nom. 





The area of a rectangle 
20080325 

From Raphael: What is the area of rectangle that measures 7 yards by 23 yards Answered by Penny Nom. 





Expected value and standard deviation 
20080319 

From Patrick: Heres a question i cant figure out:
a small airline company has only three flights per day. The number of
delayed flights per day is regarded as a random variable, and I'm
supposed to calculate the expected
value and standard deviation of the number of delays.
the probability distribution looks like:
No. of Delays: 0 1 2 3
Prob. of delay: 05. 0.3 .1 .1 Answered by Harley Weston. 





Distance seen 
20080318 

From Nev: formule: Distance Seen
S = 1.225 x square root of H
S = Distance seen in Miles
H = Height in Feet
What dose 1.225 Relate To ? Answered by Stephen La Rocque. 





A train and a boat 
20080315 

From Sabrina: A railroad bridge is 20m above, and at right angles to, a river. A person in a train travelling at 60 km/h passes over the centre of the bridge at the same instant that a person in a motorboat travelling at 20km/h passes under the centre of the bridge. How fast are the two people separating 10s later? Answered by Harley Weston. 





A fence around a rectangular region 
20080306 

From sharon: a farmer want to make a rectangular fence he has 750 feet of material . if the width is 95 feet what is the area of the rectangle Answered by Penny Nom. 





The dimensions of a rectangle 
20080306 

From Julie: Find the dimensions of a rectangle with an area of 400. Width x ft.
Length (2x7)ft. Answered by Stephen La Rocque and Penny Nom. 





Two points moving on a straight line 
20080306 

From laura: Particle A travels at constant speed of 1.0ms1 in straight line, passing particle B, at which time particle B beings traveling with constant acceleration of 0.2ms2 until reaching Particle A.
What equations represent the displacement of particle A and particle B measure from the point they first pass?
How long does it take for particle B to catch up with particle A?
What is the speed of particle B when reaching particle A?
What distance have both particles traveled from where they first pass to where they meet again?
Calculate the displacement of both particle A and B at 2 second intervals between t=0s and t=12s? Answered by Stephen La Rocque and Penny Nom. 





A dog and a fire hydrant 
20080306 

From Brittany: A bulldog is walking east along Main St. at a speed of 4 miles per hour. He wants to get to a fire hydrant on a parallel street. Initially, the bearing to the hydrant is south 62 degrees east. After 20 minutes, the bearing is south 41 degrees east. If the bulldog continues his walk, what is the closest he will be to the hydrant? Answered by Stephen La Rocque. 





Is every rectangle a square? 
20080304 

From Odette: if every square is a rectangle, is every rectangle aslo a square? Answered by Penny Nom. 





What point on the graph y = e^x is closest to the origin? 
20080303 

From elvina: What point on the graph y = e^x is closest to the origin? Justify your answer. Answered by Stephen La Rocque. 





Simultaneous equations 
20080229 

From CONOR: I was wondering if you could help me with this problem
7x  5y = 1
3y = 4x Answered by Penny Nom. 





A package of supplies is dropped from a plane 
20080229 

From beth: An airplane flies west at a speed of 200m/s. A package of supplies is dropped from the plane to some campers. if the plane is at an altitude of 1000meters, how far from the campers should the package be dropped to land near them? ignore wind resistance. Answered by Stephen La Rocque. 





Is a square a rectangle? 
20080229 

From Jaime: Is a square a rectangle? Answered by Penny Nom. 





The diagonal of a rectangle 
20080221 

From tim: is there a formula for finding the diagonal of a rectangle? 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. 





A ball bearing is placed on an inclined plane 
20080215 

From Leah: A ball bearing is placed on an inclined plane and begins to roll.
The angle of elevation of the plane is x.
The distance (in meters) that the ball bearing rolls in t seconds is s(t) = 4.9(sin x)t^2.
What is the speed of the ball bearing,
and what value of x will produce the maximum speed at a particular time? Answered by Penny Nom. 





The area of a rectangle 
20080212 

From mark: The diagonal of a rectangle is 15cm, and the perimeter is 38cm. What is the area? It is possible to find the answer without finding the dimensions of the rectangle. Please help me and show as much of the problem as possible. Thank You Answered by Penny Nom. 





The width of a rectangle is 4 less than twice its length. 
20080209 

From Shawn: The width of a rectangle is 4 less than twice its length. If the area of the rectangle is 72 cm,
what is the length of the diagonal Answered by Stephen La Rocque. 





The distance around a building 
20080206 

From olivia: If you walk around a building that is 102,869 sq ft, how many miles is that? Answered by Penny Nom. 





Two cars are on a collision course 
20080206 

From Danielle: Two cars are on a collision course, heading straight towards each other. One car is traveling 45 miles per hour and the other is traveling 75 miles per hour. How far apart will the two cars be one minute before they collide. Answered by Penny Nom. 





The equation of a circle 
20080205 

From aime: Find the equation of the circle tangent to 3x+4y15=0 at P1(1,3) and passing through P2(6,3) and P3(0,5)? Answered by Stephen La Rocque. 





How fast does each travel? 
20080205 

From kRYSTAL: May rides her bike the same distance that leah walks. May rides her bike 10km/h faster than leah walks.
Its takes May 1 hour and Leah 3 hours to travel the sam distance, how fast does each travel? Answered by Penny Nom. 





The dimensions of a rectangle 
20080201 

From Evan: you are given that the area of a rectangle is 21.6in sq. find the base and the height of the rectangle. Answered by Penny Nom. 





Driving from Mathville to Bioville 
20080201 

From Ariel: Mahtab took hours to drive from Mathville to Bioville, a total of 485 km.
She drove part by highway at 80 km/h and part by slow roads at 30 km/h.
How many hours did she drive each type of road? 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. 





2 km at 5.00 m/s 
20080129 

From Stephanie: How much time does it take for a student running at an average speed of 5.00 m/s to cover a distance of 2.00 km? Answered by Penny Nom. 





How far from the corner will the police catch the car? 
20080127 

From Joel: A car is going down the road at a speed of 90km/h in a 50km/h zone.
As the car passes a corner, a police cruiser sitting there notices it. Five
seconds later the cruiser begins accelerating at 5.0m/s squared.
Assuming that he is able to maintain this acceleration, how far from the
corner will the police catch the car? How fast will the cruiser be going? Answered by Stephen La Rocque. 





The volume of a tank 
20080127 

From Fred: A cubic tank holds 1,000 kilograms of water what are the dimensions of the tank in meters? Answered by Harley Weston. 





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. 





Two circles in a rectangle 
20080118 

From Alex: One side of a rectangle is 10 and the other is x.
Two circles with equal radii are inscribed in the rectangle and like a Venn Diagram, the circles overlap.
Each circle touches the top and bottom of the rectangle and the left circle touches the left side of the rectangle and the right circle touches the right side of the triangle.
The distance between the centre of each circle is 2x/3.
Find x Answered by Penny Nom. 





Two bikers race on a circular track 
20080117 

From Abby: Two bikers race on a circular track. Biker A can circle the track in 8 minutes, and Biker B can circle the track in 6 minutes. From the start of the race, how many minutes will it be before Biker B overtakes Biker A? Answered by Stephen La Rocque and Penny Nom. 





Driving towards each other 
20080116 

From Shanda: Paul and Charlene are 420 miles apart. They start toward each other with Paul driving 16 miles per hour faster than Charlene. They meet in 5 hours. Find Charlene's speed. Answered by Stephen La Rocque. 





The distance back to school 
20080116 

From priya: a boy starts travelling from his house to his school. He travels 1 km east and then
2km north and then 1 km East and 1km North and then 1 km east and then 1 km North.
find out the shortest distance for him to reach his shool? Answered by Harley Weston. 





Hoisting an anchor 
20080110 

From ron: four men on a boat are using a capstan for hoisting an anchor weighing 2000lbs. The diameter of the barrel of the capstan at the section in use is 8in., and the pull on the chain carrying the anchor and passing around the capstan barrel is assumed to act at a distance of 1in. from the surface of the barrel. If the distance from the axis of the barrel to each point at which effort is applied to a capstan bar is 40in., what force must be applied by each man hoisting the anchor? Answered by Stephen La Rocque. 





How fast does Kim paddle in still water? 
20080107 

From Fran: Kim paddled a canoe 10 km upstream and then paddled back to his starting point. If the rate of the current was 2 km/h that day and the whole trip took 3.75 h, how fast does Kim paddle in still water? Answered by Penny Nom. 





What is the speed of the plane in still air? 
20080105 

From oscar: A plane flies 400 miles with the wind and 340 miles against the wind
in the same length of time. If the speed of the wind is 24mph, what is
the speed of the plane in still air? Answered by Penny Nom. 





The shortest distance to a line 
20080104 

From nana: 3y+4x12=0 is the equation of the line AB on a graph......the line AB joins both y and x axises together.....point A is on y axis and its value is 3....point B is on x axis and its value is 4.....Question : from point O(0,0).find the point ont the line AB Answered by Stephen La Rocque. 





A tangent to a circle 
20080104 

From adam: Find a>0 so that the line y=x+a is a tangent to the circle x^2 +y^2=2. Answered by Stephen La Rocque and Harley Weston. 





Lining up coins visually using geometry and trigonometry 
20071231 

From Jessica: a) In what order would you arrange a penny, a nickel, a dime, a quarter, and a halfdollar so that they all have the same apparent size? The diameters of the coins, in thousandths of inches, are as follows: penny, 750; nickel, 835; dime, 705; quarter, 955; halfdollar, 1205.
b) How should the coins be placed, if the distance between the dime and the halfdollar is 100 units?
How far from thw dime should your eye be to see that all the coins have the same apparent size?
c) What angle do the coins subtend when they have the same apparent size? Answered by Stephen La Rocque. 





A rectangle is three times as long as it is wide. 
20071231 

From Robert: A rectangle is three times as long as it is wide. If the length is decreased by 2 cm and the width is increased by 3 cm, the new rectangle has an area of 42 cm. What are the dimensions of the original rectangle? Answered by Penny Nom. 





The surface area of the rectangular solid 
20071230 

From Sara: For my math homework i found the volume of a rectangular solid whose deminsions were in feet and the numbers were 10 by 20 by 30
10 = hight
20 = short side base
30 = long side base
and now i have to find the surface area of the rectangular solid....
i know how to do this but i can't get the right answer
it should be 2,200 ft squared but i keep getting 13,00 feet squared Answered by Penny Nom. 





The standard normal distribution 
20071229 

From GEORGE: Statistics texts state that in a normal distribution, 1 standard deviation covers 68%, 2SD 95% 3SD 99.7%. However, on looking at the tables for normal curve areas, the percentage for a z value of 1 is 84.13. 68 % of values are covered at a z value of 0.47. The discrepancies exist even for other values but are smaller. So why is the rule of thumb so different from the Table for Normal Curve areas? Answered by Harley Weston. 





Sally, Charlie and Snoopy in a race 
20071229 

From Marie: Sally and Charlie are having a race. Charlie gets a 900 foot lead and runs 8
inches per second. Sally begins at the starting line and runs at a rate of 5 ft per
second. Charlie's dog is also in the race. Snoopy starts 1100 feet ahead of Sally and runs
toward the starting line at a rate of 1 foot per second.
When will Charlie and Snoopy past each other and how far will they be from the starting line? Answered by Penny Nom. 





Two cars drive in opposite directions 
20071223 

From dale: 2 cars starting from the same point in opposite direction on a straight highway drove 6 miles then turn left and drove 8 miles. How far apart are the cars? Answered by Penny Nom. 





The dimensions of a rectangle 
20071222 

From Justin: I'm trying to find the width of a rectangle. I have its area and its height. The area is 32 inches square and the width is 4 feet (48 inches). Can someone help explain this to me? Answered by Penny Nom. 





A triangle and a rectangle 
20071214 

From Someone: A certain triangle has sides that are, respectively, 6inches,
8inches, and 10 inches. A rectangle with a n area equal to that of the triangle
has a width of 3 inches. What is the perimeter of the rectangle, in inches. Answered by Penny Nom. 





The dimensions of a rectangle 
20071212 

From tara: The length if a rectangle is 5 feet less than twice its width. The perimeter of the rectangle is 38 feet. let w represent the width. write an equation for the perimeter of the rectangle in terms of w. Then solve the equation to find the length and width o the rectangle. Answered by Penny Nom. 





The tangent to a curve 
20071210 

From Christy: I know this question is simple but I can't figure out what I'm doing wrong.
Find the equation of the tangent line to the curve 2x^2  y^4= 1 at the point (1,1). Answered by Penny Nom. 





Mean and standard deviation 
20071210 

From Jamie: Let n be any odd whole number.
a) Which has the greater mean: the odd whole numbers from 1 to n, or the even whole numbers from 2 to n1?
b) Which has the greater standard deviation: the odd whole numbers from 1 to n, or the even whole numbers from 2 to n1? Answered by Penny Nom. 





A triangle and a pentagon 
20071208 

From Olivia: A regular pentagon has an area of 800 square centimetres. What is the area of the triangle extended from one side of the pentagon? Answered by Stephen La Rocque. 





System of equations 
20071206 

From Jenn: change the equation,xy=4 to form y=mx+b
the solution to the system of equations y=2x and y=x+3 is Answered by Stephen La Rocque. 





Chicken and goat feet 
20071205 

From Kim: Old McDonald raises goats and chickens. The animals have a total of
100 heads adn 360 feet. How many goats and how many chickens does Mr.
McDonald have? Answered by Stephen La Rocque and Penny Nom. 





