Math Central - mathcentral.uregina.ca
Quandaries & Queries
Q & Q
 Topic: tan
start over

917 items are filed under this topic.

 Page1/1
A barrel on its side 2008-11-13
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.

The dimensions of a rectangle 2016-08-31
From Hazym:
How do I find the length(which is 15m longer than the breadth) and the breadth of a rectangle just by its perimeter which is 70 m?
The dimensions of a rectangle 2016-07-25
From Krunox:
A rectangle is twice as long as it is wide. Its perimeter (the sum of the lengths of its sides) is 60 cm. Find its length and width.
Two equations with fractions 2016-07-22
From kanesh:
p/2+q/3=3

p/4+2q/3=3

Simultaneous equations 2016-06-25
From sena:
2x/3+3y/2=-1
4x-5y=22

simultaneous equation

The difference between the ares of two rectangles 2016-06-09
From Ingrid:
I am trying to help my son with an area question.
I have the answer, from the solutions, but I cannot figure out how to teach him.

Question:

Two rectangles have lengths 13cm and 19cm respectively.
Their total area is 376cm squared.
If both their widths are whole numbers, what is the difference in their areas?

I know that this is solvable once I determine the widths of the rectangles ,
but how do I go about finding that?

Answered by Chris Fisher and Harley Weston.
John and Max walk to meet each other 2016-05-29
From abhay:
The speeds of John and Max are 30 km/h and 40 km/h.Initially Max is at a place L and John is at a place M. The distance between L and M is 650 km. John started his journey 3 hours earlier than Max to meet each other. If they meet each other at a place P somewhere between L and M, then the distance between P and M is?
The volume of a truncated rectangular pyramidal pond 2016-05-13
From Paul:
How do you calculate a partially filled truncated rectangular pyramid if you always know the bottom rectangle, the maximum height top rectangle perimeter, but have a varying height. Similar to filling up a pond you know the current height and dimensions at the max rectangle how do you calculate it half full i.e. 10x30 outside perimeter with a 2x8 base and a max height of 6ft how do you calculate it at 3ft without re-measuring the top perimeter. Thanks, Paul
A pair of equations with fractions 2016-05-11
From tiya:
hello, i want to know how to solve this question.

m/6+2n/3=6
-m/10=2n/5=2

At what time will Sara catch up with Jake? 2016-05-07
From Laura:
At 11:00 a.m., Jake started driving along a highway at constant speed of 50 miles per hour. A quarter of an hour later, Sara started driving along the same highway in the same direction as Jake at the constant speed of 65 miles per hour. At what time will Sara catch up with Jake?
A rectangular field 2016-05-07
From Jan:
A rectangular field is 63m long and 21m wide. A fence of 2m in height is needed to fence the field and fencing is also required to divide the field in three square sections. There are three wooden gates measuring at 1.5m to the three sections of the field. What is the total surface area of the fence needed for fencing and diving the field?
A 3 hour river cruise 2016-05-06
From Jan:
A 3 hour river cruise goes 15km upstream and then back again.The river has a current speed of 2km/h.what is the boat's speed and how long was the upstream journey?
15.86 acres 2016-04-21
From Ronald:
If a rectangular piece of land is 1320 ft. on one side, how many feet would be required on the other side to equal 15.86 acres?
The area and the perimeter of a rectangle 2016-04-12
From kimberly:
is there a relationship between the are and the perimeter of a rectangle? explain.
tan15° 2016-04-11
From JOHN:
find the exact value of tan15° in surd form.
A road trip word problem 2016-04-10
From Marc:
While on a road trip I imagined this random word problem. Suppose I start a trip of 75 miles. My initial speed is 75 miles per hour. After every mile traveled I decrease my speed by one mile per hour. After the first mile I decrease my speed to 74 miles per hour and so on for each subsequent mile traveled. How long will it take to complete the 75 mile journey?
A tilted cylinder tank 2016-03-28
From Astri:
I have a problem determining the fluid level for tilted cylinder tank. Actually I've found some solution here for horizontal cylinder tank. What if the cylinder is tilted at a certain degree, for example 30 degree from the vertical axis.
Thank you.

Biking and jogging 2016-03-17
From alondra:
Ricky went on a bike ride. After 6 miles he got a flat tire and had to jog home. He jogs 3mph slower than he bikes, so the jog took 1 hour longer than the bike ride. At what rate did he travel each way?
The perimeter of a rectangle 2016-03-17
From Linda:
Noel correctly adds the length of three sides of a rectangle and gets 88 cm her brother Ryan correctly adds the lengths of three sides of the same rectangle and gets 80cm. What is the number of cm in the perimeter of the rectangle
tan inverse 1/4 2016-03-14
From nazz:
prove; tan inverse 1/4=1/3 cot inverse 52/47
The area of a rectangle 2016-03-03
From Lucas:
The area of a rectangle is given by A=x2+18x+72
-use factoring to find an expression for the dimensions of the rectangle.
-if the area of the rectangle is 7 square feet, what are the possible values of x?
-what are the dimensions of a rectangle?

A rectangular prism 2016-03-02
From Paula:
Trying to help with a math problem. I don't know how to set up the equation for this.

A rectangular prism has a volume of 7.875m3rd and a height of 3.5 m. What is the area of the base of the prism?

Solve for x and y 2016-02-27
From ntshidi:
Y=1/2x+4and1/4x-6
Two equations in two unknowns 2016-02-13
From Anumba:
4x + 2y = 4
7x - y = -11

Travelling with and against he current 2016-02-09
From Lloyd:
A boat travelled 210 miles downstream and back. The trip downstream took 10hrs, the trip back took 70hrs
1. what is the speed of the current?
2. what is the speed of the boat in still water?

A two car competition 2016-02-02
From Christian:
Question: Two cars are racing to a fixed point and back. One car travels 70 MPH both ways While the other travels 60 MPH there and 80 MPH back, which car won the race? It is not a tie.
A system of linear equations 2016-01-24
From kareem:
my name is kareem
and i am a student i have a math puzzle and i tried to solved it but it always have same mistake
x-y=9
x+z=12
z-n=14
y+n=2

Complex numbers in standard form 2016-01-15
From Michael:
express the following complex numbers in standard form (2+3i)+(5-2i)
A rectangular enclosure 2016-01-15
From Amber:
A rancher wants to use 300ft of fencing to enclose a rectangular area of 4400 square feet. What dimensions should the rectangle be?
Water flowing through a rectangular drain 2016-01-08
From Tiffany:
the cross section of drain is a rectangle 30 cm wide. If water 3.5 cm deep flows through the drain at a rate of 22 cm/s, how many litres of water will flow through in one minute?
The area of a rectangle 2016-01-08
From ranjan:
if we make a rectangle with a 100cm of wire, then its area will be?
A circle is inscribed in a hexagon 2015-12-28
From Lalitesh:
A circle is inscribed in a regular hexagon ABCDEF
Prove that AB+CD+EF=BC+DE+FA

Constructing simultaneous linear equations 2015-12-28
From Deborah:
Linda thinks of a two-digit number. The sum of the digits is 8. If she reverses the digits, the new number is 36 greater than her original number. What was Linda's original number?

Thank you!

Linear equations in two variables 2015-12-13
From priya:
I)2x+y=y
II)pie*x+y=9

The dimensions of a rectangle given its area and aspect ratio 2015-12-13
From colum:
Can you work out the length and width of a rectangle where you know only the area and aspect ratio
Matthew skateboards around the school 2015-12-09
From Abigail:
Matthew skateboards 4km each hour.
How long will it take him to skateboard around the school yard measuring 300m by 200m.? Thank you.

Travelling in opposite directions 2015-12-06
From Roselyn:
Jenny and Mark commute to work, travelling in opposite directions. Jenny leaves the house at 8 AM, and averages 35 kph. Mark leaves at 8:15 AM, and averages 40 kph.At what time will they be 40 kilometers apart?
A tangent line to a parabola 2015-12-02
From pei:
Given that the line y=mx-5 is a tangent to the curve y=2x^2+3 find the positive value of M.
Riding a mountain bike up and down a mountain 2015-12-02
From sam:
Michael, can climb a mountain at 2.5km/hr on his mountain bike. he descends the mountain at 5.5km/hr. he completes the whole circuit in 7 hours. how long is the trail to the top of the mountain?
A common tangent to two general parabolas 2015-11-15
From Kind:
Hi, I want to find the common tangent of two general parabolas, but i don't know if it's possible or not.
If it's possible, please make a tutorial.

The first parabola equation : Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.
The second parabola equation : Gx^2 + Hxy + Iy^2 + Jx + Ky + L = 0.

I need this because i want to find the equation of Beloch fold. (Huzita - Hatori 6th axiom) However if you know any other method to find Beloch folds equation, I am open for any suggestions.

Fencing around a rectangular field 2015-11-11
From Darlene:
Question from Darlene, a parent: A farmer has 10,000 meters of fencing to use to create a rectangular field. He plans on using some of the fencing to divide the rectangular field into two plots of land by constructing a fence inside the rectangle that is parallel to one of the sides. Let X be the width of the rectangular field. Write an equation to express the area of the field as a function of X. Find the value of X that maximizes the area of the field.
The length of a rectangle 2015-09-26
From Tris:
Hi,
I'm trying to figure out the length of a rectangle but i forgot how. So, the width is 5cm and the perimeter is 34cm.

The dimensions of a rectangle 2015-09-25
From Erick:
A rectangular strip of land has a perimeter of 124meters and an area of 385 square meters. Find its possible dimensions
A tangent line to a circle 2015-09-03
From Jamie:
Use the Greek method to find an equation of the tangent line to the circle x^2+y^2-4x+6y+4=0 at the points (3,2square root 2-3.
The distance between two boats 2015-07-26
Two boats leave the same dock at the same time,one traveling due east at 10 mph and the other due north at 24mph,how many miles apart are the boats after 3hours ?
A waste oil tank 2015-06-13
From Angela:
a waste oil tank is 5 feet wide and 20 feet long, the empty tank on your truck holds 5000 gallons. If 7.48 gallons are in every cubic foot, what is the maximum depth the oil can be to completely fit into your truck?
A tangent to y = x^3 2015-05-31
From Brayden:
Show that a tangent line drawn to the curve y=x^3 at the point (d,f (d)), where d>0, forms a right triangle with the x and y axes in quadrant 4 whose area is (2/3)d^4.
The perimeter of a rectangle 2015-05-28
From Imran:
The length of a rectangle is x+3 centimetres.
The width of the rectangle is x-1 centimetres.

Find an expression in terms of x for the perimeter of the rectangle.
The perimeter of a rectangle The perimeter of a rectangle
Give your expressions in it's simplest form.
The perimeter of a rectangle The perimeter of a rectangle
Thank You.

