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An equilateral triangle inscribed in a circle 2017-09-15
From sumit:
what is the area (in sq. unit) of an equilateral triangle inscribed in the circle x^2+y^2-4x-6y-23=0.
Answered by Penny Nom.
Quadrilateral ABCD is inscribed in a circle 2017-09-11
From Joie:
Quadrilateral ABCD is inscribed in a circle such that side DA is the diameter. AB=2m., BC=4m., CD=6m., angle BAD=75.93degrees. Find the area of the quadrilateral.
Answered by Penny Nom.
Water leaking from a trough 2016-12-28
From Kathryn:
A trough is 6 m long, and has uniform cross-section of an equilateral triangle with sides 1 m. Water leaks from the bottom of the trough, at a constant rate of 0.1 m3/min. Find the rate at which the water level is falling when the water is 0.2m deep.
Answered by Penny Nom.
A circle inscribed in an equilateral triangle 2016-11-27
From jo:
what is the radius of the inscribed circle of an equilateral triangle with altitude 12 units?
Answered by Penny Nom.
Quadrilateral 2016-06-14
From Muhib:
Is there a quadrilateral with 0 sets of parallel sides.
Answered by Penny Nom.
The lateral side length of a cone 2016-06-05
From Diane:
Question is find the lateral side length of a right cone with area of 372 sq. cm and base circle radius of 9 cm.
Answered by Penny Nom.
The area of a 4-sided lot 2016-05-25
From prasad:
How to find area of a land whose sides are 41ft,33ft,32.3ft and 33.2 ft. Pl give me the formula and proof.
Answered by Penny Nom.
The sum of the angles of a triangle 2016-02-24
From Sophia:
Does every triangle add up to 180 degrees? (Such as a unique triangle)
Answered by Penny Nom.
The midpoints of the sides of a quadrilateral 2016-02-05
From Andrea:
The segments, joining, in order the midpoints of consecutive sides of a quadrilateral form a parallelogram.
Answered by Penny Nom.
A quadrilateral inside a square 2016-01-30
From Subrahmanya:
In a square ABCD of side 6 units P, Q are mid points of BC, CD respectively. The line segments BQ, DP intersect in R then find the area of the quadrilateral ABRD using only plane geometry.
Answered by Chris Fisher.
An equilateral triangle inscribed in a circle 2015-06-11
From Casey:
I have an equilateral triangle inscribed in a circle - this triangle has been bisected to give me 2 right triangles. I know the length of the line bisecting the equilateral triangle is 36 inches. How do I figure out the circumference of the circle and the length of the sides of the equilateral triangle?
Answered by Penny Nom.
The height of an equilateral triangle 2015-03-12
From anna:
I am anna and i am in 7th grade.
i am trying to find the height of and equilateral triangle, all sides equaling 4 inches

Answered by Penny Nom.
The area of a quadrilateral 2015-03-11
From Joel:
Diagonal ac of quadrilateral ABCD is 60cm and the lengths of perpendiculars to It from the opposite vertices are 4.2cm and 5.8 cm find the area of the quadrilateral ABCD
Answered by Penny Nom.
The area of a quadrilateral 2014-08-06
From Rahul:
find the area of the quadrilateral whose side measure9cm,40cm,28cm,15cm and in which the angle between the first 2 sides is a right angle
Answered by Penny Nom.
An equilateral triangle with vertices in 3 parallel planes 2014-05-31
From prajay:
How to construct an Equilateral Triangle whose vertices lie on three parallel lines, if the distances of two lines are 'a' and 'b' units from the middle line.What is the length of the side of the Equilateral Triangle ?
Answered by Chris Fisher.
A cyclic quadrilateral 2014-03-28
From Carly:
Suppose ABCD is a cyclic quadrilateral, i.e A, B, C, and D are the points on a circle, given in order going around the circle. Show that if we join each of A, B, C, and D to the orthocentre of the triangle formed by the other three, then the resulting line segments all intersect in a common midpoint.
Thank you.