Two cars going in opposite directions 
20071125 

From alexa: two cars leave town at the same time going opposite directions. one of them
travels at 55 mph and the other at 65 mph. in how many hours will they be
150 miles apart? Answered by Penny Nom. 





The maximum area of a rectangle 
20071123 

From Christy: Question from Christy, a student:
Show that among all rectangles with an 8m perimeter, the one with the largest area is a square.
I know this is simple but I'm not sure if I'm doing it correctly. Here is what I did.
1. A = xy
2. 8 = 2x+2y
3. y = 4x
4. A = x(4x) = 4xx^2
Not sure what to do from this point because I don't know if its right. Answered by Harley Weston. 





A ttest 
20071120 

From Rachel: I am wanting to use the ttest to find if temperature over a period of 5 days was significantly different to the mean temperature for that time of year. So i want to compare expected temps to actual temps. The problem is that because the expected temperature is the same for the 5 days it gives me a standard deviation of zero. Does this mean the ttest cannot be used because the ftest can't be calculated. If so is there an alternative test? Answered by Harley Weston. 





Standard deviation 
20071120 

From Shahzada: when and why we use standard deviation in Data analysis? Answered by Harley Weston. 





A rectangular prism 
20071116 

From nicholas: What is the height the surface area to a rectangular prism with a volume of 350 milliliters? Answered by Stephen La Rocque. 





A cylindrical tank 
20071116 

From Mario: I want to determine how many gallons i have inside a cylinder (tank) that is resting on its side (the Height), NOT standing up.
I know V=pi x r2 x H. And 1 cubic foot = 7.48 gallons. Here are the dimensions r=2' H=20'. Now my question is how do I determine how much
liquid i have inside, if the level of the liquid is about 1/2 of the way of its Diameter (in other words 2'). Remember this cylinder is lying
on its side. Answered by Penny Nom. 





A particle moves in the xyplane 
20071112 

From Russell: A particle moves in the xyplane with
X = 2t^3  12t^2 + 18t
Y = 3t^4  28t^3 + 72t^2
find an equation of the line tangent to the given curve at t_0_ = 1
note: t_0_ is t subscript 0 Answered by Harley Weston. 





Stopping distance and speed 
20071111 

From Joanna: The algebraic relation d=0.0056^2 ++ 0.14s models the relation between a vehicle's stopping distance d, in metres, and its speed s, in kilometres per hour.
(a) What is the fastest you could drive and still be able to stop within 80 m?
(b) What is the stopping distance for a car travelling at 120 km/h?
(c) Estimate the length of an average car. How many car lengths does the the stopping distance in (b) correspond to? Answered by Stephen La Rocque. 





The width of a rectangle 
20071107 

From BJ: The perimeter of a rectangular field is yards. If the length of the field is yards, what is its width? Answered by Penny Nom. 





Two cars 
20071104 

From Jalisa: If Car "A" is traveling 50 miles per hour and car "B" is traveling 60 miles per hour, how long will it take car "B" to catch up to car "A" if car "A" had a 15 mile head start. Answered by Penny Nom. 





Constantly accelerated motion 
20071029 

From Priyanka: A, B and C are three points lying in that order on a straight line. A body is
projected from B towards A with speed 3 m/s. The body experiences an
acceleration of 1 m/s^2 towards C. If BC =20 m, find the time taken to reach C and
the distance travelled by the body from the moment of projection until it reaches C. Answered by Stephen La Rocque. 





A car traveled 175m at certain speed 
20071028 

From abdi: A car traveled 175m at certain speed. if the speed had been 20 mph faster,
the trip could have been made in 1 hr less time. find the speed? Answered by Stephen La Rocque. 





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. 





The length of a rectangle is twice the width 
20071026 

From Tami: The length of a rectangle is twice the width. The number of square units in it's arear is four times the number of units in it's perimeter. What are the dimensions of the rectangle? Answered by Penny Nom. 





Given a six by six square, how rectangles are there in the square? 
20071024 

From Maria: Given a six by six square, how rectangles are there in the square? Answered by Stephen La Rocque. 





The length of a rectangle 
20071024 

From Kharez: What is the length of a rectangle with an area of 24 square feet and a width of 4 feet? Answered by Penny Nom. 





Stanley Cup costume (truncated cone pattern) 
20071019 

From Janet: You hockey fans will love this question. I am making a Stanley Cup halloween costume and need a flat pattern for the bowl portion. I believe a truncated cone will work nicely. Base circumference needs to be 32" (10.19 diameter). Top circumference needs to be 44" (14 diameter). It needs to be 8" high. Thanks for your help. Answered by Stephen La Rocque. 





Calculate the dimensions of the rectangle 
20071016 

From Sara: The perimeter of a rectangle is 62cm. The length of the diagonal is 25 cm. Calculate the dimensions of the rectangle. Answered by Stephen La Rocque. 





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. 





The dimensions of a rectangle 
20071014 

From Elizabeth: The perimeter of a rectangle is 20m. The area is 20sqm. Calculate the dimensions of the rectangle. Give your answers correct to two decimal places. Answered by Penny Nom. 





Substitution method 
20071011 

From Kevin: 3xx+2y=36y=11 Answered by Stephen La Rocque. 





Grouped data 
20071008 

From Nimra: The following sets of data represent the distributions of
house prices in the northeast and southwest of a country.
Random samples of 100 houses were selected in each region.
(a) Calculate the mean, median and standard deviation for Answered by Harley Weston. 





Coin jar 
20071007 

From a student: Sally empties his jar of coins. It contains $3.75 in nickels, dimes, and
quarters. The number of dimes is twice the number of nickels and the number
of quarters is three less than the number of nickels. Determine how many nickels,
dimes, and quarters were in the in the jar. Answered by Stephen La Rocque. 





Solving four simultaneous equations (system of four linear equations) 
20071007 

From Johan: I need some help in solving this question
x + 2y  3z + 4w = 12
2x + 2y  2z + 3w = 10
0 + y + z + 0 = 1
x  y + z  2w = 4 Answered by Stephen La Rocque. 





Equation of a tangent line to a function 
20071004 

From Princess: If f ' (x) = 3x^2 +1, find the equation of
the tangent line to f(x) = x^3 + x at x= 1. Answered by Stephen La Rocque. 





Hitting golf balls 
20071003 

From Jessi: Ben is out at the practice range hitting golf balls. How much further will a golf ball with an initial speed of 75.0 m/s go when projected at 45.0 degree than when projected at 30.0 degree? Answered by Stephen La Rocque. 





Will the stone catch up the parachute? 
20071003 

From anoi90: a small parachute dropped from a 30.0 m high cliff falls with a constant velocity of 1.20 m/s. 20.0 s after the parachute is dropped, a stone is dropped from a cliff. Will the stone catch up the parachute before it reaches the ground? (Include numerical proof!) Answered by Stephen La Rocque. 





Motion along a line 
20071002 

From Claudette: If the position function of a particle is x(t) = sin^2(2t), find the distance that the particle travels from t = 0 to t = 2 Answered by Harley Weston. 





A tangent line to a circle 
20070926 

From Randy: Find the equation of the tangent line at coordinates (1 , 4)
on the circle x^2 + y^2  4x  21 = 0
I would like to learn the fastest way to relate any coordinates of a circle
to any possible point of tangency. Answered by Stephen La Rocque. 





Can you tell me how many gallons it holds? 
20070925 

From Jeff: Hi my water tank is 10ft long and 45" around,can you tell me how many
gallons it holds.thankyou jeff Answered by Penny Nom. 





Finding equations, intersection point of two lines at right angles 
20070922 

From Yaz: Find the equation of the line joining A(1,9) to B(6,120). Another line passes through C(7,5) and meets AB at rigth angle of D. Find the euation of CD and calculate the coordinates of D. Answered by Stephen La Rocque. 





Points that are 15 units from the origin 
20070920 

From Paula: Find the coordinates of any point(s) 15 units away from the origin with an
xcoordinate of 9.
I was given the answer: (9,12) and (9,12), but I do not understand how these numbers
were calculated. Thank you for your help! Answered by Stephen La Rocque. 





A rectangle inscribed in a circle 
20070911 

From Sobeida: A rectangle that is x feet wide is inscribed in a circle of radius 8 feet. What is the area of the rectangle as a function of x.
Thanks! Answered by Stephen la Rocque. 





Water in a conical tank 
20070910 

From Greg: Joe is conducting an experiment to study the rate of flow of water from a conical tank.
The dimensions of the conical tank are:
Radius at the initial water level = 13.7 cm
Radius at the reference point = 12.8 cm
Initially the tank is full of water. There is a circular orifice at the bottom of the conical
tank with a diameter of 0.635 cm. The water drains from the conical tank into an empty
cylindrical tank lying on its side with a radius of 0.500 ft and a length L (ft).
Joe observed the water discharged with an average velocity of 1.50 m/s as the water level
lowered from the initial height of 14.0 cm to 5.00 cm in the conical tank. Answer the
following:
1. If the initial height of water in the conical tank is 14.0 cm (measured from the
reference point, see Fig. 1), how long in seconds will it take for the water level to drain to
a height of 5.00 cm?? NOTE: Height refers to the vertical height.
What formula would I use to find out how long in seconds it takes for the water level to drop? Answered by Harley Weston. 





Standard deviation 
20070905 

From Ethan: Okay I have a question about standard deviation.
Can you tell me a five number set of data that will have a standard deviation f zero and how you know that? Answered by Stephen la Rocque. 





The tangent to y = x^3 at x = 0 
20070904 

From Amit: consider the equation = x^3. The equation of tangent to this curve (which is smmetrical in Ist and IVth quadrant) at (0,0) is y=0, which is xaxis.
but graphically one can visulize that xaxis intersects the curve, so how can it be the tangent to the curve. Please help. Answered by Harley Weston. 





Standard deviation 
20070901 

From Pat: I have looked over your math question and mines is not there. for a binomiial distribution with parmeter n and p, the mean is np and the standard deviation is np(1p). I understand how to get the np but not understanding how to get the (1p). For example np=(40)(0.48)(10.48)=3.160. How can I get the (10.48) answer please Answered by Harley Weston. 





A circle and a tangent 
20070827 

From Lindsay: Hello. I'm trying to do a math problem and have searched the internet for equations but have come up empty handed. If you could help, that would be greatly appreciated!
The problem is stated thus: A circle is tangent to the yaxis at y=3 and has one xintercept at x=1.
a. Determine the other xintercept
b. deduce the equation of the circle. Answered by Penny Nom. 





Twocolumn proof for a circle geometry problem 
20070824 

From Kendra: i have to prove that tangents to a circle at the endpoints of a diatmeter are parallel by stating whats given, whats to prove and a plane, then write a two column proof i dont understand this Answered by Stephen La Rocque. 





Tangents to a circle 
20070818 

From Laura: I have tangents from point A and B that intersect at C. A third tangent XY lies in between the two lines that I have already drawn. I measured the perimeter and then I drew another line that was tangent to the circle and was inside the two lines again and measured the perimeter again. The perimeters were the same but I don't know how to prove why this happened and write a theorem for it. Answered by Chris Fisher. 





Area and perimeter 
20070816 

From sheryl: a 50*70 horse pen is 240 feet and 3500 square feet
a 60*60 horse pen is 240 feet and 3600 square feet
why is there a 100 square feet difference? Answered by Penny Nom. 





Two circles C1 and C2 meet at the points A and B 
20070815 

From Jerry: Two circles C1 and C2 meet at the points A and B. The tangent to C1 at A meets C2 at P. Point Q inside C1 lies on the circumference of C2. When produced, BQ meets C1 at S and PA produced at T. Prove that AS is parallel to PQ. Answered by Chris Fisher. 





The area and perimeter of a rectangle 
20070815 

From Brooklyn: Is there a way to find the perimeter of a rectangle if you have the area, or vice versa? If so, what is the equation? Answered by Leeanne Boehm and Penny Nom. 





Circle Geometry 
20070814 

From Robin: In a triangle ABC, angle A=75 and B=60. A circle circumscribes the triangle. The tangents of the at points A and B meet in a point D outside the circle. Show that ABD is an isosceles triangle with a right angle at D. Diagram included. Answered by Stephen La Rocque. 





A round reservoir 
20070814 

From lee: if you have a 46 acre round reservoir, how far around in feet would that be ?? Answered by Penny Nom. 





Diagonals on a cylinder 
20070810 

From John: I have a cylinder that is 37.5" width X 25.25" circumference. I need to create a repeating diagonal lined pattern on the cylinder so that when it prints it joins perfectly at the circumference repeat. The design must follow these specs.
Black diagonal lines need to be 1.250" max width X 1.5" max spacing between the black lines.
Please Help Answered by Stephen La Rocque. 





Find the dimensions of the rectangle that will contain the greatest area 
20070806 

From Julirose: The perimeter of a rectangle is 38 meters. Find the dimensions of the rectangle that will contain the greatest area. Answered by Penny Nom. 





Three runners on a circular track 
20070804 

From Arul: A, B and C run around a circular track starting from the same point simultaneously and in the same direction at speeds of 4 kmph, 6 kmph and 8 kmph respectively. If the length of the track is 400 meters, when will A, B and C meet at the starting point for the first time after they started the race?
4 In the above question, when will they meet for the first time after they started the race? Answered by Penny Nom. 





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. 





At what speed does Chuck travel? 
20070727 

From Jessica: Chuck and Dana agree to meet in Chicage for the weekend. Chuck travels
224 miles in the same time that Dana travels 204 miles. If Chuck's rate of travel
is 5 mph more than Dana's, and they travel the same length of time, at what speed
does Chuck travel? Answered by Harley Weston. 