Two lorries approaching an intersection 2015-05-15
From Nuraini:
Two straight roads intersect at the right angles. Lorry A, moving on one of the roads, Approaches the intersection at 50mi/h and lorry B, moving on the other roads, approaches the intersection at 20mi/h. At what rate is the distance between the lorry changing when A is 0.4 mile from the intersection and B is 0.3 mile from the intersection?
Folding a rectangle to preserve the aspect ratio 2015-05-09
From Anna:
If you fold a rectangular piece of paper in half and the resulting rectangles have the same aspect ratio as the original rectangle, then what is the aspect ratio of the rectangles?
A circle is tangent to the y-axis 2015-05-06
From Elynna:
What does it mean when a circle is tangent to the y-axis?

Thanks,

The method of elimination 2015-05-01
From oreanna:

Question from oreanna, a student:

How do u solve 2x+9y=3

7x-4y=-25 in elimination

A square and a rectangle 2015-05-01
From nick:
why is the area of a square of a given circumference greater than the area of a rectangle with the same circumference ?
Two concentric circles 2015-04-21
From Juniper:
Two concentric circles have radii of 4 cm and 8 cm. A segment is drawn so that it is tangent to the smaller circle and a chord of the larger circle. How long is the segment?
Two cars approaching an intersection 2015-04-16
From Engabu:
Car A is traveling west at 50km/h & car B is traveling north at 60km/h. both are headed for the intersection of the two roads. At what rate are the cars approaching each other when car A is 3km & car B is 4km from the intersection?
Two airplanes 2015-04-14
From john:
two planes leave an airport at the same time, one going northwest (N35*W)at 400 mph and the other going east at 332 mph. How far apart are the planes after 4 hours to the nearest mile?
A word problem with fractions 2015-04-09
From Lorraine:
If the numerator of a certain fraction is doubled and the denominator is increased by 1, the fraction becomes 1/2.

If the numerator of the original faction is squared and the denominator is decreased by 2, the fraction becomes equal to 1.

Let x be the numerator and let y be the denominator of the original fraction. Write down two simultaneous equation in x and y.

Solve these equations to find two possible values for the given fraction.

A tangent to y=x^3 passes through (0,2) 2015-04-05
From Kevin:
Given that the curve y=x^3 has a tangent line that passes through point (0,2). Find the equation of the tangent line
A rectangular concrete tank 2015-03-24
From mwenge:
What is the length ,width and height for the rectangular concrete tank that can have capacity of 50000 liters of water?
A train trip 2015-03-23
From Ngcebo:
A train travels a distance of 720 km at a speed of x km/h. on the return journey, it travels at an average speed of y km/h and completes the whole journey in an hour less. if the speed during the return journey was 10 km/h more, what were the speeds in m/s
Average rate for a return trip 2015-03-14
From Michael:
Jeffrey drove to a town 25 miles away at an average speed of 50 miles per hour. The return trip along the same route took 20 minutes longer than the trip to town. Determine the average speed in miles per hour for Jeffrey's round trip.
Two parallel tangents to a circle 2015-03-05
From Samantha:
The equation of a circle is x^2+y^2=25. Determine the equation of the parallel tangent lines to this circle, for which the slope is 4/3.
Istanbul to Lagos 2015-03-03
From Victor:
A plane flies from Istanbul to Lagos at 800km/h and then returns to Istanbul at 900km/h. The return trip takes 1 hour less than the flight to Lagos. What is the distance between Istanbul and Lagos?
Two equations with fractions 2015-02-26
From Pulane:
(9/x)+1=(-2/y)

Thank you

Two equations 2015-02-16
From nigel:
2x+1/2y=1
6x-3/2y=21

Distance, time and rate for three people 2015-02-15
From Mubashir:
Steven left Town A and walked towards Town B at a speed of 100m/min. At the same time, Jason and Melvin started from Town B and walked towards Town A at a speed of 80m/min and 75m/min respectively. If Steven met Melvin six minutes after passing Jason, find the distance between Town A and Town B.
Bearings and a rectangular plot 2015-02-14
From Mubashir:
A,B,C,D are the four corners of a rectangular plot marked on level ground. Given that the bearing of B from A is 040 degrees and that the bearing of C from A is 090 degrees. Calculate the bearing of
(a)B from C
(b)A from C
(c) D from C

Stopping distance 2015-02-11
From Audrey:
A Harley Davidson motor cycle weighing 650 lbs with a rider weighing 175 bs was going 40 miles per hour. He had to make a sudden stop . Slammed on brakes. How long a distance for him to stop?
A word problem with fractions 2015-02-11
From Omokayode:
A vehicle tank was 3/5 full of petrol. When 21 litres of fuel was added it was 5/6 full. How many litres of petrol can the tank hold?
A circle and a chord 2015-02-07
From Dakota:
If the diameter of a circle is 48 cm, find the shortest distance from a chord of length 34 cm to the center of the circle
Speed, distance and time 2015-02-06
From Terry:
How many seconds would it take to travel 0.18 km at a speed of 130km per hour?
Two cars pass each other going in opposite directions 2015-02-03
From Caroline:
Two cars pass each other going i opposite directions. One car is going 100 km/h and the other is going 80 km/h. How far apart will the two cars be after driving 45 minutes at these rates of speed?
A train from Vancouver to Whistler 2015-02-02
From Tea:
Serena and Nina are taking a train from Vancouver to Whistler, a 160km trip. If the average speed is decreased by 16km/hr, the trip will be 1/2 hours longer. What is the average speed of the train? Thanks :)
A motorbike race 2015-01-25
From Pramegh:
In a motorbike race of 75 km, the winner completes the race with a lead of 300 meters and 8 seconds before the second rider. Considering the riders ride with an average speed, find the difference between their speeds with which they completed the race.
(Calculate up to 2 decimal places)

Two cars 2015-01-18
From taylor:
two cars leave the park at the same time, one traveling north at a speed 10 mph faster than the other which is traveling south. after 3 hours the cars are 420 miles apart. find the speed of both cars
The length of a roll of paper 2015-01-12
From Peggy:
roll of paper 3ft wide and roll equals 500 sq ft how long would the roll be?
196 kilometer in2 hours 2014-12-29
From Ekanem:
QQ A motorist had planned to reach a place 196km in two hrs exactly. For the first 15km he was able to average only 40km/h. What average speed must he keep up for the rest of the journey if he is to arrive on time.
A tangent to a circle 2014-12-22
From azman:
Find the equation of the tangent line to the circle x^2+y^2=9 at the point P (2, square root of 5).
What is the speed of the boat in still water? 2014-10-30
The current in a stream moves at a speed of 2 km/h. A boat travels 38 km upstream and 38 km downstream in a total time of 3 hr. What is the speed of the boat in still water?
A linear system 2014-10-14
From pheter:
4/x - 1/y = 3 .... equation (1)
6/x - 2/y = 5 .... equation (2)

A rectangle and a triangle 2014-09-27
From rajesh:
The perimeter of a rectangle is equal to the perimeter of a right-angled 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?
A man a ship and a wharf 2014-09-26
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)
Two equations in x and y 2014-09-25
From seyilogo:
solve y=2x - 3 and (4x - 2y) / x + y = 1 simultaneously
Two equations in two variables 2014-09-18
From Susan:
(28x + 36y) - [20000 - .75(28x + 36y) + 60000] = 5000
x + y = 10000
solving two equations involving variables

A tangent to a curve passing through a point not on the graph 2014-09-15
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).
The perimeter and diagonal of a rectangle 2014-09-10
From niniha:
the perimeter of a rectangle is 68cm.if the diagonal is 26, find its dimensions
Problem solving 2014-09-08
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
A car passing a bus 2014-08-24
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
Distance, speed and time 2014-08-13
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?
Speed, distance, time 2014-08-13
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?
The dimensions of a rectangle 2014-08-03
From Jamaica:
if the perimeter of a rectangle is 30m and its area is 56 m2.find its length and width?
The method of elimination 2014-07-05
From leo:
please explain how can i solve this problem

3x-6y=-38
6x-9y=44

using elimination and simultaneous method thank you :)

The width of a rectangle 2014-07-02
From john:
if the area of a rectangular field is 90 sq. m and its length its is 19 m find its width
Simultaneous equations 2014-06-20
From rana:
solve the simultaneous equations
a)3x=7y
12y=5x-1

The number of standard deviations 2014-06-15
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.
A model of the sun and the Earth 2014-06-14
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?
What is the speed of the buses? 2014-05-18
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?
A circle a square and a rectngle 2014-05-12
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..
Travelling upstream and downstream 2014-05-12
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?
2 cars driving towards each other 2014-04-27
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...
What time was it when joe's brother passed him? 2014-04-25
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?
Simultaneous equations with fractions 2014-04-19
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

A tangent of the curve (x/a)^n+(y/b)^n =2 2014-04-15
From sudhir:
the equation of tangent of the curve (x/a)^n+(y/b)^n =2. at(a,b) is
Two rectangular prisms 2014-04-10
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
Two circles that touch each other externally 2014-04-08
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
The surface area of a rectangular prism 2014-04-08
From Manraj:
Find the surface area of a rectangular prism with dimensions 4, 5, and 7 units.
A cubical tank 2014-04-01
From renzo:
A cubical tank contains 2048 cubic ft of water when HALF-FULL. Find the total area of the tank and the length of its diagonal
A circle which is tangent to two perpendicular lines 2014-03-09
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! :)

A speed word problem 2014-02-24
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?
Simultaneous fractional equations 2014-02-15
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

(x-2)/(y-1)=1/3

Two bicyclists traveled in opposite directions 2014-02-07
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?
Walking up and down a hill 2014-02-06
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
Related rates 2014-01-30
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.
Two nonlinear equations 2014-01-26
From Naryn:
(1÷x) + (1÷y) = (7÷12)
xy = 12

A rectangular shaped property 2014-01-17
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
A rectangle inscribed in a circle 2014-01-10
From Marian:
A 16 cm by 12 cm rectangle is inscribed in a circle. Find the radius of the circle.
From Nathan:
Radio direction finders set up two points A and B, which are 2.5 miles apart on an east-west 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.
Two tuna boats 2014-01-09
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?
Distance from a point to a line 2013-12-28
From Sue:
I need to find the distances from the west line on 1st Take Point and 2nd Take Point.
Thanks,
Sue

Analytic Geometry 2013-12-18
From fRitz:
if (x,4) is equidistant from (5,-2) and (3,4), find x.
The area of an irregular octagon 2013-11-18
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 42-12 =30 i mean the length of base =30
One train overtaking another 2013-11-11
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
The average time per mile for a marathoner 2013-11-04
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?
Substitution type simultaneous equations 2013-11-03
From Kayla:
I am having problems with substitution type simultaneous equations, when the variable you are substituting is a algebraic one:
y=x^2-3x+4 and 3x-2y=1
I have rearranged 3x-2y=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.

The perimeter of a rectangle 2013-10-24
From sana:
if the length is given 70 m and the breadth is given as 40 m find the perimeter of the rectangle
Four tangent circles 2013-10-09
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?