Answered by Chris Fisher.
Water in a conical funnel 2014-02-11
From Marcus:
Water is running out of a conical funnel at the rate of 1 inch^3/sec. If the radius of the base of the funnel is 4 in. and the altitude is 8 in., find the rate at which the water level is dropping when it is 2 in. from the top.
Answered by Penny Nom.
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.
Answered by Penny Nom.
A man and a kite 2014-01-29
From Veronica:
A man flies a kite at a height of 120 meters. The wind carries the kite horizontally away from him at a rate of 8 meters/second. How fast is the distance between the man and the kite changing when the kite is 130 meters away from him?
Answered by Penny Nom.
The fourth side of a quadrilateral 2014-01-23
From joanna:
left vertical measurement 2560mm
right vertical measurement 1850mm
base horizontal measurement 1750mm
question - what will the 4th measurement be please.
using a scale drawing I make it approx 1900mm but require an accurate measurement

regards

Joanna

Answered by Penny Nom.
The area of a quadrilateral 2013-12-21
From khushboo:
Find the area of quadrilateral pqrs in which angle QPS=90°,PQ=12cm, PS=9cm, QR=8cm and SR=17cm. (Hint: PQRS has two parts)
Answered by Penny Nom.
A circle insubscribed in an isosceles trapezoid 2013-12-08
From Bob:
A circle is insubscribed in an isosceles trapezoid, with parallel lengths of 8cm and 18cm. What is the lengths of sloping edges and why?
Answered by Robert Dawson.
Water flowing out of a tank 2013-11-03
From Carolyn:
The flow of water out of a hole in a tank is known to be proportional to the square root of the height of water above the hole. That is,

dV/dt (proportional to) sq root (h)

The tank has a constant cross-sectional area A, show that the height of water in the tank is given by

h = ((-kt+C)/2)^2

If the tank is 9 metres high, and it takes 5 hours for it to drain from full to half full, how much longer will we have to wait until it is completely empty?

Answered by Penny Nom.
Euclid's Parallel Postulate 2013-08-20
From Justin:
Hello there,

I was wondering is Euclid's Fifth Parallel Postulate of parallel lines never intersecting, undecidable or essentially undecidable?

Thank you so much for any help you can provide!

Answered by Robert Dawson.
Related rates 2013-02-17
From Ishaak:
A hemispherical bowl is filled with water at a uniform rate. When the height of water is h cm the volume is π(rh^2-1/3 h^3 )cm^3, where r s the radius. Find the rate at which the water level is rising when it is half way to the top, given that r = 6 and the bowl fills in 1 minute.
Answered by Penny Nom.
An equilateral triangle inscribed in a circle 2013-01-17
From Nicole:
How do you find the shaded region of a circle if an unshaded equilateral triangle in inscribed in it. The only other things I know about the problem are that the side lengths of the equilateral triangle are 14 inches.
Answered by Penny Nom.
The perimeter of an equilateral triangle 2012-12-14
From shreyaarora:
if the area of on equilateral triangle is 24/3cm,then what is its perimeter
Answered by Penny Nom.
An equilateral triangle and a regular hexagon in a circle 2012-09-11
From Heidemarie:
The vertices of an equilateral triangle with side length of 10 sqrt 3 cm lie on a circle. Find the side length of the regular hexagon whose vertices lie on the same circle.
Answered by Penny Nom.
The area of a quadrilateral 2012-04-21
From Rajat:
calculate the area ABCD in which AB is 48'1'',BC is 98'4'',CD is 61'4'',DA is 102'10'',AC is 110'3'',BD is 116'9''.
Answered by Penny Nom.
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?
Answered by Penny Nom.
A circle drawn around a equilateral triangle 2012-04-01
From BIMAL:
what is the diameter of a circle drawn around a equilateral triangle of size 6 cm
Answered by Penny Nom.
Gravel, sand, cement and an equilateral triangle 2012-03-21
From saheed:
how many tonnes of gravel and sand,bags of cements will be required to concrete 5feet depth/deep of 4feet equilateral triangle?
Answered by Harley Weston.
The height of an equilateral triangle 2012-02-29
From Carley:
Hi my name is Carley. I am an 8th garder. What us the height of an equilateral triangle si the sides are 18 cm?
Answered by Penny Nom.
The weight of a steel plate 2012-02-27
From david:
what is the weight of a steel plate that is 1/2" thick, 20" wide, and 45"long if the steel weigh .28 lb per cubic inch.
Answered by Penny Nom.
If a parallelogram is a cyclic quadrilateral then it is a rectangle 2012-02-01
From Kim:
Show that if a parallelogram is a cyclic quadrilateral then it is a rectangle. Hint: Observe that in a parallelogram ABCD we always have Triangle ABC is congruent to Triangle CDA.
Answered by Robert Dawson and Chris Fisher.
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
Answered by Penny Nom.
Water is flowing into a cup 2011-12-19
From Tim:
A cup has a radius of 2" at the bottom and 6" on the top. It is 10" high. 4 Minutes ago, water started pouring at 10 cubic " per minute. How fast was the water level rising 4 minutes ago? How fast is the water level rising now? What will the rate be when the glass is full?
Answered by Penny Nom.
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