A football stand 
20070719 

From jean: a football stand 150 yd. long has 20 tiers of seats; each has a rise of 2 ft. and tread of 3 ft. it constructed of reinforced concrete with a cross section of 36*54. find the amount of material used in its construction. Answered by Harley Weston. 





Proving a quadrilateral is a rectangle 
20070714 

From Sonja: I was having this discussion with another teacher and we need a third opinion. When you are trying to prove a quadrilateral is a rectangle which method should you use:
 Prove the shape is a parallelogram by doing slope 4 times by stating that parallel lines have equal slopes. Then proving a right angle by stating that perpendicular lines have negative reciprocal slopes.
 Doing the slope 4 times and stating that the shape is a rectangle because opposite sides are parallel because of equal slopes and it contains a right angle because of negative reciprocal slopes.
I guess the real question is do you have to first state that the shape is a parallelogram? Answered by Stephen La Rocque. 





Finding the radius of an inscribed circle 
20070705 

From Maria: I need to find the radius of a circle which is inscribed inside an obtuse triangle ABC. I know all the angles and all the lengths of the triangle. Answered by Stephen La Rocque and Chris Fisher. 





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. 





Simultaneous equations : the Elimination method 
20070621 

From Patricia: I need to find the value of X and Y using the Elimination method.
5/x + 3/y=4
25/x2/y=3 Answered by Stephen La Rocque. 





How many gallons of water 
20070619 

From Marie: A water treatment plant is built with three cylindrical tanks to contaim the
water for a town. Each tank has a radius of 15 feet and a depth of 25 ft.
If there are about 7.5 gallons in a cubic foot of water, approximately
how many gallons of water can be treated at the plant at any one time? Answered by Stephen La Rocque. 





A square and a rectangle 
20070619 

From Clarence: What is the difference between rectangle and a square Answered by Penny Nom. 





Simultaneous inequalities 
20070618 

From Freddy: Watson Electric has production facilities in Valley Mills, Marlin,and Hillsboro.
Each one produces radios,stereos,and TV sets.
There production capacities are
Valley Mills: 10 radios, 12 stereos, and 6 TV sets per hour
Marlin: 7 radios, 10 stereos, and 8 TV sets per hour
Hillsboro: 5 Radios, 4 Stereos, amid 13 TV sets per hour
QUESTION
How many hours should each plant be scheduled to fill an order of 1095 radios, 1230 stereos,
and 1490 TV sets? 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. 





Standard Deviation 
20070613 

From Adrian: If you are told that the mean salary of a certain group of workers is $30,000 with a standard deviation of $4000, what proportion of workers earn over $38,000? What proportion of workers earn less than $18,000? Assume the distribution of wages is normal. Answered by Stephen La Rocque. 





Throwing a ball from the top of a building 
20070612 

From Gilligan: s = distance (in feet)
Building height = 96 feet
t = seconds
Use s = 96 + 80t  16t^2 to answer the question given below.
QUESTION:
After how many second t will the ball pass the top of the building on its way down? Answered by Penny Nom. 





Two tangent lines to y=x^3 
20070607 

From stephanie: find the equations of two tangent lines to the y=x^3 function through the point (2,8) Answered by Penny Nom. 





Water tank volume 
20070529 

From Cecelia: I HAVE A SEMI CIRCULAR TANK AGAINST A WALL MEASURING 6'10" ACROSS THE WIDEST PART AND 3' FROM THE WALL TO THE FRONT OF THE TANK. THE DEPTH IS 14". PLEASE HELP ME TO CALCULATE THE VOLUME OF WATER IN THE TANK. Answered by Stephen La Rocque. 





System of equations 
20070524 

From Chris: Find all real solutions (x,y,z,w) of the system of equations:
2y= x + x/17, 2z= y + y/17, 2w = z + z/17, 2x= w + w/17 Answered by Penny Nom. 





Normal distribution 
20070524 

From Paula: Consider a data set that is normally distributed.
The mean of the data set is equal to 10,000.
a.) Suppose that, for this data set, 10,625 has a
"zvalue" = 2.5. Solve for the standard deviation of
the data set.
b.) Solve for the "zvalue" of 9,900. Answered by Penny Nom. 





Set up two simultaneous equations 
20070521 

From Admire: The cost of producing windscreen wipers blades at a factory ais partly fixed (due to operating overheads) and partly dependent on the number of blades produced. It costs $300 to produce 1000, and $600 to produce 5000 blades. How much would it cost to produce 24000 blades? Answered by Penny Nom. 





Finding the hypotenuse without Pythagorus 
20070511 

From Shelbie: How do i find the hypotenuse of a right traingle not using the pythagorean thereom if i have the measurements of the legs? Answered by Stephen La Rocque. 





Are proofs important in geometry? 
20070507 

From BJ: Are proofs very important to know how to do?
My daughter has been in Geometry & the teacher skipped proofs. Answered by Penny Nom. 





The dimensions of a rectangle 
20070507 

From Stephanie: The perimeter of a rectangle is 54yds , and the area of the rectangle is 180yds^2 . Find the dimensions of the rectangle. Answered by Penny Nom. 





A tugboat's speed 
20070430 

From Amanda: a tugboat must travel 24 miles against a 4 mile per hour current on the Potomac River and return. At what
constant speed must the tugboat travel to make the trip in 12 hours. Round answer to the nearest tenth mph. Answered by Stephen La Rocque. 





I have N data points in mdimensional space 
20070429 

From Sid: Hi,
Given below is the problem that I am facing:
I have N data points in mdimensional space. I know the mean euclidean distance of the points from one given point (say the origin). Now I wish to find the mean Euclidean distance of the N points from another given point. How can i do this without knowing the values of the N points and only knowing the 2 origin points and the mean distance from one of the origin points ? Answered by Penny Nom. 





Incremental standard deviation 
20070428 

From Murtaza: Hi
In relation my question asked earlier, i would first like to thank you for the prompt reply. But it has not answered my query yet. Let me frame the problem again.
I have a mean value for N data items. (note that i know N but i donot know the distinct N data item values) Now the (N+1)th data item comes in and i calculate the new mean. (incremental method for that is simple). How do i calculate the new standard deviation. The formula you gave me requires me to read the data items once and at the end of the pass i will have have the standard deviation. But i need the STDDEV values at intermediate stages as well. Is it possible ?
Murtaza Answered by Penny Nom. 





What is the speed of the boat? 
20070422 

From Sonja: A boat on a river travels downstream between two points, 20 miles apart, in one hour. The return trip against the current takes 2 1/2 hours. What is the speed of the boat? The answer in the book says 14 mi/hr, but I don't understand how to figure it out. It must be very simple, but I'm stuck. Thank you so much for helping me out. This is a FANTASTIC website! Sonja Answered by Penny Nom. 





Two tangents to a circle 
20070417 

From Doug: Two distinct, nonparallel lines are tangen to a circle. The measurement of the angle between the two lines is 54 degrees (angle QVP).
Suppose the diameter of the circle is 2 cm. What is the distance VP? Suppose the distance VP is 3.93 cm. What is the diameter of the circle? Find a formula for d, the diameter of the circle, in terms of VP.
Find a formula for VP in terms of d, the diameter of the circle. Answered by Stephen La Rocque. 





A gardener has 140 ft of fencing to fence 
20070416 

From Johann: A gardener has 140 ft of fencing to fence in a rectangular shaped vegetable garden. To plant all his vegetables, the gardener needs more than 825 sq ft of space. What are the possibles values for the length of the rectangle that would meet the space requirements? You may assume that the variable x represents the length of the rectangle. Answered by Stephen La Rocque. 





Simultaneous equations 
20070416 

From kyrie: simultaneous equation
4x + 3y = 21
2x * y = 8 Answered by Penny Nom. 





How far apart are the cars? 
20070407 

From ian: 2 cars set off in opposite directions and travel for 6 miles,
they both take a left turn, and travel for a further 8 miles...........
how far apart are the cars???
a) 10 miles
b) 22 miles
c) 20 miles
d) 18 miles Answered by Penny Nom. 





A delivery driver travels from Belfast to an address in Dublin 
20070404 

From Gerry: A delivery driver travels from Belfast to an address in Dublin.The total distance fro the round trip
was x%.The time required for the forward trip was xx hours.Due to heavy traffic during the return trip an extra xx was required
How much slower was the delivery drivers speed on the return trip?.
I was wondering what equation would you use to solve this question. Answered by Penny Nom. 





Tina swims 4 miles upstream at 1 mph 
20070331 

From Michael: If Tina swims 4 miles upstream at 1 mph and back downstream to the same point to the same point at 4 mph, what is her average speed? Answered by Penny Nom. 





Acceptance sampling 
20070329 

From Katrina: The Medassist Pharmaceutical Company recieves large shipments of
asprin tablets and uses this acceptance sampling plan: Randomly select
and test 24 tablets, then accept the whole batch if there is only one or
none that doesnt meet the required specifications. If a particular shipment
of thousands of asprin tablets actually has a 4% rate of defects, what is
the probability that this whole shipment will be accepted? Answered by Penny Nom. 





The angles in a right triangle 
20070328 

From Golaan: I need the to understand the formula for finding either of the acute angles of a right triangle given it's hieght length and base length.
I want to find the degrees of either accute angle. So for this example I have a right triangle with a height of 410 meters and a base length of 1,700 meters.
I don't understand cosine, sine, and tangent or the other ones at all. So if the solution includes those (which I believe it does) could b very verbose yet in a very elementary way?
The purpose of ths is that I have to define the general incline angles (or grade) of various areas of terrain. I know the distance by map and also the the altitude at either endpoint. Answered by Penny Nom. 





An inheritance problem 
20070323 

From Carl: A father of 3 boys, who owns 17 horses dies. He leaves his first son
1/2 of the horses. The sons hate each other. The father leaves the
second son 1/3 of the horses. They are ready to kill each other. He
leaves his youngest son 1/6 of the horses.
Without cutting the horses into pieces how do they split the horses?
I heard this puzzle when I was 12 years old.
1968
The preacher rides up on his horse and said "If I give you my horse will
you quit fighting ? They agree to stop fighting?" Why? Answered by Penny Nom. 





A one pass calculation of standard deviation 
20070319 

From Murtaza: Hi
I searched the listings but couldn't find what i am looking for. I have a dataset and i am allowed only 1 pass through it. At the end of this pass i must have the mean and standard deviation. Calculating the mean is easy as also demonstrated in your listings. I think the same can be done for standard deviation as well. But the doubt that i have is this : Will the calculated standard deviation be sequence dependent ? i.e. if i change the order in which the data items enter the system, will the std deviation also change ??
Thanks in advance
Murtaza 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. 





Two busses 
20070315 

From Devon: A bus leaves a station at 1 p.m., traveling west at an average rate of 44 mi/h. One hour later a second bus leaves the same station, traveling east at a rate of 48 mi/h. At what time will the two buses be 274 mi apart? Answered by Steve La Rocque and Penny Nom. 





The dimensions of a rectangle with least perimeter for given area 
20070314 

From Karlianna: find dimensions of a rectangle with least perimeter for given area
A) 30cm2
b) 50cm2 Answered by Penny Nom. 





Angle of elevation 
20070313 

From Joslyn: A ship at sea sights a 12m high lighthouse on a cliff which is 80m above sea level.
If the angle of elevation to the top of the lighthouse is 27 degrees, calculate the distance from the ship to the shore. Answered by Haley Ess. 





Simultaneous equations with fractions 
20070228 

From Alyca: Hello Math Central, I am a grade 10 student taking Academic math. Our unit right now is method of substitution and elimination. I'm stuck on this one question that I've been doing forever. Please help =)
*For this equation I have to do method of elimination, but it's so much harder with fractions...could some one please explain to me how to do it step by step?* x y 2    =   3 6 3 x y 1    = 1 12 4 2
Answered by Steve La Rocque and Ashley Mang. 





How long does she have to get out of the way? 
20070223 

From Sharon: How do I solve this? The height h (in feet) of an object that is dropped from the height of s feet is given by the formula h = s  16t^2 , where t is the time the object has been falling. A 6 foot tall woman on a sidewalk looks directly overhead and sees a window washer drop a bottle from the 6 story. How long does she have to get out of the way? Round to the nearest tenth. (A story is 12 feet.) Answered by Penny Nom. 





Finding the equation of the circle 
20070220 

From ning: Given the radius of a circle square root of 10 tangent to the line 3x+y+19 = 0 and passing through (0,3), how can i solve the equation of circle? thank you... Answered by Chris Fisher, Steve La Rocque and Penny Nom. 





A common tangent line 
20070220 

From chris: I have this problem I have been working on for days and cannot figure it out. it states: Find the two points on the curve y=x^4  2x^2  x that have a common tangent line.
I know you use the first derivative to find the tangent line so if it is a common tangent line should you find two of the exact same tangent line equations at two coordinate points? Answered by Chris Fisher. 





How far from the port is the point where the ship turned? 
20070219 

From Chris: I was confused on this problem. If a ship leaves port and travel due east. At a certain point it turns 65 degrees south of east and travels b=322 nautical miles to a point 461 nautical miles on a direct line from port. How far from the port is the point where the ship turned? Answered by Stephen La Rocque. 





Increasing speed and decreasing time 
20070218 

From Nigel: I am completely lost...can you help with this: The time, t, to travel a distance, d, at a constant speed, v, can be obtained from the formula: d = vt. If the speed is increased by x, find an expression to represent the decrease in time to travel the same distance. Answered by Stephen La Rocque. 