A pool, a school, a park and home 2013-09-24
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.
A rectangular hyperbola 2013-09-19
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^2-y^2=a^2?
Similar rectangles 2013-08-17
From Mattie:
The dimensions of a rectangular-shaped 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

Equal ordinate and abscissa 2013-08-15
From sonit:
the slope of tangent to the curve y=(4-x^2)^1/2 at the point, where the ordinate and abscissa are equal, is
What is the original speed? 2013-08-10
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?
Simultaneous equations 2013-07-10
From Warren:
solve this simultaneous equation:
xy=4
2x+3y=14

Distance as a function of acceleration 2013-07-10
From Tom:
If you start at a stoplight and your acceleration is 16t - t^2, how far have you gone after 8 seconds?
Diego and his dog 2013-07-09
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?
Water use in a rectangular flush tank 2013-05-10
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
A triangle and an incircle 2013-05-09
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.

4 linear equations with 3 unknowns 2013-04-12
From Marian:
how to solve for 3 unknowns in 4 simultaneous equations
The distance between 2 lines in 4D 2013-04-01
From samane:
how can i measure the distance between 2 lines in 4D??
Simultaneous equations with fractions 2013-03-31
From Terence:
5/x-6/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.
A shortest distance problem 2013-03-28
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?
Tangents to the curve y = x^3 2013-03-24
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.
Trigonometry 2013-03-23
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(?)

The dimensions of a rectangle 2013-03-19
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
Fencing a parcel of land 2013-03-11
From Koleen:
How much fencing do I need for an 56,850 parcel of land for a 15 stable horse barn
6 miles in 28 minutes what's my average speed? 2013-03-05
From lynda:
6 miles in 28 minutes what's my average speed?
The tangent to a circle at a point on the circle 2013-02-22
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)
An electron in a TV tube 2013-02-15
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.
A word problem involving toys 2013-02-14
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?

Simultaneous equations 2013-02-10
From Michael:
2P + 1/3V =8
3P - 2/V=5

A journey of two parts 2013-02-06
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?
The area of a rectangle 2013-01-29
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?
How fast are we approaching each other? 2013-01-11
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?
How fast is the distance between the aircraft and the car increasing? 2012-10-24
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?
Two swimmers 2012-10-22
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?
Two congruent circles in a rectangle 2012-10-20
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.

A tank with an inner walled compartment 2012-10-12
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.
A word problem involving a fraction 2012-10-12
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?
Four tangent circles 2012-10-04
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
The perimeter of a rectangle 2012-09-19
From aretha:
calculate the perimeter of a rectangle with the long side 462ft x 9inches and the short side 50% less.
The dimensions of a rectangle 2012-09-12
From Becky:
A rectangle has an area of 48 square inches and perimeter of 32 inches. Find the dimensions of the rectangle.
The volume of fluid in a tank 2012-09-06
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?
A tangent to f(x) = 1/x 2012-09-04
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.
The area of a rectangle 2012-08-31
From mario:
The area of a triangle when on side is x and the other is x+6
Problem solving 2012-08-15
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.
A plane travelling with the wind and against the wind 2012-08-03
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?
The area of a rectangle 2012-07-24
From michael:
the dimension of the rectangle are (x+5) and (x-3) find its area
A cubical tank 2012-07-07
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
A cyclist a jogger and a fly 2012-06-04
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?
Romeo and Juliet live 40 miles apart 2012-05-18
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?

Math, time and rate 2012-05-18
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?

Cycling and running 2012-05-07
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?
The maximum distance from the vertex of a triangle 2012-05-02
From David:
There are three towns A,B,and C, equi-distant 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 2012-04-30
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?
A tangent line to a circle 2012-04-14
From Novelyn:
find an equation of the line tangent to a circle with equation x^2+y^2+6x-8y-27=0 at the point P(1,-2)
Two cars approach a right-angled intersection 2012-04-10
From Michael:
Two cars approach a right-angled 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?
A rectangular prism 2012-04-05
From Tori:
How do you find the base height if the base width is 10ft. The height is 7ft. And the volume is105ft.
How long will it take lee to catch up with jodie? 2012-03-21
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
The dimensions of a rectangle 2012-03-13
From irvyn:
if you are only given the area and the perimeter how do you find the dimension?
A water tank is in the shape of a truncated cone 2012-03-08
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?
The area and perimeter of a rectangle 2012-03-01
From RAJIB:
PEREMETER OF A RECTANGLE IS 24. FIND THE AREA ?
Measuring the liquid in a horizontal tank 2012-02-28
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.

Margie threw a ball 2012-02-16
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??

Jack and Kate set off in their cars ... 2012-02-13
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?
A road around a garden 2012-02-07
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?
There is a police officer in pursuit of suspect 2012-02-01
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.
The dimensions of a rectangle 2012-01-31
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

Two cars in a race 2012-01-30
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.
Tangent of theta 2012-01-17
From stahl:
explain what the 'tangent of theta' means. Draw and label a diagram to help with your explanation.
Brian on his bike 2012-01-16
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?
Running 5 km 2012-01-12
From Fayeann:
What amount of time will it take a person running 7 m/s to travel a distance of 5 km?
An equilateral triangle and some circles 2012-01-10
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
The dimensions of a rectangle 2012-01-06
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.
A straight line distance 2012-01-06
From Margaret:
If you traveled 300 miles east and 275 miles north, how many miles would you save by going in a straight line?
Jennifer wants to fence in her backyard 2011-12-09
From Val:
Jennifer wants to fence in her backyard. A yard is rectangular and is 15 feet by 12 feet. One 12-foot side is against the house so it does not need fencing. How many feet of fencing does Jennifer need?
A 3000 gallon tank 2011-12-08
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?
Two trains passing each other 2011-12-07
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?
Uniform acceleration 2011-12-06
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.

Two boats 2011-11-30
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?
Water pouring into a conical tank 2011-11-21
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

Lines tangent to y^2=4x 2011-11-11
From Reuchen:
Find equations of the lines tangent to y^2=4x and containing (-2,1).
The average speed for the whole journey 2011-10-30
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?
One central circle and three tangent circles 2011-10-16
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?
What is the speed of the boat in still water? 2011-10-07
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
Chuong and Hassan drive to work 2011-10-04
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.
A rectangle of largest possible area 2011-09-16
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
A tangent to the earth 2011-09-03
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?
Driving to meet Mary 2011-08-24
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?
Three tangent circles 2011-08-21
From maribie:
three discs are tangent externally distances between their centers are 23cm, 15cm, and 20cm. find their radii.t
Three tangent circles 2011-08-19
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
The height of a fluid in a horizontal tank 2011-07-24
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.
A rectangle is inscribed in a circle 2011-07-17
From Alexea:
A rectangle is inscribed in a circle of diameter 15in. Express the perimeter as a function of the width x.
Achilles and a turtle 2011-07-01
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?
Two trains 2011-06-07
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.
A line tangent to f(x)=1/x 2011-06-05
From Michael:
A line tangent to f(x)=1/x in the first quadrant creates a right triangle with legs the x-axis and the y-axis. Prove that this triangle is always 2 square units regardless of where the point of tangency is.
How many meters long should the race be? 2011-05-26
From Lee:
Nathan can walk at a rate of two meters per second while David can easily go three-and-a-half 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
The dimensions of a rectangle 2011-05-08
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?
Three tangent circles 2011-05-01
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.
The area of a rectangle 2011-04-30
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?
The quadratic with two given roots and a constant term 2011-04-19
From Lindah:
how do I food quadratic with two given roots and a constant term?
A concrete walk around a pool 2011-04-15
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
How far is it from the control tower? 2011-04-11
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?
Eliminate y 2011-04-07
From Lynn:
2x + y = 8
y + 3z =5
z + 2w =1
5w + 3x = 9

Form three equations with y eliminated

Two ships 2011-04-05
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.

The perimeter of a rectangle 2011-04-04
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?
The rectangle is reduced to 90% of its original size 2011-03-31
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

Two boats 2011-03-29
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.
Sample Standard deviation 2011-03-16
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.

A family of circles 2011-03-01
From steffi:
Find the equation of the family of the circle passing through the the point of intersection of x^2+ y^2 -4x-28=0 and x^2 +y^2 -4x-20+52=0; the member tangent to x=7.
Find the dimension of the original rectangle 2011-02-28
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
Slicing a rectangular parallelepiped 2011-02-23
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 :)....

Two conical tanks 2011-02-17
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.)
The equation of a circle 2011-02-14
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)
Two tangent circles 2011-02-09
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.
A tangent to a circle 2011-02-06
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..
Calibrating a conical tank 2011-02-05
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 2011-02-01
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.
The area of a rectangle 2011-01-31
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=w-15
Points with distance 5 from the point (-2, -1) 2011-01-19
From Alexa:
Find all points having a x-coordinate of 2 whose distance from the point (-2, -1) is 5.
A rectangle 2011-01-16
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?
A cylindrical tank 2011-01-16
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.?
Tan(x+pi)-tan(pi-x)=2tan(x). 2011-01-09
From Steven:
Verify the identity:
Tan(x+pi)-tan(pi-x)=2tan(x)

A 400 gallon oil tank 2011-01-08
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?
What is its speed in miles per hour? 2011-01-06
From Miriam:
An airliner travels 125miles in 15minutes. What is its speed in miles per hour?
A tangent line 2011-01-03
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=-6x-6
(B) y= -3x+1
(C) y= 2x+10
(D) y=3x-1
(E) y=4x+1

The length is twice its breadth 2010-12-09
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?
80 miles in 40 minutes 2010-12-08
From james:
i travel 8o miles in 40 minutes. how fast am i going in mph
A rectangular solid 2010-12-08
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!
Simultaneous equations 2010-12-05
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 2010-12-01
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?
A rectangular piece of plywood 2010-11-30
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.
What is its speed in still air? 2010-11-28
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
The perimeter of a rectangle 2010-11-24
From shericka:
a rectangle has a perimeter of 60cm. its length is 5 times greater than its width. what is its length?
How long will you and your friend be able to talk? 2010-11-23
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?
A 400 gallon drum 2010-11-04
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

A train passes a car 2010-10-24
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?
A rectangle with rounded corners 2010-10-21
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. ?
What are the speeds of the boats? 2010-10-21
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?
John and Mary are 200 miles apart 2010-10-20
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?
A commuter airline between two cities 2010-10-19
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?
Two jets leave denver at 9 am. 2010-10-15
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.
Electronic cars around a circular track 2010-10-11
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 2010-09-30
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?
Rectangular arrays 2010-09-29
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.