Answered by Penny Nom.
A reservoir has the shape of an inverted cone 2011-10-03
From Roger:
a reservoir has the shape of an inverted cone whose cross section is an equilateral triangle. if water is being pumped out of the reservoir at a rate of 2m^3/sec, at what rate is the depth of the water changing when the depth is 40 meters?
Answered by Penny Nom.
A hemispherical bowl with a lead ball inside 2011-09-27
From Jean:
"(a) Water is being poured into a hemispherical bowl of radius 3 inch at the rate of 1 inch^3/s. How fast is the water level rising when the water is 1 inch deep ?

(b) In (a), suppose that the bowl contains a lead ball 2 inch in diameter, and find how fast the water level is rising when the ball is half submerged."

Answered by Penny Nom.
A cyclic quadrilateral 2011-08-15
From Tim:
Hi! I've been working on this for a while and I'm quite stuck. If anyone can help that would be great. The sides BC and AD of a quadrilateral ABCD are parallel. A circle meets the side AB at B and E and the side CD at C and F. Prove that the quadrilateral AEFD is cyclic.
Answered by Chris Fisher.
Find the rate at which the searchlight rotates 2011-04-17
From Meredith:
A searchlight is position 10 meters from a sidewalk. A person is walking along the sidewalk at a constant speed of 2 meters per second. The searchlight rotates so that it shines on the person. Find the rate at which the searchlight rotates when the person is 25 meters from the searchlight.
Answered by Penny Nom.
A conical container and a spherical balloon 2011-04-06
From Steven:
Water is running out of a conical container 12 feet in diameter and 8 feet deep (vertex down) and filling a spherical balloon. At the instant the depth of the water in the cone is 4 feet, the radius of the sphere is approximately 4 feet.

The rate of change of the depth of the water in the cone at the instant is approximately ______________ times the rate of change of the radius of the balloon.