Square centimeters 
20070212 

From Ivan: how many square centimeters are in a rectangle that is 210 centimeters long by 39 centimeters wide.? thank you Answered by Karen McIver and Melanie Tyrer. 





Simultaneous equations with envelopes 
20070208 

From Mick: There were 17 envelopes bought, some were brown, some were white. The brown envelopes cost one cent more per envelope than the white ones. The total cost was 80 cents. How much of each type of envelope was bought? Many thanks! Answered by Stephen La Rocque. 





Romeo is throwing pebbles 
20070208 

From Jessie: Romeo is chucking pebbles gently up to Juliet's window, and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge of a rose garden 4.5m below her window and 5.0m from the base of the wall. How fast are the pebbles going when they hit her window? Answered by Stephen La Rocque. 





Area of a rectangle 
20070207 

From kyle: paul has enough material to make a fence 22 feet long. he will use this material to fence of a rectangular section of his yard. the rectangles sides must all be whole numbers. i am having a hard time finding the greatest and the least area that he can enclose his fece Answered by Haley Ess. 





A rectangle inscribed in a circle 
20070204 

From Benneth: Consider a rectangle with radius R inscribed in a circle. What are the possible areas of the rectangle? Answered by Steve La Rocque and Walter Whiteley. 





Rectangles and squares 
20070131 

From Shelby: I am doing homework and I need to know why squares are rectangles but not all rectangles are squares? Answered by Penny Nom. 





The substitution method 
20070131 

From Victoria: how do i solve this problem using the substitution method? 2x5= 14 7x+14y= 5 Answered by Stephen La Rocque. 





The elimination method 
20070131 

From Addrianna: x2y=2 3x5y=7 Answered by Stephen La Rocque. 





A thin wire 20 centimeters long is formed into a rectangle 
20070129 

From Trisha: a thin wire 20 centimeters long is formed into a rectangle. if the width of this rectangle is 4 centimeters, what is the length? Answered by Penny Nom. 





A boat travels 60 miles downstream in the same time it takes to go 36 miles upstream 
20070127 

From Liz: A boat travels 60 miles downstream in the same time it takes to go 36 miles upstream. The speed of the boat in still water is 15 mi/h greater than the speed of the current. Find the speed of the current. Answered by Stephen La Rocque. 





Freefalling objects 
20070125 

From Patricia: How long will it take a stone dropped from atop a 1000meter tall building to reach the ground? Answered by Stephen La Rocque. 





A college student jogs from his home to the beach 
20070123 

From Garmani: A college student jogs from his home to the beach at 8 miles per hour. He visits with his friends on the beach for 4 hours, and then his friends drive him home at the rate of 40 miles per hour. If the student returns home after 6 hour, what is the distance from his home to the beach? Answered by Penny Nom. 





What is the speed of each boat per hour? 
20070122 

From Garmani: Two tuna boats leave the same port traveling in opposite directions along the west coast of the United States. One boat travels 5 miles per hour faster than the other. At the end of one day's travel they are 1,080 miles apart. What is the speed of each boat per hour? Answered by Penny Nom. 





A formula for figuring a tanks volume at various levels 
20070120 

From Dave: I know there has to be a general formula to figure out a tanks volume where as you know the total volume but you need to know what it will hold at various levels measured in 1/8th inches in depth and that you may be able to plug this formula into a program like say excel and thus create a chart unique to that tank. But for the lack of me I can not figure it out. Answered by Stephen La Rocque. 





Depth and volume in a cylindrical tank 
20070120 

From Andy: I need to fill a 10 foot diameter by 35 foot long cylinder 85% full. Is there a way to calculate at what depth equals 85%? ie, if I put a stick in the tank would it be at 8.5 feet? Answered by Stephen La Rocque. 





At what speeds were they travelling? 
20070116 

From Maria: Kim and Julie are joining Nicole at her parents cottage for the weekend. The cottage is 150km away from their neighbourhood. Kim can leave directly after school but Julie will be leaving after band practice, an hour and a quarter later. Kim took her time and drove slowly, averaging 20km/h slower than Julie. They both arrived at the same time. At what speeds were they travelling? Answered by Stephen La Rocque. 





Standard deviation 
20070115 

From Kayleigh: After i have added up all the squared deviations what do i do???, what is meant by "divide by one less than the sample size" Answered by Stephen La Rocque. 





What is his rate of walking for the entire trip? 
20070112 

From Garmani: A man walks 500 feet at 4 miles per hour and returns to the starting point at 3 miles per hour. What is his rate of walking for the entire trip? Answered by Stephen La Rocque. 





Throwing a stone downwards 
20070112 

From Momo: a stone is thrown vertically downward with an initial speed of 14m/s from a height of 65 m above the ground. A) how far does the stone travel in the first 2.0 s? B) what is the stone velocity just before it hits the ground? Answered by Stephen La Rocque. 





Find the area of the rectangle 
20070109 

From Mike: The perimeter of a rectangle is 72 in. The base is 3 times the height. find the area of the rectangle? Answered by Penny Nom. 





What is the speed of the current? 
20070107 

From Bob: A motorboat can maintain a constant speed of 16 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes. What is the speed of the current? Answered by Haley Ess. 





Are all rectangles trapezoids? 
20070105 

From Sarah: Are all rectangles trapezoids? Answered by Chris Fisher. 





A quuadratic equation 
20061222 

From Harold: L=3w4 A=96Square I used the quadratic equation to solve and my answer is still wrong
I convert the square of 1168 to decimal.
here is where i start (3w4) x w=96
could you give me an example Answered by Stephen La Rocque. 





Cary was going to meet Jane at the airport, ... 
20061211 

From Carmen: cary was going to meet jane at the airport, if he traveled 60mph, he would arrive one hour early, and he traveled 30 mph, he would arrive one hour late. how far was the airport? recall: distance=speed(time) Answered by Stephen La Rocque. 





Rate of a boat and a river 
20061209 

From Dale: If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hour, the rate of the river and the rate of the boat in still water respectively are ____? Answered by Stephen La Rocque. 





The Metra and the Amtrack 
20061203 

From Amy: A Metra commuter train leaves Union Station in Chicago at 12 noon. Two hours later, an Amtrak train leaves on the same track, traveling at an average speed that is 50 miles per hour faster than the Metra train. At 3PM the Amtrak train is 10 miles behind the commuter train. How fast is each going? Answered by Stephen La Rocque and Penny Nom. 





A trip on the Grand River 
20061130 

From Kristy: Romo decided to make a 28km trip up and 28km trip down the Grand River. the speed of the current is 3km. one way Romo travelled with the current and the other way against the current. During his trip, Romo stopped for half an hour for lunch. if Romo's total trip lasted 6hours, how fast did he travel? Answered by Stephen La Rocque. 





Dimensions of a rectangle 
20061122 

From Terri: How can you find the dimensions of a rectangle that has a perimeter of 18 feet? Answered by Stephen La Rocque. 





Circle geometry 
20061119 

From Namrata: AB is a diameter and AC IS A CHORD OF A CIRCLE SUCH THAT angle=30. the tangent at C intersect AB produced in a pointD. Prove that BC=BD. Answered by Stephen La Rocque. 





Two trains left the station at the same time and traveled in opposite directions. 
20061118 

From Tori: Two trains left the station at the same time and traveled in opposite directions. The E train averaged 130 km/h. The A train's speed was 110 km/h. In how many hours were they 480 km apart? Answered by Stephen La Rocque. 





Find the distance function s(t) given the acceleration function a(t) 
20061116 

From David: Find the distance function s(t) of the acceleration function: a(t)= sin(0.1t)/ cos^3(0.1t) Answered by Penny Nom. 





Tangent lines 
20061109 

From Melissa: let f be a function with f(1)=4 such that for all points (x,y) on the graph of f the slope is given by (3x^(2)+1)/(2y)
a.)Find the slope of the graph of f at the point where x=1. b.)Write an equation for the line tangent to the graph of f at x=1 and use it to approximate f(1.2) c.) Find whether f is concave up or concave down when x=1. Is your answer in part b an overestimate or an underestimate? Answered by Stephen La Rocque. 





Simultaneous equations 
20061106 

From An other: e^2yx+2=0 ln(x+3)2y1=0 Answered by Penny Nom. 





Going from one town to another 
20061104 

From Austin: Going from one town to another,a man drives his car at 35 miles an hour and returning he drives at 25 miles an hour. the round trip takes 6 hours. Find the distance between the towns. Answered by Stephen La Rocque. 





The dimensions of a rectangle 
20061102 

From Ben: A rectangle's length is 8 cm. greater than its width. Its perimeter is 128 cm. Find its dimensions. Answered by Penny Nom. 





Paddeling on the Alleman River 
20061031 

From Anita: Len is planning a threehour trip down the Alleman River and back to his starting point. He knows that he can paddle in still water at 3 mph and that the rate of the current is 2 mph. How much time can he spend going downstream? How far downstream can he travel? Answered by Penny Nom. 





The distance from a point to a line in 3 space 
20061029 

From Marie: find the distance from the point (1, 2, 3) to the line x = y = z2 Answered by Penny Nom. 





How do you find the length and width of a rectangle if you know ... 
20061015 

From Anne: How do you find the length and width of a rectangle if you know the perimeter of the rectangle is 48 m and the area is 144 m squared? Answered by Stephen La Rocque and Penny Nom. 





Standard deviation 
20061004 

From Jennifer: I was wondering how to figure out a standard deviation if you only have the mean of the data and no other information? Answered by Stephen La Rocque. 





A 5x2 rectangle 
20061003 

From Stanley: Cut a 5x2 rectangle into 4 pieces, and then put them back into as a square. Answered by Claude Tardif and Penny Nom. 





How long will it be before the two snails meet? 
20060921 

From Brett: Two snails are 8.5 feet apart. They start to crawl toward each other at the same time. One of them travels at the speed of 6 in. per minute, while the other zips along at 11 inches per minute. How long will it be before the two snails meet? Answered by Penny Nom. 





A rectangular tank 
20060919 

From Milton: What size rectangular tank will I need to hold 841.5 gallons of water. The water level is 3'0" from the bottom of tank. Answered by Penny Nom. 





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. 





How high (in feet) is the mountain? 
20060829 

From Briana: A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 29 degrees. From a point 2000 feet closer to the mountain along the plain, they find that the angle of elevation is 31 degrees.
How high (in feet) is the mountain? Answered by Stephen La Rocque. 





The capacity of our hexagon fish tank 
20060726 

From Doug and Andrea: My name is Andrea and my son, Doug, and I were wondering what the capacity of our hexagon fish tank was but it’s been so long since I’ve been to school that I’ve forgotten the formula to do so. Would you please help us? The dimensions are: 27 ¾ W x 24L x 29H or one side (glass panel) is 14W x 29H. Answered by Penny Nom. 





The dimensions of a rectangle 
20060709 

From Lori: The length of a rectangle is 1 cm more than 3 times its width. If the area of the rectangle is 61 cm2, find the dimensions of the rectangle to the nearest thousandth. Answered by Penny Nom. 





Flying with and against the wind 
20060706 

From Tim: When a plane flies with the wind, it travels 800 miles in 4 hours. Against the wind it takes 5 hours to cover the same distance. Find the rate of the plane in still air and the rate of the wind. Answered by Stephen La Rocque. 





A tangent to a circle 
20060705 

From Izumi:
I have problems finding the point of tangency between the circle C
x^{2} + y^{2} + 4x  6y  12 = 0
and the tangential line that passes through the point P (6, 1).
Answered by Stephen La Rocque. 





A boat travels 60 miles upstream ... 
20060528 

From Teenarick: A boat travels 60 miles upstream against the current in 3 hours. It takes 2 hours for the return trip. Find the speed of the boat in still water. Answered by Penny Nom. 





Simultaneous Equations 
20060524 

From Angie:
Question: solve the equations
2x3yz=0
3x2y+z=5
x+3y2z=14
for x,y,z
Answered by Stephen La Rocque. 





The interior angles of a right triangle 
20060520 

From Greg: I am wondering if there is a way to figure out the interior angles of a right triangle if we know ONLY the side lengths, and the trick is, we CANNOT use arctangent! Answered by Leeanne Boehm and Penny Nom. 





The distance to the moon from earth 
20060519 

From Maira: Using trigonometric functions first, show how to find the distance to the moon from earth and then find the radius of the moon. Answered by Stephen La Rocque. 





Absolute Value vs. Standard Deviation ? 
20060424 

From Sonia: Why we don't just take the average of the absolute value of difference scores (use the mean deviation) to describe variability instead of calculating the standard deviation? Answered by Claude Tardif. 





Geometry proof 
20060423 

From Jade: From a point P outside a circle with centre O, tangents are drawn to meet the circle at A and B.
a) Prove that PO is the right bisector of the chord AB.
b) Prove that Answered by Stephen La Rocque. 





Distance to the horizon 
20060420 

From Raymond: If I stand on the edge of the sea on a beach and look into the horizon, is there a way or formula for calculating the distance from myself to the horizon? Answered by Stephen La Rocque. 





Two circles 
20060407 

From Louisa: One circle of radius 7cm is touching another circle of radius 4cm. These circles are on a line and the problem is to find the length AB where A is the point marking the bottom of the radius of one circle and B is the point marking the bottom of the radius of the other circle. Answered by Stephen La Rocque. 





2x+5y=3 And x+3y=7 
20060403 

From Lloyd: simplify 2x+5y=3 And x+3y=7
Answered by Penny Nom. 