The distance between the origin and a moving point 2010-09-24
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
Limiting Cases in Geometry 2010-09-22
From Niki:
Consider a rectangle inscribed in a circle with a radius or R. What are the possible perimeters for the rectangle?
What is the average speed? 2010-09-21
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?
40 mph for 6 minutes 2010-09-20
From Andy:
If i was traveling at 40 mph for 6 minutes, what is my distance in miles?
How many cubic metres of water can safely be stored in the tank? 2010-09-10
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.
Driving north, east and west 2010-09-02
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?
Three cars 2010-08-30
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 ?
Running 100 km 2010-08-12
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?
Two cars on a circular track 2010-08-12
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
How fast is the second car taveling? 2010-07-26
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?
How much longer will it take to reach Toronto 2010-07-22
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?
An 18ft round pool 2010-07-19
From christine:
will an 18ft round pool fit on a 12x16 ft rectangular cement slab?
Pursuing Car 1 2010-07-13
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?
Half a mile at 50 mph 2010-07-13
From Mark:
How long will it take a car to travel 1/2 mile at 50 mph?
3 equidistant points on a circle 2010-06-21
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.

How many gallons do I need to finish filling the tank? 2010-06-14
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?
Standard Deviation from a Proportion 2010-06-08
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.
Going to the bike shop 2010-06-07
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?
A fuel tank with a broken gage 2010-05-28
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.
Liquid in a horizontal tank 2010-05-26
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!
How wide a strip has he cut when the lawn is half mowed? 2010-05-24
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?
What is the distance from A to C via B? 2010-05-24
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?
When will the second truck catch up to the first? 2010-05-22
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?
How far am I from the starting point? 2010-05-18
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
Sammy and his motorboat 2010-05-11
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.
Line of sight 2010-05-06
From David:
I live in St. Joseph, Michigan and there is an ongoing argument regarding line-of-sight 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 direct-line-of-sight.

So, to settle the argument, I'd sure like some simple explanation for this, even if-and I hope not-I am incorrect.

David

The equation of a circle 2010-05-04
From crystal:
find the standard form of the circle with center (-2,3) and tangent to the line y=1
40 miles at 50mph 2010-05-02
From gill:
if a car travelled 40miles at 50mph, how long would it take?
When are the cars exactly 40 miles apart? 2010-05-01
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.
A rectangular prism 2010-04-27
From Savannah:
A rectangular prism is made of exactly 8 cubes. Find the length, width, and height.
If (x, 4) is equidistant from (5, -2) and (3, 4), find x. 2010-04-21
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).

A tangent line to a circle 2010-04-15
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).
What are the dimensions of the box? 2010-04-13
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?
A rectangle problem 2010-04-12
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?
The perimeter of a rectangle 2010-04-12
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.
The diagonals of a rectangle 2010-03-30
From Tabatha:
The diagonals of a rectangle are 8 units long and intersect at a 60 degree angle. Find the dimensions of the rectangle.
A rectangle inscribed in a circle 2010-03-24
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^2-b^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).
What is the speed of the current? 2010-03-17
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?
Constants and coefficients 2010-03-12
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

The perimeter of a rectangle 2010-03-12
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?
The distance travelled by a minute hand 2010-03-06
From Patric:
How much distance will the minutes hand of length 14mm of a clock cover in moving from 5 to 10?
Standard form 2010-03-05
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 4x-3y=-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.
The base area of rectangular prism 2010-03-05
From Desiree:
How do you find the base area of rectangular prism that has 4 cm by 4cm by 6cm ?
At what time would Joan catch Jo? 2010-03-04
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?
The dimensions of a rectangle 2010-03-03
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?
The vertices of an equilateral triangle 2010-02-19
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.
The equation of a circle 2010-02-18
From AHMED:
find the equation to the circle with centre at the point (1,-1) and touching the straight line 5x+12y=7.
The center of a rectangular room 2010-02-16
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?
The distance from a chord to an arc 2010-02-11
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?
Fencing a garden 2010-02-04
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?
A decrease in travel time 2010-01-30
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%
The perimeter of a rectangle 2010-01-27
From debbie:
how many dimensions are there to get a perimeter of 400 feet for a rectangle?
A tunnel from Toronto to Montreal 2010-01-25
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 2010-01-25
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
Angle of incline 2010-01-20
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
How long will it take to go 1 mile at 80 mph? 2010-01-19
From Susann:
How long will it take to go 1 mile at 80 mph?
How fast am I walking? 2010-01-10
From KEVIN:
IF I WALK 3 MILES IN 28 MINUTES, HOW FAST AM I WALKING?
Gail and Bill drove to the beach 2010-01-10
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?
A pair of simultaneous equations 2010-01-09
From Yumiko:
Solve the following pair of simultaneous equations.

x^2 -4x = y^2-4
3y=2x - 3

The maximum area of a rectangle 2010-01-03
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

Write a function for the area in terms of x 2010-01-01
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.
A circle problem 2009-12-14
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.
f(x)=x+2sinx 2009-12-12
From amroziz:
for which values of x does the graph of f(x)=x+2sinx have horizontal tangent
... the original speed of the car was? 2009-12-08
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 .

Walking at 4/5 of his usual speed 2009-12-05
From venkatesh:
walking at 4/5 of his usual speed a man is 10 minutes too late .find his usual time.
The dimensions of a rectangular room 2009-11-26
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?
Solving two equations, one with a square root 2009-11-23
From kacie:
y = square root of x+3
x-4y = -7

im having trouble with this problem...i have to find where they intersect.

The triangle formed by the tangent and the coordinates axes 2009-11-23
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.
The fourth vertex of a rectangle 2009-11-11
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.
At what rate are the people moving apart? 2009-11-01
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 ?
Is it a rectangle? 2009-10-29
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)

Standard deviation 2009-10-27
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?
How far will it travel in 45 mins? 2009-10-27
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
The area of a rectangle 2009-10-10
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
Two rectangles 2009-10-08
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
Two jets are traveling towards each other 2009-10-05
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?
Three circles 2009-10-02
From Brandon:
There is a quarter circle with a radius of 1. along one eged of it, there is a semi-circl with a diameter of 1, and its center is on the drawn line. there is another semi-circle 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 2009-10-01
From kanchan:
for what value of c a line y=mx+c touches a parabola y^2=4a(x-a)
How long (distance)did it take to stop? 2009-09-30
From mary:
a car travelling at 50km/h stops in 4 seconds.how long (distance)did it take to stop?
How fast am i going? 2009-09-28
From ron:
how fast am i going if i drive 40 miles in 20 minutes...what is the formula for figuring this out.
How long would it take the students to arrive at their campsite 2009-09-18
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???
Average speed 2009-09-11
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?

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?
Simultaneous equations 2009-08-28
From onias:
solve 3/a - 2/b = 1/2 , 5/a + 3/b = 29/12
The distance traveled on a bike 2009-08-28
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.
The area of a rectangle 2009-08-21
From roxanne:
the dimensions of the rectangle: 3x length and 4x width. What is the area of the rectangle in square units?
Two cars 2009-08-09
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?
A degreaser for a fish tank 2009-07-23
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?
A tangent to a circle 2009-07-14
From Eric:
Hi I am trying to complete a packet that has a list of questions to brush up on pre-calculus 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 y-intercept of the tangent line. Please help. Thanks.
The surface area of a rectangular pyramid 2009-07-13
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.
Simultaneous Equations 2009-07-06
From Mukulu:
Solve the equation simultaneously X/5=(Y+2)/2= (Z-1)/4 ……………….eqt 1 3X+4Y+2Z-25=0 ………………eqt 2
A diagonal of a rectangle 2009-07-01
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
A boat goes up stream 30 miles and ... 2009-06-29
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.

Thanks

The surface area of a tank 2009-06-25
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.
A train crosses a tunnel 2009-06-25
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
The Pythagorean theorem 2009-06-24
From supreet:
What are some real-world applications of the Pythagorean theorem?
and
How are the Pythagorean theorem and the distance formula related?

Is one Infinity larger than another in the extended real number system? 2009-06-24
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

An aeroplane flying in a wind 2009-06-02
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

Stones around a pool 2009-06-01
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

The dimensions of a rectangle 2009-05-30
From Linda:
A rectangle has a perimeter of 38 feet & an area of 48 square feet. What are the dimensions of the rectangle?
The width of a rectangle 2009-05-19
From Stacey:
If the length of rectangle is fixed at 29 cm, what widths will make the perimeter greater than 82 cm?
4 tan(360/(2n)) 2009-05-18
From molly:
in the formula to find the area of any regular polygon how do you figure out 4tan part of the formula
Driving to school and back 2009-05-17
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?
The dimensions of a toy chest 2009-05-07
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
What was her rate of speed? 2009-05-06
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 2009-05-01
From deborah:
Could you please tell me some examples of different objects in the real world of rectangular prisms?
Two airplanes are 300 miles apart 2009-04-22
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
The center of an ellipse 2009-04-21
From Nae:
what is the ellipse center of 5x^2+3y^2=15
Volume of a prism 2009-04-21
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 2009-04-21
From Kristy:
Can you help me with this equation? Find the equation, in standard form of the line perpendicular to 2x-3y=-5 and passing through (3,-2) With the equation in standard form with all integer coefficient.
Two similar rectangles 2009-04-19
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?
Passing three cars 2009-04-16
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?
A man travels a total of 8km in 6 hours 2009-04-10
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 8-x/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

How many miles per hour was it traveling? 2009-04-04
From Regina:
a car traveled 16 miles in 30 minutes. How many miles per hour was it traveling?
310,000 cubic yards of concrete 2009-03-31
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!
A trip at two different speeds 2009-03-28
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?

The speed of a tire in revolutions per minute 2009-03-28
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.)
Subdividing a four-sided lot 2009-03-27
From kannan:
i have a 1.5 acre land having four sides
A-B=64.8 meters
B-C=94.2 meters
C-D=54.4 meters
D-A=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

A 5 ounce object traveling at 60 mph 2009-03-27
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.
Depth to height ratio 2009-03-26
From Janet:
Is there a formula to determine how deep something (a cabinet) should be based on how tall it is?
The rate of change of the volume of a sphere 2009-03-25
From Kaylin:
why the rate of change of volume of a sphere is not constant even though dr/dt is constant?
Z-score 2009-03-25
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.
A 1.5:1 rectangle 2009-03-23
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.
A rectangular open box 2009-03-21
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.
The perimeter of a rectangle 2009-03-18
From marylyne:
the perimeter of the rectangular is 70 meters. if the width is 40% of the length, find the dimensions?
Water drains from a conical tank 2009-03-11
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.