Answered by Penny Nom.
[(90+36-4) ÷ 2] x 15 = 2011-03-30
From ken:
[(90+36-4) ÷ 2] x 15 =
Answered by Penny Nom.
A camera's line of sight 2011-02-26
From MJ:
A rocket that is rising vertically is being tracked by a ground level camera located 3 mi from the point of blast off when the rocket is 2 mi high its speed is 400mph At what rate is the (acute) angle between the horizontal and the camera's line of sight changing
Answered by Penny Nom.
At what rate is the grain pouring from the chute? 2011-02-26
From MJ:
Suppose that grain pouring from a chute forms a conical heap in such a way that the height is always 2/3 the radius of the base. At the moment when the conical heap is 3 m high, its height is rising at the rate of 1/2 m/min. At what rate (in m^3/min) is the grain pouring from the chute?
Answered by Penny Nom.
Cutting the top off a conical tent 2011-02-22
From tom:
how far from the top must you cut a conical tent in order to cut the cloth in half...
Answered by Penny Nom.
A player runs from second base to third base 2011-01-30
From Marie:
A baseball diamond is a square with side 90 feet in length. A player runs from second base to third base at a rate of 18 ft/sec. At what rate is the area of the trapezoidal region, formed by line segments A, B, C, and D changing when D is 22.5
Distance A is the players distance from first base when running from 2nd to third. Distance D is his distance from 3rd base. Distance C is the distance from 3rd to 3rd to Home. Distance B is the distance from Home to First. I have found dA/dt in a previous problem.

Answered by Penny Nom.
The sides of an equilateral triangle 2011-01-27
From Cristal:
Hello :) How can i find the sides of an equilateral triangle when only given the height 10m?
Answered by Penny Nom.
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?
Answered by Penny Nom.
The area of an equilateral triangle 2010-11-11
From ginny:
If a equilateral triangle has side lengths of 41.33m how would i calculate the area? if i don't know the height of the triangle?
thank you.

Answered by Penny Nom.
A circular oil slick of uniform thickness 2010-05-22
From Susan:
Hi, I have this problem on a homework assignment and just can't seem to figure it out:
A circular oil slick of uniform thickness is caused by a spill of 1 m^3 of oil. The thickness of the oil is decreasing at the rate of .001m/h. At what rate is the radius of the slick increasing when the radius is 8.

Answered by Penny Nom.
Exactly two lines of symmetry 2010-04-11
From debbie:
i am looking for a quadrilateral with exactly two lines of symmetry. please help! thank you.
Answered by Tyler Wood.
Related rates and a rectangular sponge 2010-04-06
From Heather:
A rectangular sponge is increasing its length at 4cm/min, decreasing its width at 2cm/min, and increasing its height at 3cm/min. When its length, width and height are 40, 30, and 20 respectively, find the rate of change of volume and surface area.
Answered by Penny Nom.
Sand falling off a conveyer 2010-04-02
From Katherine:
sand is falling off a conveyer onto a pile at the rate of 1.5 cubic feet per minute. The diameter of the base is approximately twice the altitude. At what rate is the height of the pile changing when it is 10 feet high?
Answered by Penny Nom.
Sand in an hourglass 2010-03-20
From Luke:
question
Answered by Harley Weston.
A quadrilateral with 4 known sides and 1 known angle 2010-03-19
From samuel:
Name: Samuel
Status: Student

I have a quadrilateral with 4 known sides and 1 known angle, and I'm trying to evaluate the other angles of my quadrilateral.

By the law of cosines, I can easily find my opposite angle (using the diagonal as a basis for the equation).

However, to find the two remaining angles, I have found no other way so far than to use the other diagonal, which can be found with the equation attached (from geometry atlas).

Is there any simpler way?