Wes and Tony live 360 km apart. 
20060401 

From Thiru: Wes and Tony live 360 km apart. If Wes travels at 80 km/h towards Tony. And Tony travels at 100 km/h towards Wes, how long will it take before they meet. Answered by Penny Nom. 





How far from Earth is Neptune? 
20060321 

From Scott: A laser beam travelling at the speed of light bounces off the planet Neptune and returns to Earth in 29 960.72 s. The speed of light is 299 792.5 km/s. How far from Earth is Neptune? Answered by Penny. 





If a circle is elongated into an oval .. 
20060316 

From Bruce: If a circle is elongated into an oval, with constant circumference, does the area remain constant? Answered by Walter Whiteley. 





A 3dimensional star 
20060315 

From Rachel: I am trying to figure out the name of a figure that consists of 8 (I think) square pyramids. There is a net drawing of this figure somewhere and I can't find it because I don't know the name. When all 8 pyramids are connected, they form a '3dimensional star'. We did this project when I was 14 years old and I am now a 27 year old teacher and I would love to do this project with my kids.
Answered by chris Fisher. 





Rectangles with the same perimeter 
20060314 

From Kristine: If two rectangles have the same perimeter, will they also have the same area? Why Answered by Penny Nom. 





2x+3y=0 and 3xy=0 
20060314 

From Lisa: my name is lisa I am doing math for work and i have a math problem to solve and i need help with it here is the question 2x+3y=0 and 3xy=0 this is one question can you help me please Answered by Penny Nom. 





The number of gallons in a tank 
20060309 

From Doug: We have a round tank that is 216 inches long 64 inches wide across ; how do we find the number of gallons it could hold ? Answered by Stephen La Rocque. 





The volume & surface area of a rectangular pyramid. 
20060227 

From Cheryl: My daughter is working on a math project & we are having a hard time finding the volume & surface area of a rectangular pyramid. Can you help us with this? Answered by Penny Nom. 





Luke and Slim have only one horse. 
20060226 

From Emily: Luke and Slim have only one horse. Luke rides for the agreed on distance and then ties up the horse for Slim, who has been walking. Meanwhile, Luke walks on ahead. They alternate walking and riding. If they walk 4 miles per hour, and ride 12 miles per hour, what part of the time is the horse resting? Answered by Penny Nom. 





Traveling from Asheville to Indianapolis 
20060221 

From Grace: Carol was traveling from Asheville, North Carolina, to Indianapolis, Indiana, by bus. At the halfway point of her trip, in terms of distance, she fell asleep. When she awoke, her distance to Indianapolis was half the distance that she had traveled while she slept. For what fraction of her trip did Carol sleep? Answered by Penny Nom and Stephen La Rocque. 





Related rates and an oil spill 
20060212 

From Brandon:
An Oil Tanker Spills 100,000 cubic meters of oil, which forms a slick that spreads on the water surface in a shape best modeled by a circular disc is increasing at a rate of 3m/min (it doesn't state what is increasing at 3m/min, so I'm assuming Radius until I can ask my teacher.) At t=T, the area of the "circular" slick reaches 100pi Sq. meters.
A) how fast is the area of the slick increasing at t=T
B)How fast is the thickness of the slick decreasing at t=T
C)Find the rate of change of the area of the slick with respect to the thickness at t=T.
Answered by Penny Nom. 





Degree 
20060209 

From Jessica: I am a 9th grade home school student and have started doing degrees of terms in my math book. The following is some examples they give:
25a to the 4th power is a 4th degree term
67c to the 9th power is a 9th degree term
x is really x to the 1st power so it is a 1st degree term
10 is really 10x to the 0 power so it is a 0 degree term
They go on to say that every constant is a zero degree term.
My question is why isn't a constant, like 10, simply to the 1st power (making is a 1st degree term) like x. Answered by Claude Tardif. 





A locus problem 
20060208 

From Jason: If the distance from p(1,5) is 3/4 that of the distance of a(4,3)? find the equation of a locus. Answered by Penny Nom. 





One boundary of a pond is parabolic in shape. 
20060120 

From Glenn: One boundary of a pond is parabolic in shape. The boundary passes through the points A(20,45), B(40,40) and E(30,35). The equation of the parabola is of the form y=ax2+bx+c. Find the equation of the parabola and the coordinates of the vertex of the parabola. Any assistance you could provide would be greatly appreciated. Answered by Penny Nom. 





A sequence of circles and tangents 
20060116 

From Paul: Consider a circle whose center is (2,2) and whose radius is 1, and the
straight line that goes through the origin and that is tangent to this
circle so that the intersection between them is as shown in the attached
picture. With this new point we make a new circle whose radius is half
of the first one, and we calculate the corresponding intersection point
with the same suppositions as in the first case. We repeat the process
to the infinite. Find the distance between the center of the circle in
the infinite and the origin (point (0,0)). Answered by Chris Fisher. 





What initial velocity is required to double the maximum height 
20060114 

From A photographer: A body is thrown into the air with an initial velocity V ft./sec. What initial velocity is required to double the maximum height previously obtained? Answered by Penny Nom. 





60.5 ft at 90 mi/hr takes how long? 
20060113 

From Bree: A ball travels over 60.5 ft at 90 mi/hr. How fast does the ball travel? Answered by Penny Nom. 





A rectangle has a length that is 7cm more than twice the width 
20051221 

From Stephanie: A rectangle has a length that is 7cm more than twice the width. The area of the rectangle is 60cm squared. Find the dimensions of the rectangle. Answered by Penny Nom. 





Simultaneous Equations 
20051221 

From Matt: I have these two equations,
336 = 60a + 10b
and
432 = 84a + 6b
Am I right in saying both a and b are 4.8? Answered by Penny Nom. 





Four tangent circles 
20051206 

From Ananth:
I have one bigger circle A with radius 15.
Inside this bigger circle i have another circle B with radius 3 which touch this bigger circle. Have another circle C with radius 4 which touches A and B. I would like to draw a biggest circle which touches A,B and C.
Answered by Chris Fisher. 





A long distance call 
20051205 

From A student: The Small World long distance phone company charges 55cents for the first minute of a long distance call and 23cents for each additional minute.
1. How much would a 10 minute longdistance call cost?
2. If a call costs $4.55. how long did the call last?
3. Write an equation for the total cost, C, of an mminute longdistance call. Answered by Penny Nom. 





A standard normal probability 
20051119 

From Pat: Find the probability of Z when it lies between 1.10 and 0.36 Answered by Penny Nom. 





A variable rectangle 
20051108 

From Mussawar: find the lengths of the sides of a variable rectangle having area 36 cm^{2} when its perimeter is minimum i do not want solution of this question. i would like to know what is mean by variable rectangle.and what is difference between rectangle and variable rectangle.also what is mean by when its perimeter is minimum. Answered by Penny Nom. 





Equidistant from the points (2,1,1) and (0,1,3) 
20051106 

From Roy:
Find the point on the yaxis that is equidistant from the points (2,1,1) and (0,1,3).
Find the point not on the yaxis that is equidistant from the points (2,1,1) and (0,1,3).
Answered by Penny Nom and Walter Whiteley. 





A tangent to a parabola 
20051102 

From A student: Find the point on the curve y=x^{2} where the tangent to the curve is parallel to the secant line connecting (1,1) and (2,4) Answered by Penny Nom. 





Simultaneous equations 
20051013 

From Daniel: 5x + 3y = 22
4x  7y = 20 Answered by Penny Nom. 





Means of sample means 
20051012 

From Fareeha: A population consists of six numbers 1,2,3,4,5,6
a) How many different samples of two numbers can be selected with replacement? and list them.
b) Calculate the mean and standard deviation of the population
b2) Calculate the mean and standard deviation of the mean of the samples.
c) Find the standard error of your estimated mean in question b2 and compare with the estimated standard deviation in b2. Answered by Penny Nom. 





Coefficients, constants and like terms 
20051005 

From Elizabeth: In the equation 8y+6ab+73ab what are the coefficients; the like terms and constants? Answered by Penny. 





City A is 30 miles directly north of City C 
20051004 

From A student: City A is 30 miles directly north of City C, and City B is 40 miles directly east of City C. Cities A and B are connected by a straight road. Find the length of the shortest path from City C to the road that connects A and B. Answered by Penny Nom. 





Volume of a tank 
20050911 

From Jim: We own an Rv and need to actually know the volume of our fresh water tank. I think I'm getting the run around from the manufacturer. I'm unable to locate my chemistry books from from collage. I know there is a formula for the volume of a rectangle some place. Answered by Penny Nom. 





A normal distribution problem 
20050808 

From Brad: The life of a toy is normally distributed. Suppose 92.51% of the items lives exceeding 2,160 hours and 3.92% have lives exceeding 17,040 hours. Find the mean and the standard deviation. Answered by Penny Nom. 





Two tangents to a circle 
20050618 

From Tej: The tangents drawn from points M and N of a circle
having centre O intersect each other at point P. If
angle MPN=60 degrees, NM=10, then find the radius of
the circle and Area of quadrilateral OMPN. Answered by Penny Nom. 





Gallons in a tank 
20050402 

From Jim: Would you be so kind as to help me with a problem? My memory has failed me in remembering how to calculate how much liquid in gallons a tank will hold. The tank is 8 feet long and 44 inches in diameter. Answered by Penny Nom. 





The integral of tan^4x 
20050331 

From Nicole: college student. need help with tough integral.
the integral of 2tan^{4}xdx
Answered by Penny Nom. 





The shortest distance from a point to a line 
20050330 

From carly: Find the shortest distance from the point (15, 2.5) to the line 5x+6y=30. Answered by Penny Nom. 





Gasoline in a cylindrical tank 
20050323 

From Jennifer:
Gasoline is stored in a tank which is a cylinder on its side. Height of fuel is "h" meters and the diameter is "d". The length is "l".
I need to find the amount of gas in the tank when the height is h and also to calculate the fraction of how full it is.
Also, the part I am really confused on is this one,
E(h/d) is the error of the function of h/d, when h/d is used to measure how full the tank is. For what value of h/d is the error maximal?
Answered by Penny Nom. 





Tangents to a circle 
20050319 

From Sue:
You're given the equation to a circle (x3)^{2 }+ (y3)^{2} = 4
and you need to do 3 things:
1. Find a point on the circle
2. Construct an equation for a tangent line to the circle and through the point
3. Plot the circle, point and the tangent line on one graph
Answered by Penny Nom. 





The volume of a stock tank 
20050313 

From Cord: I am a farmer and I have recently installed a new stock tank which is 1650" in circumference and 10' deep. How many gallons of water will it hold? Answered by Penny Nom. 





Three tangent circles 
20050125 

From Kate: Two circles, C1 and C2, touch each other externally; and the line l is a common tangent. The line m is parallel to l and touches the two circls C1 and C3. The three circles are mutually tangent. If the radius of C2 is 9 and if the radius of C3 is 4, what is the radius of C1? Answered by Chris Fisher. 





Standard deviation 
20050102 

From Urial: Find the standard deviation of the given data set
To get the best deal for CD dealer, Jessica called eight appliance stores and asked the cast of a specific model. The prices she quoted are listed below.
$300, $203, $272, $332, $440, $119, $129,$254
Answered by Penny Nom. 





The gradiant of a hill is 9% 
20041218 

From Jim: The gradiant of a hill is 9%. What angle is created by the run/rise of the hill and 0 degrees? Answered by Penny Nom. 





The tangent line at an inflection point 
20041128 

From Louise: the equation of the tangent line to the curve y = x^{3}  6x^{2} at its point of inflection is... Answered by Penny Nom. 





Is a square a rectangle? 
20041121 

From Carol: I am a teacher. In an FCAT sixth grade review test, there was a question to the students to draw a square and then they referred to it as a rectangle.
What is the definition that makes a rectangle a square that can be taught to the students without confusing them. Answered by Walter Whiteley. 





A standard deviation test 
20041109 

From Karen: How do you compare to see if a sample standard deviation is different than the population standard deviation? I know how to compare means, but not standard deviations. Answered by Penny Nom. 





The combined force of two vectors 
20041030 

From Brian: Two teams are playing push ball with a large 8 foot diameter ball. One team exerts a force represented by the vector a = 2i + 5j, and the other team exerts a force represented by the vector b = 8i3j.
1.Determine the direction of movement of the ball if the i axis is due east.
2.Determine the combined force magnitude. Answered by Harley Weston. 





The force of a 5000 tonne lorry 
20041027 

From Aaron: A 50 tonne lorry is parked on a slope with a gradient of 4%.
Due to the self weight of the lorry, what is the force
* acting down the slope
* acting normal (at right angles) to the slope Answered by Penny Nom. 





A rate of change problem 
20041015 

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





A common tangent line 
20041005 

From Shanup: The xaxis is a common tangent of y = x^2 and y = x^3. Find the equation of another common tangent. Answered by Penny Nom. 





The length of a rectangle 
20040926 

From Rebecca: My question is each side of a square S is 18 inches long and the area of S is at least 3 times the area of a rectangle that is 9 inches wide. What is the greatest possible length in inches of the rectangle? Answered by Penny Nom. 





Incremental variance 
20040923 

From Carlos: I must keep statistical data (mean and variance) in 3 granularity levels depending on the age of the data (daily for older than 1 year, hourly for older than 1 month and quarterhour for older than 1 day). How can I calculate the resulting variance from a set of variances previously calculated supposing I have the count and mean for each member of the set? Answered by Andrei Volodin 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. 