A common tangent to two curves 2009-03-02
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)?
Two racers going around a track 2009-02-26
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?
A rectangular prism 2009-02-25
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
Fred in his canoe 2009-02-21
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)
How long will it take Jake to catch up? 2009-02-20
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 ?
Joggong in opposite directions 2009-02-19
From Mallory:
Emma and her mother jog along a mile-long 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?
The surface area of a cube and rectangular prism 2009-02-16
From Mhiko:
how to derived the total surface area of a cube and rectangular prism using geoboard??
Solid figures 2009-02-10
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
A rectangular park 2009-02-06
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.
Catching up to the car ahead 2009-02-06
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 one-qarter mile up the road. Exactly six minutes later, Car B catches Car A. How fast was the car going?
A point on -8x^2+5xy+y^3=-149 2009-02-04
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

Simultaneous equations with an xy term 2009-02-01
From angelee:
xy+5x-2y-10=0 2x+y=1
The amount of concrete in a football stand 2009-01-30
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.
Find area of the rectangle in terms of L. 2009-01-27
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.
How long will it take to make 50 miles? 2009-01-26
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 2009-01-25
From gina:
Suppose one edge of a cubic tank is 8m; Find the volume of the tank in cubic meters
Two tangent circles 2009-01-23
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.
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 2009-01-22
From jerry:
1 foot drop every 25 feet what is the angle of the degree
A tortoise and a hare 2009-01-20
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?

The number of gallons in a tank 2009-01-19
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.
The dimensions of a pool 2009-01-18
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
Fuel in a tank 2009-01-16
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
Parallel distances from arc of circle to its chord 2009-01-16
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 arch-topped bed head board.)
Answered by Chris Fisher and Stephen La Rocque.
A rectangular prism 2009-01-13
From nika:
How many bases does a rectangular prism have? What are they?
Two trains 2009-01-12
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?
A stack of rectangles 2009-01-11
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
Constants, and coeficiants 2009-01-10
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.
Two rectangular plots have the same area 2008-12-23
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
A standard bill on a highway 2008-12-19
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 2008-12-14
From nekasia:
what is the area of a rectangle with a diagonal of 8.5 inches PLEASE SHOW WORK
The sides of a rectangle 2008-12-08
From Mitchell:
The perimeter of rectangle ABCD (represented on a Cartesian plane) is 52cm. The equation associated with segment AD is 3x+4y-60=0 Point C is at (18, 14). What is the length of segment AD?
3 equidistant points 2008-12-01
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?
Two tangent circles and common tangents 2008-12-01
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
Two tangents to a circle 2008-11-26
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?
Tan(3x) 2008-11-23
From Evan:
Derive an expression for tan3x in terms of tanx
Sigma in a normal distribution 2008-11-18
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

How far are the boats apart? 2008-11-14
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?
The dimensions of a rectangle 2008-11-07
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?
A circle tangent to a line and with its centre on another line 2008-11-01
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.
The speed of the boat and the river 2008-10-28
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?
Three congruent rectangles 2008-10-27
From Meagan:
Here is my problem: Three congruent (non-square) 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.
Tangent line 2008-10-27
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. 2008-10-26
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.
Two tangent lines to a parabola 2008-10-26
From Marcus:
Show that the tangent lines to the parabola y = ax^2 + bx + c at any two points with x-coordinates p and q must intersect at a point whose x-coordinate is halfway between p and q.
The height of a tank 2008-10-26
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 ?
The amount of diesel fuel in a tank 2008-10-26
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.
The slope of a tangent line 2008-10-18
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?
Travelling home o the train 2008-10-18
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?
If you are driving 40mph, how long does it take to go 2.5 miles? 2008-10-18
From Nathan:
If you are driving 40mph, how long does it take to go 2.5 miles?
Two equations in two unknowns 2008-10-17
From Dushayne:
a. 3x-4y=32
5x+2y=10

b. 2x+3y=11
4x+3y=10

A tangent line to f(x) = 1/(x - 1) 2008-10-16
From Amanda:
If f(x)=1/(x-1) then what is the slope of the tangent line at x=-2?
Two planes flying in opposite directions 2008-10-16
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.
The dimensions of a rectangle 2008-10-16
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....
Finding the Raw Score for a Mean of 0 and Standard Deviation of 1 2008-10-02
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.
The length of a tank 2008-10-01
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?
How many parallel tangents may a circle have? 2008-09-29
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..
What is the perimeter of the rectangle? 2008-09-27
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?
The standard form Ax+By=C 2008-09-26
From Susan:
I am having difficulty changing the point-slope form of the equation of the line y-y1=m(x-x1) 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.
5 units from (1,2) and 5 units from y-axis 2008-09-26
From Shaun:
Find the points (x,y) in the plane that are 5 units from (1,2) and 5 units from y-axis. I am more interested in the approach, in general terms, than the numerical values.
Parallel Tangents 2008-09-24
From manish:
how many parallel tangents may a circle have? the text book shows two.but a crcle can have infinite tangents.
Limit as it Approaches a Constant 2008-09-16
From Brooks:
what is the limit as x approaches 10 for f(x) = sqrt(x-1) = 3 pleeeeeaase help me out here
Distance, time and rate 2008-09-11
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?
A tangent to a circle 2008-09-06
From Jake:
Find an equation of the line that is tangent to the circle x^2 + y^2 = 3 at the point (1,√2)
Largest Inscribed Rectangle 2008-09-03
From astrogirl:
find the shape and area of the largest rectangle that can be inscribed in a circle of a diameter a=2
A rectangular tank of water 2008-09-02
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?
The lengths of the sides of a rectangle are in ratio 5:3 2008-08-29
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
Two tangent circles 2008-08-22
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.
Irregular polygon and Circle that Intersects All Sides 2008-08-20
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
Coefficients, Like Terms, and Constants 2008-08-14
How Would I Answer This Problem?

Coefficients Like Terms Constants
3x+7
4m+(-3n)+n
6kp+9k+kp-14
-8y+6ab+7-3ba
c+2c+c-5c+1

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

A linear function 2008-08-07
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?
The volume of a fuel tank 2008-08-01
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?
Area of triangle formed by three tangent circles 2008-07-31
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?
Inscribed Rectangle 2008-07-30
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.
Running in opposite directions 2008-07-29
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 2008-07-27
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 2008-07-23
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?
Simultaneous equations 2008-07-23
From Franco:
Solve

3 D + E - F = -10
-2 D - F = -4
-3 D - 4 E - F = -25

Franco

A tangent to a curve through a point not on the curve 2008-07-23
From Carter:
How does one find the tangent points on a curve, given only the curve's function and the x-intercept 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.

A tangent line to a circle 2008-07-09
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

Going from 45 mph to 35 mph 2008-07-09
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?
Two trains 2008-07-07
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 ... 2008-07-07
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?
Fit 7 different rectangles on grid paper 2008-07-02
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.
A rectangular room 2008-06-30
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?
A rectangle 2008-06-26
From SEBASTIAN:
How to arrange quadrilateral in the form of a rectangle?
Two forces acting on a body 2008-06-21
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.
How far from each other will they be? 2008-06-18
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?
A space camera circles the Earth 2008-06-16
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?

Escort cards on a rectangular table 2008-06-13
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
-2(x - 1)^2 + 8 2008-06-12
From kasondra:
y=-2(x-1)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

tan(4a - b) 2008-06-12
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(4a-b) thanks alot in advance
The length and width of a rectangle 2008-06-11
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?
What are the dimensions of the rectangle? 2008-06-11
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 2008-06-04
From Jacob:
If three circles are mutually tangent, does that mean that the two tangent lines are perpendicular?
The area of a rectangle 2008-05-27
From Becky:
the area of a rectangular lot is represented by 6t^2+13t-5. What are the length and the width of the rectangular lot?
The length of a shadow 2008-05-27
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 2008-05-25
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?
How many bricks I can place around a 26-inch circle? 2008-05-22
From Jon:
I want to know how many bricks I can place around a 26-inch circle? There must be a formula other than trial and error. The length of the bricks is 6-inches. [How many 6-inch tangents can be in a 26-inch circle? Thank you very much. Jon
55 mi/h for 4 h 2008-05-21
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.
The sides of a rectangle 2008-05-16
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
Fencing around a playground 2008-05-15
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?
A crate is launched from an airplane 2008-05-10
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.
How far is it from the top to the bottom of the mountain? 2008-05-09
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?
The surface area of a tank 2008-05-09
From jack:
i'm looking for the square footage of a tank that is 10'diameter x 23'high,floor,ceiling and walls
The standard form of an ellipse 2008-04-30
From Rebecca:
I have to write the following equation into standard form of an ellipse:

9(X-1)^2 + (Y+1)^2 = 1

Answered by Stephen La Rocque and Harley Weston.
5 miles per hour for 30 minutes 2008-04-29
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?
A rectangle inscribed in a circle 2008-04-27
From sridhar:
A rectangle with perimeter 28 cm inscribed in a circle of radius 5 cm find the area ?
An octagonal prism 2008-04-27
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
Driving home from work 2008-04-25
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?
Find the length and the width of the rectangle 2008-04-24
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.
The dimensions of a rectangle 2008-04-20
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.
45 miles at 50 mph 2008-04-18
From Willie:
If you travel at 50 mph, how long does it take to go 45 miles?
A solid figure with 3 rectangular faces and 2 triangular faces 2008-04-17
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?
A tangent to two circles 2008-04-13
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

A tangent to a circle 2008-04-13
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.
Jill and Matt run on a 400 meter long oval track 2008-04-11
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?
Two trains left the city at the same time 2008-04-11
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.
A rectangle word problem 2008-04-10
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.
A river boat 2008-04-09
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
The shortest distance from a point to a line 2008-04-03
From Katherine:
How do I find the shortest distance from the point (3,5) to the line x = -2
Perimeter, area and diagonals of a rectangle 2008-04-03
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 2008-04-01
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
A rectangular prism 2008-03-31
From Chanlie:
i need need to find a rectangular prism with a total surface area of 210 units.
The area of a rectangle 2008-03-25
From Raphael:
What is the area of rectangle that measures 7 yards by 23 yards
Expected value and standard deviation 2008-03-19
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

Distance seen 2008-03-18
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 ?