Answered by Robert Dawson and Harley Weston.
A related rates problem 2010-03-03
From Amanda:
A circle is inscribed in a square. The circumference of the circle is increasing at a rate of 6 inches per second. As the circle expands, the square expands to maintain the tangency. Determine the rate at which the area of the region between the circle and square is changing at the moment when the cricle has an area of 25(pi) square inches.
Answered by Penny Nom.
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.
Answered by Tyler Wood.
Related Rates Problem 2010-01-12
From Neven:
A woman raises a bucket of cement to a platform 40 ft above her head by means of a rope 80 ft long that passes over a pulley on the platform. If she holds her end of the rope firmly at head level and walks away at 5ft/s, how fast is the bucket rising when she is 30 ft away from the spot directly below the pulley? (G. F. Simmons, Calculus with Analytic Geometry, pg.142)
Answered by Penny Nom.
Related Rates of a Cylinderical Trough with a Horizontal Axis 2009-12-26
From Emily:
A cylinder is lying on it's side and being filled with water at a constant rate. Let the current height of water be t=0. When t=4, the cylinder is half full. When t=12, the cylinder is completely full. When is the rate of the height change increasing?
Answered by Janice Cotcher.
How fast is the distance between the two cars decreasing? 2009-12-08
From Jenny:
Two cares are on a collision course toward point P. The paths of the two cars make a 30 degree angle with each other. The first car is 40 km from P, and traveling toward P at 16 km/hour. The second car is 50 km from P, traveling at 20 km/hour. How fast is the (straight line) distance between the two cars decreasing. (Hint: Law of Cosines)
Answered by Harley Weston.
An irregular quadrilateral 2009-10-29
From riya:
what is irregular quadrilateral?
Answered by Penny Nom.
Solve for s 2009-08-12
From Michelle:
My daughter and I are having trouble with this problem...All it says i solve thr formula for the indicated variable.
Height of an Equilateral Triangle.

Solve for s:

H= square root of 3/2 * S

Answered by Penny Nom.
The lateral area of a cone 2009-07-15
From ashley:
What is the radius of a cone with the lateral area being 443.3 mm^2 and the slant height being 14.7 mm.
Answered by Penny Nom.
Sand falls from a conveyor belt 2009-04-01
From Tracy:
Sand falls from a conveyor belt at the rate of 10 cubic feet per minute onto a conical pile. The radius of the base is always equal to half the pile's height. How fast is the height growing when the pile is 5ft high?
Answered by Stephen La Rocque.
A spherical Tootsie Roll Pop 2009-04-01
From Tracy:
A spherical Tootsie Roll Pop you are sucking on is giving up volume at a steady rate of .8 ml/min. How fast will the radius be decreasing when the Tootsie Roll Pop is 20 mm across?
Answered by Harley Weston.
Related rates 2009-03-14
From Jeevitha:
The side of an equilateral triangle decreases at the rate of 2 cm/s. At what rate is the area decreasing when the area is 100cm^2?
Answered by Stephen La Rocque.
License plates and poker hands 2009-03-14
From CC:
You have a license plate it can have 6 numbers/letters you can use the numerals 0-9 and the letters A-Z how many combos are possible and how did you figure it out?

Question 2,

Your dealt an Omaha hand You have KKKQQ, how many different hands can consist of the same cards.

Answered by Harley Weston.
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.