A tangent to a hyperbola 
20040802 

From A student: The equation of a hyperbola is 32x*2 18Y*264x +72y +248=0. The equation of a tangent line to this hyperbola is y= (16/15)X + 10/3 I have been trying to find the point where this line intersects the graph. What I did was solve for x and then plugged in the result into the equation of the hyperbola, but I am getting two answers and I am supposed to get only one because the line is tangent to the graph. For this reason, I would like to know what I am doing wrong or what I have to do to know which answer is correct. Answered by Penny Nom. 





Two vector problems 
20040714 

From Jaye: Two force, 120lb and 200lb, act on a body and make a 52 degree angle w/ ea. other. What's the magnitude of the resultant of the forces and what is the measure, to the nearest degree, of the angle that it makes with the 200lb force? Answered by Penny Nom. 





The tangent of theta 
20040710 

From Jacob: P is a point on a unit circle with coordinates(0.6,0.8). Find tan of theta. My book shows me how to do it,"tan of theta=opp./adj.=0.8/0.6=4/3,"and leaves it as that's the answer(4/3).When do we know from a problem to find the angle measure (in this case, the angle measure of theta) and how do we know when to give something like 4/3 without converting it to the angle measure? Answered by Penny Nom. 





What is the name of a 3D rectangle? 
20040607 

From Jack: if a cube is a 3D square, what is the name of a 3D rectangle? Answered by Penny Nom. 





A tangent to a quadratic 
20040604 

From Jem: I have a question on the tangent to a quadratic curve.
Say I have a curve y = ax^{2} + bx + c. The gradient, using the derivative of y, at any point x on the curve is: 2ax + b right? Then, for the tangent that cuts the curve at a point x, the equation of the tangent can be: y1 = (2ax + b)x1 + d.
My question is, how is the point d of this tangent determined? It is the point on the yaxis where the tangent cuts isn't it? Is there a formula for it? Answered by Penny Nom. 





The center of a circle 
20040526 

From Wan: I am trying to find the radius of an arc. The only things i know about the arc is all referenced from the line of tangency to the arc. on both sides i have a differnt horizontal perpendicular distance to the point of tangency.
left side * right side (*=point of tangency). Then i have 2 difference vertical perpendicular distance of the end points to the line of tangency. I know it sounds very bad in text but this is all i know about the arc. Can you help me find the radius? Answered by Penny Nom. 





How far apart are they? 
20040523 

From A student: 2 cars start at same loc. drive opposite direction for 6 miles then they each turn left and travel for 8 miles how far apart are they? Answered by Penny Nom. 





The dimsenions of a room 
20040518 

From Estella: I have a room that is rectangular the area is 159.5 feet, the perimeter is 51 feet what would the dimensions of the room. Answered by Penny Nom. 





Area and perimeter 
20040312 

From Sandy: The rectange has an area of M square units and a perimeter of 2M units. What is the value of x?
The length of the rectange is 3, while the width of the rectange is x1. Answered by Penny Nom. 





Distance, time and rate 
20040309 

From Peter: A car travels from one city to another at the speed of 32mph, if it had gone 4mph faster it could have made the trip in one half hour less. How far apart are the cities?
Answered by Penny Nom. 





A geometry problem 
20040304 

From Jennifer: I need help with this problem: Square ABCD has side length 2. A semicircle with diameter AB is constructed inside the square, and the tangent to the semicircle from C intersects side AD at E. What is the exact length of CE?o Answered by Chris Fisher. 





Volume of a fuel tank 
20040301 

From Mike: I have a fuel ank for my big truck that has a radius of 24inches and a length of 65 inches. I am trying to compute the volume of fuel in the tank. I tried pie x the radius squared times the length but no usable results.
Can you help me please? Answered by Penny Nom. 





The dimensions of a rectangle 
20040221 

From Jane: A rectangular label has an area of 176cm2 and a perimeter of 54cm. Find the dimensions of the label. Answered by Penny Nom. 





A pyramidshaped tank 
20040213 

From Annette: The base of a pyramidshaped tank is a square with sides of length 9 feet, and the vertex of the pyramid is 12 feet above the base. The tank is filled to a depth of 4 feet, and water is flowing into the tank at a rate of 3 cubic feet per second. Find the rate of change of the depth of water in the tank. (Hint: the volume of a pyramid is V = 1/3 B h , where B is the base area and h is the height of the pyramid.) Answered by Harley Weston. 





Driving from Sarnia 
20040211 

From Jane: "Crystal drove from Sarnia at 80km/hr. Emily left Sarnia one hour later and drove along the same road at 100km/hr. How far from Sarnia did Emily overtake Crystal?" Answered by Claude Tardif. 





The London marathon 
20040127 

From Nina: After a years training, Minnie Midriffe increased her average speed in the london marathon by 25%. By what percentage did her time decrease?o Answered by Penny Nom. 





Business trip 
20031219 

From Ameer: A businnessman drives from Washington, D.C., to Boston, a distance
of 442 miles, and then makes the return trip. On the way to Boston,
he drives 65 miles per hour, taking an 1hour rest stop during the
drive. After finishing his business in Boston, he make the return
trip driving at 60 miles per hour and takes a 45minute rest stop
halfway through the trip. Which leg of the journey, Washington, D.C.
to Boston, or Boston to Washington, D.C., takes the longer time? Answered by Penny Nom. 





A fish tank 
20031126 

From Bill: How do I work out the volume and weight of water in a fish tank that is 36in x 14in x 12in? Answered by Penny Nom. 





A point and a line 
20031119 

From Meenakshi:
Given a line segment L(x_{1},y_{1})
to (x_{2},y_{2}) and a Point P(x_{3},y_{3}).
I need the formula to find a point on the line L that is closest to
the point (x_{3},y_{3}). Answered by Penny Nom. 





A rectangle on a disk 
20031029 

From Arthur: How do I go about solving the following problem: What is the width of the largest rectangle with a length of 16 inches you can cut from a circular piece of cardboard having a 10 inch radius? Answered by Penny Nom. 





Squares in a rectangle 
20031021 

From Raj:
Draw a rectangle with sides of 3 and 4. Divide the sides into 3 and 4 equal parts respectively. Draw squares joining the points on the sides of the rectangle. You will have 12 small squares inside the 3 x 4 rectangle. If you draw a diagonal of the rectangle, it will intersect 6 of the the 12 smaller squares. Similarly, if you have a 4 x 10 rectangle, the diagonal would intersect 12 of the 40 squares inside the rectangle. Is there an algebric equation that determines the number of squares that will be intersected by the diagonal of a rectangle? Answered by Chris Fisher. 





Statistics from grouped data 
20031009 

From Rebecca:
I have to use a suitable computer package (ie. Excel) to work out the mean and standard deviation of the following:
Price Range No of Houses No of Houses
£`000 Area 1 Area 2
45 and under 50 4 5
50 and under 55 7 12
55 and under 60 14 16
60 and under 70 19 18
70 and under 80 8 3
80 and under 100 5 2
I have used excel to work out mean and standard deviation before, but not in a more complicated example like this. Any advice on where to start would be greatly appreciated. Answered by Penny Nom. 





Standard Deviation 
20031007 

From Rebecca:
I have a task to complete, which is to calculate the mean and standard deviation of something. I have done this but am then asked to write a short explanation of my findings.
I know what the mean is about, and I thought I knew what the standard deviation meant too  shows the variation from the mean. However, on a task I completed earlier the feedback I got said 'you need to tell us that it is talking about the middle 66% of the data'  that has thrown me, I don't understand that. Can anyone help me get my head round this??? Answered by Penny Nom. 





The sketch of a graph 
20031007 

From A student: I was wondering how do you figure out if a graph has a horizontal tangent line. One of my homework problem was to sketch the graph of the following function; (4/3)x^{3}2x^{2}+x. I set f''(x) ( the second derivative) of the function equal to zero and got the inflection point:(1/2,1/6). Also i am having trouble finding the concavity for x>1/2 and x<1/2, i am getting a different answer from the back of the book, the graph i draw looks completely different from the correct answer. Answered by Penny Nom. 





The slope of a tangent 
20031001 

From A student:
find the slope of the tangent to each curve at the given point f(x)=square root 16x, where y=5 Answered by Penny Nom. 





A rectangle in a circle 
20030927 

From Abdu: A rectangle ABCD is inscribed in a circle. If the length of AB is 5 and length of BC is 12, what is the area of circle outside the rectanlge ABCD? Answered by Penny Nom. 





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. 





Area of a rectangular room 
20030911 

From Kelly: The area of a rectangular room is 238 square feet. The width is 3 feet less than the length. What are the dimensions? Answered by Penny Nom. 





A boat travels 12 km upstream... 
20030903 

From Sohaib: A boat travels 12 km upstream and back in 1 hour 45 minutes. If the speed of the current is 3km/hr throughout, find the speed of the boat in still water, giving your answerÝcorrect to 3 decimal places. Answered by Penny Nom. 





Water in a tank 
20030902 

From A parent: if a tank is 48 inches long 14 inches wide and 18 inches deep if a yardstick was inserted into the tank and measured 2 inches of water in the tank how many gallons of water would be in the tank. Answered by Penny Nom. 





A theorem in geometry 
20030902 

From Diego: Please refer to figure in attached file. P is a point on the chord AB of a circle such that the tangent PT which touches the circle at T is equal to AB. How do we prove that PT^{2} = AP x BP. Answered by Dieter Ruoff and Penny Nom. 





A rule with a variable 
20030824 

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





The volume of a fuel tank 
20030816 

From Phil: I hope you can help me out with a small problem. My boat has a fuel tank measuring 1680mm long x 630mm wide x 130mm high. Can you tell me how much fuel it will hold in both litres and imperial gallons. Answered by Penny Nom. 





Two cars 
20030709 

From Nicole: Two cars start off at the same point on a striaght highway facing opposite directions. Each car drives 6 miles, talkes a left turn, and drives for 8 miles. How far apart are the two cars. Answered by Penny Nom. 





Is 3/5 CLOSEST to 0, 1/2 or 1? 
20030709 

From A student: I would like to know is 3/5 CLOSEST to 0, 1/2 or 1. And can 3/10 go either way as to be closest to 0 or 1/2. Answered by Penny Nom. 





The weight of a fish tank 
20030520 

From A ponderer: I had a question pertaining conversion units..I have a fish tank at home and the dimensions are 24, 44, and 48 inches, I want to find out how much it weighs in pounds when filled up with water...knowing water is 62.4 pounds per cubic feet...do I just divide the 62.4 pounds to 12 because I"m trying to find out through cubic inches. Answered by Penny Nom. 





sin theta = 7/8 
20030507 

From Patty: If sin0 = 7/8 and 0 is in quadrant 2, find the other five trigonometric functions of 0. (report your answers in radical form) Answered by Penny Nom. 





A circle, tangent to two circles and a line 
20030430 

From Keith: I have a horizontal line (that is treated as a datum line or the X axis), with two circles having their center points at different heights from that line (X1,Y1 & X2,Y2). The two circles are also at different diameters (R1 & R2). Both circles and the line (XAxis) do not intersect nor are they tangent. My goal is to determine the maximum diameter of an inscribed circle that will fit between all three. Answered by Chris Fisher and Harley Weston. 





A tangent to a circle 
20030418 

From Lech: The line with equation y=mx is a tangent to the circle with equation x2+y26x6y+17=0. Find the possible values of m. Answered by Harley Weston. 





Incremental standard deviation 
20030412 

From Carlos: I need to calculate the standard deviation for a group of data, but I don't know in advance what is the mean. Is there a way to adjust the STDV for each datum without keeping all of the previous values? This is needed basicaly for performance, so I won't need to read twice the same data (spend processing time) nor save the previous values (spend memory). Answered by Andrei Volodin and Penny Nom. 





Can a square be considered a rectangle? 
20030227 

From Carla:
Can a square be considered a rectangle? (since opposite sides are same length and parallel) Would a regular hexagon or octagon be considered a parallelogram since its opposite sides are parallel? or does a parallelogram HAVE to have only 4 sides? Answered by Penny Nom. 





Two airplanes leave Dallas 
20030206 

From A student: TWO AIRPLANES LEAVE DALLAS AT THE SAME TIME AND FLY IN OPPOSITE DIRECTIONS. ONE AIRPLANE TRAVELS 80 MILES PER HOUR FASTER THAN THE OTHER. AFTER THREE HOURS, THEY ARE 2940 MILES APART. WHAT IS THE RATE OF EACH AIRPLANE? Answered by Penny Nom. 





A train with 2 cars 
20030204 

From Michael: A train with 2 cars is traveling at a speed of 80 km/hr from town X to town y, located 800 km from each other. At the same moment that the train departed, a passenger started to walk back and forth from one end of car B to the other at a speed of 100cm/sec. Arriving in town Y, the passenger had already gone and returned 720 times. The length of car A is that of car B plus one fourth of the length of the locomotive, and the length of the locomotive equals the length of Car A plus one fifth of the length of car B. What is the total length of the train? Answered by Penny Nom. 





A rectangular prism 
20030109 

From Julie: How many faces on a rectangular prism and how many bases? Can the base also be a face and can a face also be a base? Answered by Diane Hanson. 





Trigonometry problems 
20021201 

From Chiara:
 Find tan 35pi/4
 Graph y = cos^{2}x  2sinx
Answered by Penny Nom. 





Constructing a tangent to two circles 
20021128 

From Tom: I have two circles, different sizes a known distance from each other. We know the radii of the circles. How do I construct a line that is tangent to both circles relative to the segment that connects the centers of both circles? Answered by Chris Fisher and Penny Nom. 





Miles per hour 
20021128 

From Liz: If a car has traveled 16 miles in 30 minutes, how many miles per hour did they go? Answered by Penny Nom. 