A train and a boat 2008-03-15
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?
A fence around a rectangular region 2008-03-06
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
The dimensions of a rectangle 2008-03-06
From Julie:
Find the dimensions of a rectangle with an area of 400. Width x ft. Length (2x-7)ft.
Answered by Stephen La Rocque and Penny Nom.
Two points moving on a straight line 2008-03-06
From laura:
Particle A travels at constant speed of 1.0ms-1 in straight line, passing particle B, at which time particle B beings traveling with constant acceleration of 0.2ms-2 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 2008-03-06
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?
Is every rectangle a square? 2008-03-04
From Odette:
if every square is a rectangle, is every rectangle aslo a square?
What point on the graph y = e^x is closest to the origin? 2008-03-03
From elvina:
What point on the graph y = e^x is closest to the origin? Justify your answer.
Simultaneous equations 2008-02-29
From CONOR:
I was wondering if you could help me with this problem

7x - 5y = -1
3y = 4x

A package of supplies is dropped from a plane 2008-02-29
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.
Is a square a rectangle? 2008-02-29
From Jaime:
Is a square a rectangle?
The diagonal of a rectangle 2008-02-21
From tim:
is there a formula for finding the diagonal of a rectangle?
The equation of a line 2008-02-17
From Jennifer:
Given the point A(3,2)B(5,8) find the equation of the line AB ( in standard form )
A ball bearing is placed on an inclined plane 2008-02-15
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?
The area of a rectangle 2008-02-12
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
The width of a rectangle is 4 less than twice its length. 2008-02-09
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
The distance around a building 2008-02-06
From olivia:
If you walk around a building that is 102,869 sq ft, how many miles is that?
Two cars are on a collision course 2008-02-06
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.
The equation of a circle 2008-02-05
From aime:
Find the equation of the circle tangent to 3x+4y-15=0 at P1(1,3) and passing through P2(6,3) and P3(0,5)?
How fast does each travel? 2008-02-05
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?
The dimensions of a rectangle 2008-02-01
From Evan:
you are given that the area of a rectangle is 21.6in sq. find the base and the height of the rectangle.
Driving from Mathville to Bioville 2008-02-01
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?
The standard form of a line 2008-01-30
From Thomas:
I'm attempting to get this in standard form

slope=3;(1,5)

2 km at 5.00 m/s 2008-01-29
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?
How far from the corner will the police catch the car? 2008-01-27
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?
The volume of a tank 2008-01-27
From Fred:
A cubic tank holds 1,000 kilograms of water what are the dimensions of the tank in meters?
The standard form of a line 2008-01-24
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
The equation of a line 2008-01-20
From Sara:
The question is:

Write the equation of a line that is parallel to y=3x-2 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 2008-01-18
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

Two bikers race on a circular track 2008-01-17
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 2008-01-16
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.
The distance back to school 2008-01-16
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?
Hoisting an anchor 2008-01-10
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?
How fast does Kim paddle in still water? 2008-01-07
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?
What is the speed of the plane in still air? 2008-01-05
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?
The shortest distance to a line 2008-01-04
From nana:
3y+4x-12=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
A tangent to a circle 2008-01-04
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 2007-12-31
From Jessica:
a) In what order would you arrange a penny, a nickel, a dime, a quarter, and a half-dollar 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; half-dollar, 1205.
b) How should the coins be placed, if the distance between the dime and the half-dollar 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?

A rectangle is three times as long as it is wide. 2007-12-31
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?
The surface area of the rectangular solid 2007-12-30
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

The standard normal distribution 2007-12-29
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?
Sally, Charlie and Snoopy in a race 2007-12-29
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?

Two cars drive in opposite directions 2007-12-23
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?
The dimensions of a rectangle 2007-12-22
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?
A triangle and a rectangle 2007-12-14
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.
The dimensions of a rectangle 2007-12-12
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.
The tangent to a curve 2007-12-10
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).

Mean and standard deviation 2007-12-10
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 n-1?
b) Which has the greater standard deviation: the odd whole numbers from 1 to n, or the even whole numbers from 2 to n-1?

A triangle and a pentagon 2007-12-08
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?
System of equations 2007-12-06
From Jenn:
change the equation,x-y=4 to form y=mx+b the solution to the system of equations y=2x and y=-x+3 is
Chicken and goat feet 2007-12-05
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 2007-11-25
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?
The maximum area of a rectangle 2007-11-23
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 = 4-x
4. A = x(4-x) = 4x-x^2

Not sure what to do from this point because I don't know if its right.

A t-test 2007-11-20
From Rachel:
I am wanting to use the t-test 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 t-test cannot be used because the f-test can't be calculated. If so is there an alternative test?
Standard deviation 2007-11-20
when and why we use standard deviation in Data analysis?
A rectangular prism 2007-11-16
From nicholas:
What is the height the surface area to a rectangular prism with a volume of 350 milliliters?
A cylindrical tank 2007-11-16
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.
A particle moves in the xy-plane 2007-11-12
From Russell:
A particle moves in the xy-plane 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

Stopping distance and speed 2007-11-11
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?

The width of a rectangle 2007-11-07
From BJ:
The perimeter of a rectangular field is yards. If the length of the field is yards, what is its width?
Two cars 2007-11-04
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.
Constantly accelerated motion 2007-10-29
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.
A car traveled 175m at certain speed 2007-10-28
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?
How to solve related rates problems 2007-10-27
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.

Area of a triangle formed by three points on a graph 2007-10-26
From Betty:
My question is 'find the are of a triangle whose vertices have coordinates (3,5),(6,-5), and (-4,10)
The length of a rectangle is twice the width 2007-10-26
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?
Given a six by six square, how rectangles are there in the square? 2007-10-24
From Maria:
Given a six by six square, how rectangles are there in the square?
The length of a rectangle 2007-10-24
From Kharez:
What is the length of a rectangle with an area of 24 square feet and a width of 4 feet?
Stanley Cup costume (truncated cone pattern) 2007-10-19
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.
Calculate the dimensions of the rectangle 2007-10-16
From Sara:
The perimeter of a rectangle is 62cm. The length of the diagonal is 25 cm. Calculate the dimensions of the rectangle.
Four triangles in a square 2007-10-15
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.
The dimensions of a rectangle 2007-10-14
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.
Substitution method 2007-10-11
From Kevin:
3xx+2y=-36-y=11
Grouped data 2007-10-08
From Nimra:
The following sets of data represent the distributions of
house prices in the north-east and south-west of a country.
Random samples of 100 houses were selected in each region.
(a) Calculate the mean, median and standard deviation for

Coin jar 2007-10-07
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.
Solving four simultaneous equations (system of four linear equations) 2007-10-07
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

Equation of a tangent line to a function 2007-10-04
From Princess:
If f ' (x) = 3x^2 +1, find the equation of the tangent line to f(x) = x^3 + x at x= -1.
Hitting golf balls 2007-10-03
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?
Will the stone catch up the parachute? 2007-10-03
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!)
Motion along a line 2007-10-02
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
A tangent line to a circle 2007-09-26
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.

Can you tell me how many gallons it holds? 2007-09-25
From Jeff:
Hi my water tank is 10ft long and 45" around,can you tell me how many gallons it holds.thankyou jeff
Finding equations, intersection point of two lines at right angles 2007-09-22
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 co-ordinates of D.
Points that are 15 units from the origin 2007-09-20
From Paula:
Find the coordinates of any point(s) 15 units away from the origin with an x-coordinate 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!

A rectangle inscribed in a circle 2007-09-11
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!
Water in a conical tank 2007-09-10
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?

Standard deviation 2007-09-05
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?
The tangent to y = x^3 at x = 0 2007-09-04
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 x-axis. but graphically one can visulize that x-axis intersects the curve, so how can it be the tangent to the curve. Please help.
Standard deviation 2007-09-01
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(1-p). I understand how to get the np but not understanding how to get the (1-p). For example np=(40)(0.48)(1-0.48)=3.160. How can I get the (1-0.48) answer please
A circle and a tangent 2007-08-27
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 y-axis at y=3 and has one x-intercept at x=1.
a. Determine the other x-intercept
b. deduce the equation of the circle.

Two-column proof for a circle geometry problem 2007-08-24
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
Tangents to a circle 2007-08-18
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.
Area and perimeter 2007-08-16
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?
Two circles C1 and C2 meet at the points A and B 2007-08-15
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.
The area and perimeter of a rectangle 2007-08-15
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 2007-08-14
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.
A round reservoir 2007-08-14
From lee:
if you have a 46 acre round reservoir, how far around in feet would that be ??
Diagonals on a cylinder 2007-08-10
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
Find the dimensions of the rectangle that will contain the greatest area 2007-08-06
From Julirose:
The perimeter of a rectangle is 38 meters. Find the dimensions of the rectangle that will contain the greatest area.
Three runners on a circular track 2007-08-04
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?

A statistics example 2007-08-02
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?

At what speed does Chuck travel? 2007-07-27
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?
A football stand 2007-07-19
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.
Proving a quadrilateral is a rectangle 2007-07-14
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:
1. 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.
2. 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?

Finding the radius of an inscribed circle 2007-07-05
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 2007-07-02
From Juan:
The general "Standard" form of an equation is Ax+By=C. Re-Write this equation in slope-intercept (y=mx+b) form.
Simultaneous equations : the Elimination method 2007-06-21
From Patricia:
I need to find the value of X and Y using the Elimination method.

5/x + 3/y=4
25/x-2/y=3

How many gallons of water 2007-06-19
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?

A square and a rectangle 2007-06-19
From Clarence:
What is the difference between rectangle and a square
Simultaneous inequalities 2007-06-18
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?

Circumscribing a golden cuboid with a sphere: surface areas 2007-06-14
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.

Angles of depression 2007-06-13
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.
Standard Deviation 2007-06-13
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.
Throwing a ball from the top of a building 2007-06-12
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?

Two tangent lines to y=x^3 2007-06-07
From stephanie:
find the equations of two tangent lines to the y=x^3 function through the point (2,8)
Water tank volume 2007-05-29
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.
System of equations 2007-05-24
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

Normal distribution 2007-05-24
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 "z-value" = 2.5. Solve for the standard deviation of the data set.
b.) Solve for the "z-value" of 9,900.

Set up two simultaneous equations 2007-05-21
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?
Finding the hypotenuse without Pythagorus 2007-05-11
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?
Are proofs important in geometry? 2007-05-07
From BJ:
Are proofs very important to know how to do?
My daughter has been in Geometry & the teacher skipped proofs.

The dimensions of a rectangle 2007-05-07
From Stephanie:
The perimeter of a rectangle is 54yds , and the area of the rectangle is 180yds^2 . Find the dimensions of the rectangle.
A tugboat's speed 2007-04-30
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.
I have N data points in m-dimensional space 2007-04-29
From Sid:
Hi, Given below is the problem that I am facing: I have N data points in m-dimensional 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 ?
Incremental standard deviation 2007-04-28
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
What is the speed of the boat? 2007-04-22
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
Two tangents to a circle 2007-04-17
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.
A gardener has 140 ft of fencing to fence 2007-04-16
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.
Simultaneous equations 2007-04-16
From kyrie:
simultaneous equation 4x + 3y = 21 2x * y = 8
How far apart are the cars? 2007-04-07
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

A delivery driver travels from Belfast to an address in Dublin 2007-04-04
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.

Tina swims 4 miles upstream at 1 mph 2007-03-31
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?
Acceptance sampling 2007-03-29
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?
The angles in a right triangle 2007-03-28
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.

An inheritance problem 2007-03-23
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?
A one pass calculation of standard deviation 2007-03-19
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
Triple angle tangent formula 2007-03-15
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
Two busses 2007-03-15
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 2007-03-14
From Karlianna:
find dimensions of a rectangle with least perimeter for given area
A) 30cm2
b) 50cm2

Angle of elevation 2007-03-13
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.
Simultaneous equations with fractions 2007-02-28
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? 2007-02-23
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.)
Finding the equation of the circle 2007-02-20
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 2007-02-20
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?