Answered by Penny Nom.
Related rates 2009-03-09
From Megan:
A plane flying with a constant speed of 330 km/h passes over a ground radar station at an altitude of 3 km and climbs at an angle of 30°. At what rate is the distance from the plane to the radar station increasing a minute later?
Answered by Harley Weston.
Water flowing from a cone to a cylinder 2009-01-23
From Ray:
Water is passing through a conical filter 24 cm deep and 16 cm across the top into a cylindrical container of radius 6 cm. At what rate is the level of water in the cylinder rising when the depth of the water in the filter is 12 cm its level and is falling at the rate of 1 cm/min?
Answered by Harley Weston.
A cyclic quadrilateral 2009-01-23
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.
The area of a quadrilateral shape 2009-01-19
From craig:
how do u work out the area of a quadrilateral shape
Answered by Robert Dawson.
An equilateral triangle 2008-12-17
From lorraine:
an equilateral triangle has side lenghts of10.the length of its altitude is?
Answered by Penny.
A quadrilateral with two pairs of congruent sides 2008-12-10
From nicole:
what is the name of a figure that has 2 sides that measure 25 feet each and 2 sides that measure 10 feet each?
Answered by Robert Dawson.
A quadrilateral with exactly 1 pair of parallel sides and no congruent sides 2008-12-10
From alie:
a quadrilateral with exactly 1 pair of parallel sides and no congruent sides is what?
Answered by Robert Dawson.
Related rates 2008-11-26
From Lyudmyla:
How fast is the volume of a cone increasing when the radius of its base is 2 cm and growing at a rate of 0.4 cm/s, and its height is 5 cm and growing at a rate of 0.1 cm/s?
Answered by Harley Weston.
How fast is the length of his shadow changing? 2008-11-22
From Desiree:
A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 2.3 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?
Answered by Harley Weston.
License plates 2008-11-17
From Clayton:
Okay, so in this situation a license plate must have four letters (A-Z) and four numbers (0-9), ex. ABCD-1234, where repeating a letter or number is allowed ex. AAAA-1234, or ABCD-1111, or AAAA-1111. The order of letters first numbers second, or number first, letters second is allowable, and each state has its own plates, so ABCD-1234 from New York, and ABCD-1234 from Minnesota are considered different combinations, how many different license plates could there be?
Answered by Penny Nom.
A conical funnel 2008-11-12
From Rachael:
Hello, I am a 10th grader in AP Calc, and can not figure out this question: Water is running out of a conical funnel at the rate of 1 inch^3/sec. If the radius of the base of the funnel is 4 in. and the altitude is 8 in., find the rate at which the water level is dropping when it is 2 in. from the top.
Answered by Harley Weston.
The height of an equilateral triangle 2008-11-06
From touqeer:
My question is that how can we find the height of an equilateral triangle without using pythagoras theorem?
Answered by Penny Nom.
Water is leaking from a conical tank 2008-10-24
From Kimberly:
Water is leaking out of an inverted conical tank at a rate of 12000 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank.
Answered by Stephen La Rocque.
Melting ice on a hemisphere 2008-10-20
From heather:
The top of a silo is the shape of a hemishere of diameter 20 ft. if it is coated uniformly with a layer of ice, and if the thickness is decreasing at a rate of 1/4 in/hr, how fast is the volume of ice changing when the ice is 2 inches thick?
Answered by Penny Nom.
A geometric construction 2008-10-17
From M:
Given any 3 parallel lines on a plane, how to construct an equilateral triangle with each vertex on each line?
Answered by Chris Fisher.
Related rates 2008-10-16
From Gisela:
As sand leaks out of a hole in a container, it forms a conical pile whose altitude is always the same as its radius. If the height of the pile is increasing at a rate of 6 in/min, find the rate at which the sand is leaking out when the altitude is 10in.
Answered by Penny Nom.
The rate of change of the volume of a cone 2008-10-15
From Barbara:
Suppose that both the radius r and height h of a circular cone change at a rate of 2 cm/s. How fast is the volume of the cone increasing when r = 10 and h = 20?
Answered by Harley Weston.
The area of a quadrilateral 2008-09-11
From Mike:
How do I find the area of a quadrilateral that has one sloped side?
Answered by Penny Nom.
The perimeter of an equilateral triangle 2008-09-11
From Gerry:
How can I find the perimeter (length of side) of an equilateral triangle if the only information I have is the altitude?
Answered by Penny Nom.
An equilateral triangle 2008-07-21
From Meagan:
An equilateral triangle has vertices at (0,0) and (6,0) in a coordinate plane. What are the coordinates of the third vertex? You may want to sketch it out. Note: The sides of an equilateral triangle are identical in length.
Answered by Harley Weston.
A convex quadrilateral in spherical geometry 2008-07-09
From Joan:
What is the min and max number of obtuse angles possible ia a convex quadrilateral in Spherical Geometry? I know that the Saccheri has 2 obtuse angles and the Lambert has one, but are there other possibilities? Thanks for your help.
Answered by Chris Fisher.
Two triangles and a circle 2008-07-03
From Anita:
An equilateral triangle with side of length 1 cm is inscribed in a circle. A second equilateral triangle is circumscribed about the circle with all sides tangent to the circle. Find the length of a side of the second triangle.
Answered by Harley Weston.
A rectangle 2008-06-26
From SEBASTIAN:
How to arrange quadrilateral in the form of a rectangle?
Answered by Penny Nom.
Liquid is being pored into the top of a funnel 2008-05-25
From Stella:
Liquid is being pored into the top of a funnel at a steady rate of 200cm^3/s. The funnel is in the shape of an inverted right circular cone with a radius equal to its height. It has a small hole in the bottom where the liquid is flowing out at a rate of 20cm^3/s. How fast is the height of the liquid changing when the liquid in the funnel is 15cm deep?
At the instance when the height of the liquid is 25cm, the funnel becomes clogged at the bottom and no mo re liquid flows out. How fast does the height of the liquid change just after this occurs?