Two tanks of water 
20021108 

From A student: A 2000 L tank containing 550 L of water is being filled with water at the rate of 75 L per minute from a full 1600 L tank. How long will it be before the two tanks have the same amount of water? Answered by Penny Nom. 





Variance 
20021029 

From Ade: I am trying to solve a standard deviation question, I have 30 data points to use, should I group the data before solving for variance or should I just use the raw data. Answered by Andrei Volodin. 





Is a square a rectangle? 
20021020 

From Nona: Are squares rectangles? Third grade math teacher told a student this was true. Grandmother needs confirmation on this! Answered by Claude Tardif and Harley Weston. 





How long will it be before you reach your friend? 
20020916 

From Margaret: Your friend runs at 8 miles per hour and you drive at 40 miles per hour, hence the diatance between you is decreasing at 32 miles per hour. You firend left 2 hours before you so how far has he gone in that 2 hours? How long will it take for the distance between you to decrease to 0 miles if the distance is decreasing at 32 miles per hour? Answered by Penny Nom. 





The tangent to a curve and the tangent of an angle 
20020826 

From A teacher: Is there a relationship between the tangent of a curve(line touching the curve at one point) and tangent (the trigonometric function)? Answered by Chris Fisher. 





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. 





Two equations 
20020726 

From Derek: 1. 3x + 2y = 4 2. 7x + 2y = 24 finding x and y. Answered by Penny Nom. 





Bob swam across a river 
20020522 

From Torri: Bob swam across a river 420 ft wide. A strong current carried him 580ft downstream as he swam. Find x, the distance bob actually swam. Answered by Penny Nom. 





Day care 
20020513 

From Sonam: In many familes, both parents work. as a result, there is increasing need for day care. data was collected; and in one year in Canada, approximately 32% of children aged 0 to 11 years were in day care for at least 20h per week. (a) what is the probability, in a random poll of 60 children form the age of 0 to 11, that more than 15 children are in day care at least 20 h per week? nearest tenth of one %
ANSWER: P(children are in daycare at least 20h)= 60/60C14 = to the answer (b) what is the probability, in a random pool of 60 children that fewer than 20 are in day care at least 20 h per week?
ANSWER: P= 20/60= 33.3% stay in day care for 20h per week, I dont know if these answers are right please help me out. Answered by Andrei Volodin. 





Trains and cracker boxes 
20020429 

From Lindsay: 1)Two trains are 250 miles apart on the same track heading towards eaxh other at 7AM The first train travels at 55mph, the second at 75mph. At what time would they crash? 2)A cracker box measures 12 by 2 by 18 inches. The company wants to double the amount of crackers, but keep the shapes the same[similar] Find the new length[nearest tenth of an inch] Answered by Penny Nom. 





A test drive 
20020423 

From Jennie: At 9 A.M. a test car driving at a constant speed passes a marker 50 miles from it's starting point. At noon the car is about 130 miles from the marker. If the test drive ends at 1:30 P.M., how far will the car be from its starting point? Answered by Penny Nom. 





Pairs of equations 
20020404 

From A student:
high school level student is asking
y=4x x=4y
x+y=5 3x+2y=20
y=x1 3xy=4
x+y=3 2x3y=9
x+5y=4
3x+15y=1
. . .
Answered by Penny Nom. 





Range of values for standard deviation 
20020322 

From Susan: What is the range of values for standard deviation? Is it between 0 and +3? Is it between +1 and +3? Answered by Andrei Volodin. 





15 miles at 13 miles per hour 
20020312 

From Rich: If I were traveling 15 miles at 13 miles per hour how long will it take? Answered by Penny Nom. 





The slope of a tangent line 
20020304 

From Ridley: Suppose a function f(x) has the line 3x+4y=2 as its tangent line at x=5. Find f'(5). Answered by Harley Weston. 





Two circles inscribed in a rectangle 
20020227 

From Amina: Given a rectangle with dimensions L=6, H=5. Two circles are inscribed such that they touch each other(circles are adjacent to each other) and also their circumferences touch 2 sides of the rectangle. One of the circles has radius=4. Find the radius of the other circle. Answered by Penny Nom. 





The substitution method 
20020224 

From Joe: whats the answer to this question? 3x+y=11 x+2y=3 its substitution method i am having alot of trouble figuring it out. send the answer as soon as possible. thank you Answered by Penny Nom. 





Can the standard deviation ever = 0? 
20020216 

From Karen: If given a class of 30 people who take a test with a mean of 80. Can the standard deviation ever = 0? If so, why? Answered by Penny Nom. 





Normal distribution 
20020121 

From Danielle: A teacher gave a test on which the students' marks were normally distributed, but the results were pathetic. The mean was 52% and the standart deviation was 12%. The teacher decided that the top 10% of the students should get A's, the next 20% should get B's, the next 40% should get C's, the next 20% should get D's, and the bottom 10% should get F's. To the nearest percent, what are the cutoff marks that will result in an A, B, C, D, and F? Answered by Penny Nom. 





The distance across a circle 
20020118 

From Douglas: If you know how far around a circle is (say earth) 25000 miles how do you calculate the distance across? Answered by Penny Nom. 





The tangent function 
20020112 

From Justine: if you know that sin45degress = cos45degrees, how do you know that tan45degrees = 1? Answered by Penny Nom. 





The famous "train problem" 
20020112 

From Karen: How do you solve the famous "train problem"? For example, 2 trains leave different stations at the same time. One is traveling at 50 mph and the other at 40 mph. How long does it take them to meet? Answered by Penny Nom. 





Simultaneous equations 
20011217 

From Matthew: 4x + y = 4 2x  3y = 5 what is x and y Answered by Penny Nom. 





Two equations in two unknowns 
20011204 

From Courtney: y = 3x + 2 y = 4x  5
solve for x Answered by Penny Nom. 





Undetermined coefficients 
20011122 

From Hoda: The equation is: y"  2y' + y = t e^{t} + 4 We need to use The method of Undetermined coefficients. I have tried assuming that the solution is Ate^{t}+Be^{t}+C, but all I get is C=4 and I tried (At^{2}+Bt+C)e^{t}+D, but again I get 0=0 when I calculate the first and second derivatives, so i get no information on the constants. Any suggestions? Answered by Harley Weston. 





A tangent line 
20011121 

From A student: write an equation of the line tangent to the graph of
e^{y} + ln(xy) = 1 + e at (e,1) Answered by Harley Weston. 





Area of a quilt 
20011014 

From Jack:
 how would you find the area of the quilt? which is a square
 how would you fined the area of each square?
Answered by Penny Nom. 





Joan and Jan work together 
20010926 

From Karyna: Joan and Jan work together and they set up a bandstand in just 24 minutes, but if Joan does it by herself she takes 1 hour. How long would it take Jan to set up the bandstand by himself? Answered by Claude Tardif. 





Julia goes to work 
20010925 

From Karyna: On one October morning, Julia rides her bike (at 12 miles per hour) from her home to her friend Ida's house; then the two of them walk (at 6 miles per hour) to work. If it takes an hour for Julia to go the 10 miles from her home to work, how far does she walk? Answered by Penny Nom. 





Ciefficient of variation 
20010923 

From Carmen: I have a question from my OAC finite class. I've come across a problem with the coefficient of variation. I have taught my students that there are no units for coefficient of variation and it can be expressed as a percent. So, for example, a set of data with mean of 5 and standard deviation of 100 would have a CV of 5%. But what happens in this situation: the mean is 4meters and the standard deviation is 0.7mm. Is the CV 1.75% or 0.00175% or 0.0175%? I've had some students change leave the units as is, change them both to mm or change them both to meters...so which is it and why? Answered by Penny Nom. 





Standard deviation 
20010922 

From Doug: I was wondering if anybody knows who the founder of standard deviation was? Answered by Penny Nom. 





Ray and Jane 
20010906 

From A student: If Ray and Jane live 150 miles apart and they both leave their house at the same time, Ray goes 30 mph the whole time and Jane goes 50 mph the whole time how many miles are they from Ray's house when they meet? And what is the exact travel time untl they meet. Answered by Penny Nom. 





Joe and his dad 
20010828 

From Sarah: Joe Spout left a campsite on a trip down the river in a canoe, traveling at 6 km/h. Four hours later, Joe's father set out after him in a motorboat. The motorboat traveled 30 km/h. How long after Joe`s father started did he overtake the canoe? How far had Joe traveled down the river when his father overtook him? Answered by Leeanne Boehm. 





Standard angles 
20010805 

From Nagaraj: Why 0^{o} , 30^{o} , 45^{o} , 60^{o} ,and 90^{o} are taken as standard angles in Trigonometry? Why can't we take some other angles as standard angles? Answered by Chris Fisher. 





Linear regression 
20010801 

From A student and a mother: My mom is taking a correspondence course in Simple Linear Regression and Correlation Analysis and we've been arguing about the relationship between the correlation rxy and standard estimate of errorSy.x. I took statistics last year in high school and I remember something about the Sy.x being proportionate to the r. Are they inversely related, directly related, not related, or can only range from 0 to 1.00? Her book doesn't say very much and I believe they are inversely related. She says they're directly related. Answered by Chris Fisher and Penny Nom. 





A trig identity 
20010727 

From Jeff: prove this identity and show steps tan(x/2+pi/4)=secx+tanx Answered by Harley Weston. 





Comparing means and standard deviations 
20010711 

From Shelly: Is there a way to compare means and standard deviations that come from different size samples? Is there an equation that can normalize sample size? Answered by Andrei Volodin. 





Three tangents to a circle 
20010627 

From Stephanie: The three lines PS, PT, and RQ are tangents to the circle. The points S, X, and T are the three points of tangency. Prove that the perimeter of triangle PQR is equal to 2PT. Answered by Chris Fisher. 





The shortest distance from a point to a line 
20010605 

From Kat: Find the shortest distance from the given line. Round to the nearest tenth. (2,1) and x+5y+20=0 Answered by Penny Nom. 





Common solution 
20010602 

From Samantha:
 Solve for common solution: x+y=6 2x3y=2
 Solve for y in terms of x: 3xy=4
Answered by Penny Nom. 





Squares on a chess board 
20010411 

From Tom: It was once claimed that there are 204 squares on an ordinary chessboard (8sq. x 8sq.) Can you justify this claim? "PLEASE" include pictures. How many rectangles are there on an ordinary chessboard? (8sq. x 8sq.) "PLEASE" include pictures. Answered by Penny Nom. 





Prisms 
20010410 

From A fourth grade class: A fourth grade class is curious about the names that have been given to various solid geometric figures based on their shapes: are there names for solids based on a rhombus, a trapezoid, a parallelogram, a decagon, and/or a quadralateral? Answered by Chris Fisher. 





The normal to a curve 
20010408 

From Varenne: I am having SO much trouble tackling this question and don't know what the right answer is... can you help me out? The question is
Find the equation of the normal to the curve y=(x2)^{2}/(1x)^{2} that is parallel to the line x+4y+7=0 Answered by Harley Weston. 





Common tangents 
20010408 

From Anne: I have been working on this problem for a while but I'm not sure I'm getting the right answer: Find the common tangents of 2y=x^{2} and 2y=x^{2}16 Thanks for the help. :) Answered by Harley Weston`. 





Where do the lines y=2x4 and y=x1 intesect? 
20010406 

From Bryce: solve the following problem by setting them equal to each other. Solve for x and y. Where do the lines y=2x4 and y=x1 intesect? Answered by Penny Nom. 





The unit circle and trigonometry 
20010405 

From Ashley: "My teacher wants us to find out what a unit circle is, which I found out, a circle with the radius of 1, but the problem is he wants us to show the relationship between the unit circle and the sine(30,45,60 degrees), cosine(30,45,60 degrees),and tangent ratios(30,45,60 degrees). I need help with this and my teacher will not help us out. Thanks very much ... Answered by Penny Nom. 





Sigma 
20010331 

From A student: What does the Sigma symbol mean in mathematics? Answered by Penny Nom. 





Systems of equations 
20010316 

From joy: How do u solve problems using systems of equations? ~ finding x and y~ ex:
26 = 3x  2y 42 = 4x + y Answered by Penny Nom. 





The angle of elevation 
20010308 

From Jeffrey: At a Certain time, a vertical pole 3m tall cast a 4m shadow. What is the angle of elevation of the sun? Answered by Harley Weston. 





The substitution method 
20010305 

From A student: Solve each system of equations by the substitution method. Show your work.  y = 8
7x = 1  y
 y = x  1
4x  y = 19 Answered by Penny Nom. 





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. 





cot(arcsin 3/5) 
20010107 

From Jason: Find value. Assume that all angles are in Quadrant 1. cot(arcsin 3/5) Answered by Harley Weston. 





Filling a tank 
20010102 

From Liting: Water flows into a rectangle tank which measures 4 m by 3 m by 2.8 m through a cylindrical pipe of radius 2.4 cm. If the rate at which the water flows into the tank is 8 km/h, find how long it takes to fill the tank. Answered by Penny Nom. 





The aspect ratio of a rectangle 
20001204 

From Ron Delavigne: The aspect ratio of this rectangle is 4:3. That is A to B is 3. And B to C is 4. If I know the lenght of A to C is 19 inches, how can I find the length of A to B, and B to C. Answered by Penny Nom. 





Triangles and trigonometry 
20001130 

From Mose: If I have a right triangle, and I know the lengths of all three sides, is there a formula that will allow me to determine the measurements of the 2 non right angles? Answered by Harley Weston. 