How far from the port is the point where the ship turned? 2007-02-19
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?
Increasing speed and decreasing time 2007-02-18
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.
Square centimeters 2007-02-12
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 2007-02-08
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!
Romeo is throwing pebbles 2007-02-08
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?
Area of a rectangle 2007-02-07
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
A rectangle inscribed in a circle 2007-02-04
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 2007-01-31
From Shelby:
I am doing homework and I need to know why squares are rectangles but not all rectangles are squares?
The substitution method 2007-01-31
From Victoria:
how do i solve this problem using the substitution method?
2x-5= -14
-7x+14y= -5

The elimination method 2007-01-31
x-2y=2
3x-5y=7

A thin wire 20 centimeters long is formed into a rectangle 2007-01-29
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?
A boat travels 60 miles downstream in the same time it takes to go 36 miles upstream 2007-01-27
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.
Freefalling objects 2007-01-25
From Patricia:
How long will it take a stone dropped from atop a 1000-meter tall building to reach the ground?
A college student jogs from his home to the beach 2007-01-23
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?
What is the speed of each boat per hour? 2007-01-22
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?
A formula for figuring a tanks volume at various levels 2007-01-20
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.
Depth and volume in a cylindrical tank 2007-01-20
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?
At what speeds were they travelling? 2007-01-16
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?

Standard deviation 2007-01-15
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"
What is his rate of walking for the entire trip? 2007-01-12
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?
Throwing a stone downwards 2007-01-12
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?
Find the area of the rectangle 2007-01-09
From Mike:
The perimeter of a rectangle is 72 in. The base is 3 times the height. find the area of the rectangle?
What is the speed of the current? 2007-01-07
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?
Are all rectangles trapezoids? 2007-01-05
From Sarah:
Are all rectangles trapezoids?
From Harold:
L=3w-4
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
(3w-4) x w=96

could you give me an example

Cary was going to meet Jane at the airport, ... 2006-12-11
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)
Rate of a boat and a river 2006-12-09
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 ____?
The Metra and the Amtrack 2006-12-03
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 2006-11-30
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?
Dimensions of a rectangle 2006-11-22
From Terri:
How can you find the dimensions of a rectangle that has a perimeter of 18 feet?
Circle geometry 2006-11-19
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.
Two trains left the station at the same time and traveled in opposite directions. 2006-11-18
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?
Find the distance function s(t) given the acceleration function a(t) 2006-11-16
From David:
Find the distance function s(t) of the acceleration function: a(t)= sin(0.1t)/ cos^3(0.1t)
Tangent lines 2006-11-09
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?

Simultaneous equations 2006-11-06
From An other:
e^2y-x+2=0
ln(x+3)-2y-1=0

Going from one town to another 2006-11-04
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.
The dimensions of a rectangle 2006-11-02
From Ben:
A rectangle's length is 8 cm. greater than its width. Its perimeter is 128 cm. Find its dimensions.
Paddeling on the Alleman River 2006-10-31
From Anita:
Len is planning a three-hour 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?
The distance from a point to a line in 3 space 2006-10-29
From Marie:
find the distance from the point (1, -2, -3) to the line x = y = z-2
How do you find the length and width of a rectangle if you know ... 2006-10-15
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 2006-10-04
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?
A 5x2 rectangle 2006-10-03
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? 2006-09-21
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?
A rectangular tank 2006-09-19
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.
Convert a standard form to a slope intercept form 2006-09-14
From Maiko:
I need to know step by step procedures to convert a standard form to a slope intercept form?
How high (in feet) is the mountain? 2006-08-29
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?
The capacity of our hexagon fish tank 2006-07-26
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.
The dimensions of a rectangle 2006-07-09
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.
Flying with and against the wind 2006-07-06
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.
A tangent to a circle 2006-07-05
From Izumi:

I have problems finding the point of tangency between the circle C

x2 + y2 + 4x - 6y - 12 = 0

and the tangential line that passes through the point P (6, -1).

A boat travels 60 miles upstream ... 2006-05-28
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.
Simultaneous Equations 2006-05-24
From Angie:

Question: solve the equations
2x-3y-z=0
3x-2y+z=-5
x+3y-2z=14

for x,y,z

The interior angles of a right triangle 2006-05-20
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 2006-05-19
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.
Absolute Value vs. Standard Deviation ? 2006-04-24
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?
Geometry proof 2006-04-23
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
Distance to the horizon 2006-04-20
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?
Two circles 2006-04-07
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.
2x+5y=3 And -x+3y=-7 2006-04-03
From Lloyd:
simplify 2x+5y=3 And -x+3y=-7
Wes and Tony live 360 km apart. 2006-04-01
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.
How far from Earth is Neptune? 2006-03-21
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?
If a circle is elongated into an oval .. 2006-03-16
From Bruce:
If a circle is elongated into an oval, with constant circumference, does the area remain constant?
A 3-dimensional star 2006-03-15
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 '3-dimensional 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.
Rectangles with the same perimeter 2006-03-14
From Kristine:
If two rectangles have the same perimeter, will they also have the same area? Why
2x+3y=0 and 3x-y=0 2006-03-14
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 3x-y=0 this is one question can you help me please
The number of gallons in a tank 2006-03-09
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 ?
The volume & surface area of a rectangular pyramid. 2006-02-27
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?
Luke and Slim have only one horse. 2006-02-26
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?
Traveling from Asheville to Indianapolis 2006-02-21
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 2006-02-12
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.

Degree 2006-02-09
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.

A locus problem 2006-02-08
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.
One boundary of a pond is parabolic in shape. 2006-01-20
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.
A sequence of circles and tangents 2006-01-16
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)).
What initial velocity is required to double the maximum height 2006-01-14
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?
60.5 ft at 90 mi/hr takes how long? 2006-01-13
From Bree:
A ball travels over 60.5 ft at 90 mi/hr. How fast does the ball travel?
A rectangle has a length that is 7cm more than twice the width 2005-12-21
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.
Simultaneous Equations 2005-12-21
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?

Four tangent circles 2005-12-06
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.

A long distance call 2005-12-05
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 long-distance 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 m-minute long-distance call.

A standard normal probability 2005-11-19
From Pat:
Find the probability of Z when it lies between -1.10 and -0.36
A variable rectangle 2005-11-08
From Mussawar:
find the lengths of the sides of a variable rectangle having area 36 cm2 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.
Equidistant from the points (2,-1,1) and (0,1,3) 2005-11-06
From Roy:

Find the point on the y-axis that is equidistant from the points (2,-1,1) and (0,1,3).

Find the point not on the y-axis 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 2005-11-02
From A student:
Find the point on the curve y=x2 where the tangent to the curve is parallel to the secant line connecting (-1,1) and (2,4)
Simultaneous equations 2005-10-13
From Daniel:
5x + 3y = 22 4x - 7y = -20
Means of sample means 2005-10-12
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.

Coefficients, constants and like terms 2005-10-05
From Elizabeth:
In the equation -8y+6ab+7-3ab what are the coefficients; the like terms and constants?
City A is 30 miles directly north of City C 2005-10-04
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.
Volume of a tank 2005-09-11
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.
A normal distribution problem 2005-08-08
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.
Two tangents to a circle 2005-06-18
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.
Gallons in a tank 2005-04-02
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.
The integral of tan^4x 2005-03-31
From Nicole:
college student. need help with tough integral.

the integral of 2tan4xdx

The shortest distance from a point to a line 2005-03-30
From carly:
Find the shortest distance from the point (-15, 2.5) to the line 5x+6y=30.
Gasoline in a cylindrical tank 2005-03-23
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?

Tangents to a circle 2005-03-19
From Sue:

You're given the equation to a circle (x-3)2 + (y-3)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

The volume of a stock tank 2005-03-13
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?
Three tangent circles 2005-01-25
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?
Standard deviation 2005-01-02
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

The gradiant of a hill is 9% 2004-12-18
From Jim:
The gradiant of a hill is 9%. What angle is created by the run/rise of the hill and 0 degrees?
The tangent line at an inflection point 2004-11-28
From Louise:
the equation of the tangent line to the curve y = x3 - 6x2 at its point of inflection is...
Is a square a rectangle? 2004-11-21
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.

A standard deviation test 2004-11-09
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.
The combined force of two vectors 2004-10-30
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 = -8i-3j.

1.Determine the direction of movement of the ball if the i axis is due east.

2.Determine the combined force magnitude.

The force of a 5000 tonne lorry 2004-10-27
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

A rate of change problem 2004-10-15
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.
A common tangent line 2004-10-05
From Shanup:
The x-axis is a common tangent of y = x^2 and y = x^3. Find the equation of another common tangent.
The length of a rectangle 2004-09-26
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?
Incremental variance 2004-09-23
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 quarter-hour 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 2004-09-04
From Joe:
Why do we use square roots and squares in the distance formula Wholdnt they cancel each other out?
A tangent to a hyperbola 2004-08-02
From A student:
The equation of a hyperbola is 32x*2 -18Y*2-64x +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.
Two vector problems 2004-07-14
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?
The tangent of theta 2004-07-10
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?
What is the name of a 3D rectangle? 2004-06-07
From Jack:
if a cube is a 3D square, what is the name of a 3D rectangle?
A tangent to a quadratic 2004-06-04
From Jem:
I have a question on the tangent to a quadratic curve. Say I have a curve y = ax2 + 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 y-axis where the tangent cuts isn't it? Is there a formula for it?

The center of a circle 2004-05-26
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?
How far apart are they? 2004-05-23
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?
The dimsenions of a room 2004-05-18
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.
Area and perimeter 2004-03-12
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 x-1.

Distance, time and rate 2004-03-09
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?
A geometry problem 2004-03-04
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
Volume of a fuel tank 2004-03-01
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?
The dimensions of a rectangle 2004-02-21
From Jane:
A rectangular label has an area of 176cm2 and a perimeter of 54cm. Find the dimensions of the label.
A pyramid-shaped tank 2004-02-13
From Annette:
The base of a pyramid-shaped 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.)
Driving from Sarnia 2004-02-11
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?"
The London marathon 2004-01-27
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
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 1-hour 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 45-minute 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?
A fish tank 2003-11-26
From Bill:
How do I work out the volume and weight of water in a fish tank that is 36in x 14in x 12in?
A point and a line 2003-11-19
From Meenakshi:

Given a line segment L(x1,y1) to (x2,y2) and a Point P(x3,y3).
I need the formula to find a point on the line L that is closest to the point (x3,y3).

A rectangle on a disk 2003-10-29
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?
Squares in a rectangle 2003-10-21
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?

Statistics from grouped data 2003-10-09
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.

Standard Deviation 2003-10-07
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???

The sketch of a graph 2003-10-07
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)x3-2x2+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.
The slope of a tangent 2003-10-01
From A student:

find the slope of the tangent to each curve at the given point

f(x)=square root 16-x, where y=5

A rectangle in a circle 2003-09-27
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?
Notation 2003-09-15
From Kim:

Question:
i have a couple of questions

1. write in standard form
a)4x2x8 b) 5 to the power of 4

.
.
.