Answered by Stephen La Rocque.
A quadrilateral 2008-05-08
From reena:
two exterior angles quadrilateral are 100 degrees 110 degrees each. two remaing interior one angle twice size other find size of each angle
Answered by Penny Nom.
The Pythagorean theorem with triangles rather than squares 2008-04-29
From Zachary:
I need to figure out how to prove the pythagorean theoorem using equilateral triangles instead of using square. I know that A^2+B^2=C^2, but how do you get that by using equilateral triangles. I know the area of a triangle is BH1/2=Area. So what i need to know is how to derieve the formula of a triangle to get the pythagorean theorem
Answered by Penny Nom.
Related rates 2008-04-25
From Mary:
A rectangular box is 10 inches high. It's length increases at a rate of 2 inches per second and it's width decreases at the rate of 4 inches per second. When the length is 8 inches and the width is 6 inches, what is the rate of change of the volume?
Answered by Stephen La Rocque.
The area of an equilateral triangle 2008-03-28
From Elizabeth-Morgan:
I have a problem that reads: Find the area of a triangle with sides of 4 cm. Find the height first.

This means that I have an equilateral triangle, and I need a formula to calculate the height using the base, and the sides.

Answered by Stephen La Rocque.
The area of an equilateral triangle 2008-03-16
From michael:
my daughter has been given a task and I'm stuck too. if an area of an equilateral triangle = 85cm squared there are no other dimensions provided. how do I calculate the length of each side ? please
Answered by Penny Nom.
A 6 pointed star 2008-03-04
From Siddharth:
When 2 congruent equilateral triangles share a common center, their union can be a star If their overlap is a regular hexagon with an area of 60, what is the area of one of the original equilateral triangles?

a) 60 b) 70 c) 80 d)90 e)100

Answered by Stephen La Rocque.
A proof in geometry 2008-02-27
From Kimberly:
I'm trying to write a proof for the following: If all altitudes are equal in an equilateral triangle then all sides are equal.
Answered by Stephen La Rocque and Penny Nom.
A spherical bubble gum bubble 2007-12-31
From Houston:
Bazooka Joe is blowing a spherical bubble gum bubble. Let V be the volume in the bubble, R the inside of the bubble, and T the thickness of the bubble. V, T, and R are functions of time t.

(a) Write a formula for V in terms of T and R. Hint: Draw a picture
(b) Assume that the amount of bubble gum in the bubble is not changing. What is V'(t)?
(c) After 5 minutes of blowing a bubble gum bubble, the bubble is 3ft in diameter and .01 feet thick. If the inside radius of the bubble is expanding at a rate of .5 feet per minute, how fast is the thickness changing? Hint: Remember that the volume of gum in the bubble does not change over time.