Connecting to a water line 
20001020 

From Vanja: My question is...A house is to be connected to a new water main that runs along the line y=2/3x1. The connection point at the house has coordinates (2,9), where the units represent metres. What lenght of plastic pipe is needed to connect to the water main at the closest point? Answered by Penny Nom. 





Two linear equations 
20000914 

From David Dean: 2a + 1b = 3.39 3a + 3b = 6.59 What formula do I use to find what a = ? Answered by Harley Weston. 





Two geometry problems 
20000909 

From Becky: What are all the real values of x that are solutions for the inequality [x2] < 6? ( it's less than or equal to) What is the distance between the points with (x,y) coordinates (3,2) and (3,1)? Answered by Peny Nom. 





Euclidean distance 
20000906 

From Velma ZahirovicHerbert: If d(x,y) is euclidean distance between x and y Prove that d(x,y)>=0 if d(x,y)=0 than x=y and d(x,y)=d(y,x) Answered by Paul Betts. 





A trig question 
20000701 

From Will: An open rectangular tank a units deep and b units wide holds water and is tilted so that the base BC makes an angle theta with the horizontal. When BC is returned to the horizontal, who that the depth of the water is (a squared) * cot theta div 2b units Answered by Harley Weston. 





Parallel tangents 
20000630 

From Ebony Indalecio: I need to prove the theroem: Tangents to a circle at the end points of a diameter are parallel. Answered by Walter Whiteley. 





Rectangles and algebra 
20000613 

From Kirstin: A rectangle's length is 4 more than twice its width. The area of the rectangle is 336m squared. What is its length? Answered by Paul Betts and Penny Nom. 





A centroid problem 
20000602 

From Kerstin: An isoceles triangle has sides measuring 13 cm, 13 cm, and 10 cm. Find the distance from the centroid to the vertex of a base angle. 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. 





Sample variance 
20000416 

From Jonathan Freeman: I was just reading your article entitled "A Note on Standard Deviation" I'm now teaching a unit on s.d. and my students were wondering why one uses a denominator of n for a population and n1 for a sample. I saw in your article that this is because "[the quantity] tends to underestimate sigma... and other technical reasons." To which my students again asked... "Why?" Could you please elaborate a bit on the "other technical reasons" perhaps in terms a high school senior (or their teacher...) could understand? Answered by Harley Weston. 





A parabola problem 
20000323 

From Morin: I need to prove that if parabola x^{2}=4py has a chord (not necessarily a focal chord) intersecting it at points A and B, with tangents to the parabola at points A and B that intersect at C, then a line drawn through C and the midpoint of the chord M is parallel to the yaxis. Further, prove that the point D where this line intersects the parabola is the midpoint of line CM. Answered by Penny Nom. 





Simultaneous equations 
20000311 

From Laura Molck: My name is Laura Molck and I am in Year 11 in Australia. Please help me with the following. I know that they are all simultaneous equations which I can do but I have trouble with the formulae to work the equations. Can you please help!! 1. A tent manufacturer produces 2 models, Outback and Bushwalker. From earlier sales records it is known that 20% more of the Outback model is sold than the Bushwalker. A profit of $200 is made on each Outback sold, but $350 is made on each Bushwalker. If during the next year a profit of $177,000 is planned how many of each model must be sold? Answered by Penny Nom. 





Systems of linear equations 
20000310 

From Ann Marie Devereux: hi there!!, I guess I have a problem!!! 3x+4y=10 (over) 4x+y=9 2x=5y+3 (over) x=3y+1 Answered by Penny Nom. 





Angle of Intersection of Two Lines 
20000302 

From Veronica Patterson: I am having a real hard time trying to figure out this problem. Could you please help me! The homework question says to find the acute angle of intersection between the two lines y=3x+1 and y=(1/2)x1. (It also says to use the results of a problem I had already figured out.) That problem was to use information from a picture shown that tan(theta sub1theta sub2)= ((m sub2 m sub1)/(1+(m sub1 * m sub2))). I used the difference identity of tangent to figure out the answer. Any help on this problem would be greatly appreciated. Answered by Harley Weston. 





Is a square a rectangle? 
20000215 

From Jaireh: This is something that aroused a debate in class: A rectangle was defined as a parallelogram with 4 right angles. A square was defined as a parallelogram with 4 congruent sides and 4 right angles. I need written and conclusive proof that some rectangles can or cannot be squares. I tried insisting that some of them can.. but without proof nobody will listen. Answered by Walter Whiteley. 





Taxicab geometry 
20000116 

From Jack: Im doing an investigation entitled 'taxicab geometry', ive attempted it and have done most of the practical part of it. But i cant seem to see the equation behind it all. please guide me in the right direction. They provide a regular grid with regular horizontal and vertical lines. The lines are roads and the actual squares are blocks of hoouses/ buildings. In taxicab geometry the distance between place A & B is worked out by adding together the horizontal and vertical distances. each square is counted as i unit. Part 1 (I've done this) A taxix cab firm is based at A. the posistion B is 7 units away from A. investigate all the posistions of B at 7 units. investigate for different distances. . . . Answered by Penny Nom. 





Three dimensional rectangle 
20000111 

From Dennis Murphy: I would like to find out the name of a Three dimensional rectangle. Answered by Harley Weston. 





Rectangular hyperbola 
19991215 

From Aarti Chand: Why do they call a rectangular hyperbola, rectangular and where the normal hyperbola looks like a rectangle and the rectangular hyperbola looks like a sqaure? Answered by Chris Fisher. 





Systems of equations 
19991206 

From Roger Hornbaker: I am having problem figuring out x and y solutions.  5x + y = 4
3x  y = 4  3x + 2y = 6
 3x + y = 0 Answered by Penny Nom. 





An area problem 
19991129 

From Vicky Birch: The length of a rectangle is three times it's breadth. If the length were 6 meters less, and the breadth were 6 meters more, the rectangle would be a square. Make a mathematical model and solve the resulting equation to find the breadth of the original rectangle. What is the area of the square? Answered by Penny Nom. 





Estimating the population mean 
19991113 

From John Barekman: Statitistics: Estimating the population mean when the standard deviation is known: I am not sure which n to use in the formula for the confidence interval equation: x +/ z*(standard deviation/sqrt(n)) If we have data of ten people, and if we have the data of ten sets of ten people each, what is the difference in the n that we use? What is the difference between the standard deviation and the standard error? Are we using the number of sampling means or just the number of samples? Answered by Harley Weston. 





Distance between the windows 
19990919 

From Lawrence: An observer on level ground is at distance d from a building. The angles of elevation to the bottom of the windows on the second and third floors are a and b respectively. Find the distance h between the bottoms of the windows in terms of a b and d Answered by Harley Weston. 





Standard Deviation 
19990711 

From Anthony Fama: I have seen several answers to this question: If one standard deviation represents 68% of the population, what does two, three, four and five sigma [std deviation] represent? As stated, I have seen several different answers and thus, the impetus for my question. Answered by Harley Weston. 





Girth 
19990526 

From Carolyn Bulkley: I am trying to explain to my son (who is in the 8th grade) how to figure girth. I'm afraid I have just confused him. Is there a simply formula to figure the girth of a box. for example: I have a box that is 27" L X 22" W X 21" H. Answered by Penny Nom. 





A bike race 
19990423 

From Bill Gepford: Bill was in a bike race and his friend kyle calculated that if he went 15mph that he would cross the noontime checkpoint one hour early but if he rode 10mph he would arrive one hour late. How far away is the checkpoint? Answered by Penny Nom. 





Universal Area 
19990408 

From Karen Richardson: I need a formula for area that works for a square, a rectangle, a parallelogram, a trapezoid, and a triangle. Answered by Jack LeSage, Chris Fisher and Harley Weston. 





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. 





An airplane problem 
19990308 

From B.M.R.: A plane left New York and headed East to its destination 3600 miles away across the Atlantic. On the way back its speed was boosted by a 50 mph tail wind and it arrived an hour early. What was its normal speed? Answered by Jack LeSage. 





Absolute value of i 
19990106 

From Wayne Bagley: I would like to know what is the absolute value of i. I need an answer suitable for the secondary level. Answered by Harley Weston. 





Two Chords 
19980929 

From Jennifer Cane: Question: two parallel chords of a circle, AB and CD, have lengths of 10 cm and 17 cm respectively. The diameter of the circle is 21 cm. Find the shortest distance between the chords. Answered by Harley Weston. 





Nickles on the Highway 
19980922 

From Ronnie Mac Donald: How many nickels would it take to cover 226km of highway,each nickel is 2cm in diameter? Answered by Penny Nom. 





Area and Volume 
19980728 

From James Pulver: I am going into 12th grade and am practicing for the SAT II. I have come across a problem that I cannot solve. It states that the front, side , and bottom faces of a retangular solid have areas of 24 square centimeters, 8 square centimeters, and 3 square centimeters, respectively. What is the volume of the solid. I need to know how to solve similar problems so is there a formula to go from area to volume? Answered by Jack LeSage. 





Trigonometry history 
19980526 

From Joeseph Huckler: Can you please tell me some history of the trigonometric ratio Tangent? who discovered it? when was it discovered and some other useful info... Answered by Penny Nom. 





Mean and Standard Deviation 
19980422 

From Kit: i have a problem of maths. i think the level of the question is secondary. question: Find the mean and the standard deviation of the numbers:1, 3, 4, 5, 7. i hope u solve this question. thank you so much! Answered by Harley Weston. 





Tangrams 
19980224 

From Allison: Do you know the story behind the tangram? I know that it is a Chinese puzzle about 200 years old. If there is a story about its creation, I would love to share it with my 7th graders. Thanks. Answered by Diane Hanson and Penny Nom. 





Octants 
19971110 

From Jason Watkins: I know which octant is octant 1 because all variables are positive. How do we number the other octants? Answered by Harley Weston. 





The Length of a Chord. 
19970726 

From Nathan Arthur: Picture a 9 inch diameter circle. Inside that circle is a 6 inch diameter circle tangent to it. Then, tangent to both circles is a 3 inch diameter circle. So there are three circles, two smaller ones inside a big one, all of them just touching but not overlapping. Now picture a chord on the 9 inch circle that is created by making a line that is tangent to both the 6 and the 3 inch circles and extending it to the edge of the 9 inch circle. I need the length of that cord. Answered by Chris Fisher. 





The angle between two tangents. 
19970609 

From Felix Ho: Two tangents are drawn from the origin to the circle (x)(x)+(y)(y)4x6y+9=0. If the angle between the tangents is m, fine the value of tan(m). P.S. (x)(x)=square x Answered by Harley Weston. 





A trig problem 
19961213 

From S. Johnson: sin t + cos t = 1/5. Find ALL exact values of cot t, given the original equation. Answered by Harley Weston. 





Height of a Hotel 
19961107 

From Irene: "Irene" is to determine the # of floors in a hotel 500 feet up the street. Irene is on the 10th floor of an office building and can measure the angle of elevation to the top of the hotel, 57 degrees. Her view of the entire building is obstructed. If the street rises at an angle of 8 degrees from the office building to the hotel and the average distance between floors is 11 feet, how many floors are on the hotel? Answered by Penny Nom. 





A tangent to a circle is perpendicular to the radius at the point of contact. 
19961022 

From Rita Leung: I wonder if there is any proof for this theorem  A tangent to a circle is perpendicular to the radius at the point of contact. If there is any proof for that, can you tell me please? Answered by Chris Fisher and Harley Weston. 





Un volume d'une capacité minimal 
20090105 

From Pauline: je doit faire un volume d'une capacité minimal de 2500 cm 3 en quell matiere que ce soit
* un prisme a base pentagonale non réguliere
* une sphere
* stella octangula Answered by PierreLouis Gagnon. 





les données sont inconsistantes 
20071003 

From Mikee: Bonjour,
Je me casse la tete depuis ce matin et la je donne ma langue au chat.
Je n'arrive pas a resoudre ce probleme.
J'ai 30 agents qui appellent dans la journee et realisent 322 questionnaires (long+court) telephonique avec une duree moyenne de conversation 294 secondes.
dans ces 322 qestionnaires :
ils realisent 313 questionnaires Long avec une duree moyenne de 317 secondes.
ils realisent 9 questionnaires Court avec une duree moyenne X.
je cherche X.
((Interviews réalisées*Durée moyenne de conversation)(Interviews réalisées avec la question Q2*Durée moyenne de conversation avec la question Q2))/(Interviews réaliséesInterviews réalisées avec question Q2)=Durée moyenne de conversation sans la question Q2
Q2=questionnaire Long Answered by Claude Tardif. 





5 points équidistants sur la surface d' une sphère 
20050815 

From Jean: J' aimerais placer 5 points équidistants sur la surface d' une sphère.
Si vous aviez une formule simple pour un néophyte, cela m' aiderais beaucoup. Answered by Claude Tardif. 





Les dimensions d'un rectangle 
20010409 

From Un elévè: 1. Les dimensions d'un rectangle sont a et b Si on augmente a de 3cm et b de 2cm, l'aire du rectangle augmente de 37 cm^{2}, mais si on diminue a de 2cm et b de 1cm, l'aire du rectangle diminue de 16cm^{2}. Quelles sont les valeurs de a et b? 2. Quelle est la valeur numerique de l'expression (ac+bd)+(adbc) sachant que a+b=1 et que c+d=1? Quelles sont les regles essentielles qui me manquent pour resoudre ceci? Answered by Claude Tardif. 





Septante 
19991218 

From Guillaume Bessis: Pourqoui et depuis quand en France emploieton l'expression 'soixantedix' et non septante pour désigner 70 ? (idem pour 90 et nonante) Answered by Claude Tardif. 