Area of a rectangular room 2003-09-11
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?
A boat travels 12 km upstream... 2003-09-03
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.
Water in a tank 2003-09-02
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.
A theorem in geometry 2003-09-02
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 PT2 = AP x BP.
Answered by Dieter Ruoff and Penny Nom.
A rule with a variable 2003-08-24
From Crystal:
what is a rule with a variable
The volume of a fuel tank 2003-08-16
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.
Two cars 2003-07-09
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.
Is 3/5 CLOSEST to 0, 1/2 or 1? 2003-07-09
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.
The weight of a fish tank 2003-05-20
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.
sin theta = 7/8 2003-05-07
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)
A circle, tangent to two circles and a line 2003-04-30
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 (X-Axis) 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 2003-04-18
From Lech:
The line with equation y=mx is a tangent to the circle with equation x2+y2-6x-6y+17=0. Find the possible values of m.
Incremental standard deviation 2003-04-12
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? 2003-02-27
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?

Two airplanes leave Dallas 2003-02-06
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?
A train with 2 cars 2003-02-04
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?
A rectangular prism 2003-01-09
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?
Trigonometry problems 2002-12-01
From Chiara:
1. Find tan 35pi/4
2. Graph y = cos2x - 2sinx

Constructing a tangent to two circles 2002-11-28
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 2002-11-28
From Liz:
If a car has traveled 16 miles in 30 minutes, how many miles per hour did they go?
Two tanks of water 2002-11-08
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?
Variance 2002-10-29
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.
Is a square a rectangle? 2002-10-20
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? 2002-09-16
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?
The tangent to a curve and the tangent of an angle 2002-08-26
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)?
Distance in 3-space 2002-08-16
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.
Two equations 2002-07-26
From Derek:
1. 3x + 2y = 4
2. -7x + 2y = 24

finding x and y.

Bob swam across a river 2002-05-22
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.
Day care 2002-05-13
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 %

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?

P= 20/60= 33.3% stay in day care for 20h per week,

Trains and cracker boxes 2002-04-29
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]

A test drive 2002-04-23
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?
Pairs of equations 2002-04-04
From A student:

high school level

```y=4x x=-4y
x+y=5 3x+2y=20

y=x-1 3x-y=4
x+y=3 2x-3y=-9

x+5y=4
3x+15y=-1

. . .
```

Range of values for standard deviation 2002-03-22
From Susan:
What is the range of values for standard deviation? Is it between 0 and +3? Is it between +1 and +3?
15 miles at 13 miles per hour 2002-03-12
From Rich:
If I were traveling 15 miles at 13 miles per hour how long will it take?
The slope of a tangent line 2002-03-04
From Ridley:
Suppose a function f(x) has the line 3x+4y=2 as its tangent line at x=5. Find f'(5).
Two circles inscribed in a rectangle 2002-02-27
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.
The substitution method 2002-02-24
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

Can the standard deviation ever = 0? 2002-02-16
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?
Normal distribution 2002-01-21
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?
The distance across a circle 2002-01-18
From Douglas:
If you know how far around a circle is (say earth) 25000 miles how do you calculate the distance across?
The tangent function 2002-01-12
From Justine:
if you know that sin45degress = cos45degrees, how do you know that tan45degrees = 1?
The famous "train problem" 2002-01-12
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?
Simultaneous equations 2001-12-17
From Matthew:
4x + y = 4
2x - 3y = 5

what is x and y

Two equations in two unknowns 2001-12-04
From Courtney:
y = 3x + 2
y = 4x - 5

solve for x

Undetermined coefficients 2001-11-22
From Hoda:
The equation is:

y" - 2y' + y = t et + 4

We need to use The method of Undetermined coefficients. I have tried assuming that the solution is Atet+Bet+C, but all I get is C=4 and I tried (At2+Bt+C)et+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?

A tangent line 2001-11-21
From A student:
write an equation of the line tangent to the graph of

ey + ln(xy) = 1 + e at (e,1)

Area of a quilt 2001-10-14
From Jack:
1. how would you find the area of the quilt? which is a square

2. how would you fined the area of each square?

Joan and Jan work together 2001-09-26
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?
Julia goes to work 2001-09-25
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?
Ciefficient of variation 2001-09-23
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?
Standard deviation 2001-09-22
From Doug:
I was wondering if anybody knows who the founder of standard deviation was?
Ray and Jane 2001-09-06
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.
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?
Standard angles 2001-08-05
From Nagaraj:
Why 0o , 30o , 45o , 60o ,and 90o are taken as standard angles in Trigonometry? Why can't we take some other angles as standard angles?
Linear regression 2001-08-01
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 error-Sy.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 2001-07-27
From Jeff:
prove this identity and show steps
tan(x/2+pi/4)=secx+tanx

Comparing means and standard deviations 2001-07-11
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?
Three tangents to a circle 2001-06-27
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.
The shortest distance from a point to a line 2001-06-05
From Kat:
Find the shortest distance from the given line. Round to the nearest tenth. (-2,-1) and x+5y+20=0
Common solution 2001-06-02
From Samantha:
1. Solve for common solution: x+y=6 2x-3y=2

2. Solve for y in terms of x: 3x-y=4

Squares on a chess board 2001-04-11
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.

Prisms 2001-04-10
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?
The normal to a curve 2001-04-08
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=(x-2)2/(1-x)2 that is parallel to the line x+4y+7=0

Common tangents 2001-04-08
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=x2 and 2y=-x2-16 Thanks for the help. :)
Where do the lines y=2x-4 and y=x-1 intesect? 2001-04-06
From Bryce:
solve the following problem by setting them equal to each other. Solve for x and y. Where do the lines y=2x-4 and y=x-1 intesect?
The unit circle and trigonometry 2001-04-05
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 ...
Sigma 2001-03-31
From A student:
What does the Sigma symbol mean in mathematics?
Systems of equations 2001-03-16
From joy:
How do u solve problems using systems of equations?
~ finding x and y~

ex:

26 = 3x - 2y
42 = 4x + y

The angle of elevation 2001-03-08
From Jeffrey:
At a Certain time, a vertical pole 3m tall cast a 4m shadow. What is the angle of elevation of the sun?
The substitution method 2001-03-05
From A student:
Solve each system of equations by the substitution method. Show your work.
1. y = 8
7x = 1 - y

2. y = x - 1
4x - y = 19

A problem with distance 2001-01-16
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.
cot(arcsin 3/5) 2001-01-07
From Jason:
Find value. Assume that all angles are in Quadrant 1.

cot(arcsin 3/5)

Filling a tank 2001-01-02
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.
The aspect ratio of a rectangle 2000-12-04
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.
Triangles and trigonometry 2000-11-30
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?
Connecting to a water line 2000-10-20
From Vanja:
My question is...A house is to be connected to a new water main that runs along the line y=2/3x-1. 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?
Two linear equations 2000-09-14
From David Dean:
2a + 1b = 3.39 3a + 3b = 6.59
What formula do I use to find what a = ?

Two geometry problems 2000-09-09
From Becky:
What are all the real values of x that are solutions for the inequality [x-2] < 6? ( it's less than or equal to)

What is the distance between the points with (x,y) coordinates (3,-2) and (-3,-1)?

Euclidean distance 2000-09-06
From Velma Zahirovic-Herbert:
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)

A trig question 2000-07-01
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

Parallel tangents 2000-06-30
From Ebony Indalecio:
I need to prove the theroem: Tangents to a circle at the end points of a diameter are parallel.
Rectangles and algebra 2000-06-13
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 2000-06-02
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.
A conic in standard form 2000-05-18
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 16x2-9y2-160x-18y+247=0
Sample variance 2000-04-16
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 n-1 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?
A parabola problem 2000-03-23
From Morin:
I need to prove that if parabola x2=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 y-axis. Further, prove that the point D where this line intersects the parabola is the midpoint of line CM.
Simultaneous equations 2000-03-11
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?

Systems of linear equations 2000-03-10
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

Angle of Intersection of Two Lines 2000-03-02
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)x-1. (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 sub1-theta 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.
Is a square a rectangle? 2000-02-15
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.

Taxicab geometry 2000-01-16
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.

.
.
.

Three dimensional rectangle 2000-01-11
From Dennis Murphy:
I would like to find out the name of a Three dimensional rectangle.
Rectangular hyperbola 1999-12-15
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?
Systems of equations 1999-12-06
From Roger Hornbaker:
I am having problem figuring out x and y solutions.
1. 5x + y = 4
3x - y = 4

2. 3x + 2y = 6
- 3x + y = 0

An area problem 1999-11-29
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?
Estimating the population mean 1999-11-13
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?

Distance between the windows 1999-09-19
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
Standard Deviation 1999-07-11
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.
Girth 1999-05-26
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.

A bike race 1999-04-23
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?

Universal Area 1999-04-08
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 1999-03-30
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

An airplane problem 1999-03-08
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?
Absolute value of i 1999-01-06
From Wayne Bagley:
I would like to know what is the absolute value of i. I need an answer suitable for the secondary level.
Two Chords 1998-09-29
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.

Nickles on the Highway 1998-09-22
From Ronnie Mac Donald:
How many nickels would it take to cover 226km of highway,each nickel is 2cm in diameter?
Area and Volume 1998-07-28
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?
Trigonometry history 1998-05-26
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...
Mean and Standard Deviation 1998-04-22
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!

Tangrams 1998-02-24
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 1997-11-10
From Jason Watkins:
I know which octant is octant 1 because all variables are positive. How do we number the other octants?
The Length of a Chord. 1997-07-26
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.

The angle between two tangents. 1997-06-09
From Felix Ho:
Two tangents are drawn from the origin to the circle (x)(x)+(y)(y)-4x-6y+9=0. If the angle between the tangents is m, fine the value of tan(m).

P.S. (x)(x)=square x

A trig problem 1996-12-13
From S. Johnson:
sin t + cos t = 1/5. Find ALL exact values of cot t, given the original equation.
Height of a Hotel 1996-11-07
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?
A tangent to a circle is perpendicular to the radius at the point of contact. 1996-10-22
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 2009-01-05
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

les données sont inconsistantes 2007-10-03
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 réalisées-Interviews réalisées avec question Q2)=Durée moyenne de conversation sans la question Q2

Q2=questionnaire Long

5 points équidistants sur la surface d' une sphère 2005-08-15
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.
Les dimensions d'un rectangle 2001-04-09
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 cm2, mais si on diminue a de 2cm et b de 1cm, l'aire du rectangle diminue de 16cm2. Quelles sont les valeurs de a et b?

2. Quelle est la valeur numerique de l'expression (ac+bd)+(ad-bc) sachant que a+b=1 et que c+d=1? Quelles sont les regles essentielles qui me manquent pour resoudre ceci?