Answered by Harley Weston.
Finding all the angles 2007-12-13
From Rajesh:
An eqilateral triangle is drawn in a square with one of the side as its base and draw the lines from the other angular sides such that there are four triangles formed inside the square which includes the equilateral triangle.I want to know all the angles of all the triangles formed inside the square.
Answered by Stephen La Rocque and Penny Nom.
Related rates - tree growth 2007-12-09
From Christy:
How do I go about answering this question, I know I have to find dv/dt, but I'm not sure how to start.
The volume of a certain tree is given by V= 1/12pie C^2h where C is the circumference of the tree at the ground level and h is the height of the tree. If C=5feet and growing at the rate of 0.2feet per yer, and if h=22feet and is growing at 4 feet per year, find the rate of growth of the volume, V.

Answered by Stephen La Rocque and Harley Weston.
Proving a quadrilateral is a rhombus 2007-12-03
From Jeanie:
How do you prove that a quadrilateral is a rhombus because the diagonals of the quadrilateral are perpendicular and bisect each other using the 2-column proof method?
Answered by Stephen La Rocque.
Related Rates (streetlamp and shadow) 2007-11-09
From Casey:
A street light is mounted at the top of a 15ft pole. A man 6ft tall walks away from the pole at a rate of 5ft per second. How fast is the tip of his shadow moving when he is 40ft from the pole?
Answered by Stephen La Rocque and Penny Nom.
Related Rates (a water trough) 2007-11-07
From Christina:
A rectangular trough is 3ft long , 2ft across the top and 4 ft deep. If water flows in at the rate of 2ft^3/min, how fast is the surface rising when the water is 1 ft deep ?
Answered by Stephen La Rocque.
The length of the side of a triangle 2007-10-28
From devon:
hay ok i have the height of a triangle but how do i find the length od the side if all of the sides are the same length
Answered by Penny Nom.
An equalateral triangle is 30 acres 2007-10-28
From mike:
If the area of an equilateral triangle is 30 acres, what is the length of each side in feet or miles?
Answered by Penny Nom and Victoria West.
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.

Answered by Stephen La Rocque.
Related rates 2007-10-26
From David:
A trough is 12 feet long and 3 feet across the top.(look like an upsidedown triangle square). Its ends are isosceles triangles with altitudes of 3 feet.

a) If water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level rising when h is 1 foot deep?

b) If the water is rising at a rate of 3/8 inch per minute when h=2, determine the rate at which water is being pumped into the trough. thank you so much for helping me out

Answered by Stephen La Rocque.
An equilateral triangle with height 2 inches 2007-10-23
From Christine:
I'm doing an project in school about tessellations. But first, I have to construct an equilateral triangle with an altitude of exactly 2 inches. I know how to draw an equilateral triangle...but I don't know what I have to do in order for the triangle to have an altitude of 2 inches.
Answered by Penny Nom.
The rate of change of the area of a triangle 2007-10-22
From Ahlee:
So my question is: The included angle of the two sides of a constant equal length s of an isosceles triangle is ϑ.
(a) Show that the area of the triangle is given by A=1/2s^2 sinϑ
(b) If ϑ is increasing at the rate of 1/2 radian per minute, find the rate of change of the area when ϑ=pi/6 and ϑ=pi/3.
(c) Explain why the rate of change of the area of a triangle is not constant even though dϑ/dt is constant

Answered by Penny Nom.
A rectangular trough 2007-10-18
From David:
A rectangular trough is 2 meter long, 0.5 meter across the top and 1 meter deep. At what rate must water be poured into the trough such that the depth of the water is increasing at 1m/min. when the depth of the water is 0.7m. I know this involves implicit differentiation somehow, but the 3 variables, since V=l*w*h for a rectangle is confusing me. I'm not sure whether one of the variables should be fixed or not, since I'm not getting anywhere with this right now. Any help would be great.
Answered by Stephen La Rocque and Penny Nom.
A conical cup 2007-10-18
From Nicholas:
Water is leaking out of a small hole at the tip of a conical paper cup at the rate of 1cm^3/min. The cup has height 8cm and radius 6cm, and is initially full up to the top. Find the rate of change of the height of water in the cup when the cup just begins to leak. Since V= (pi/3)r^2h, how do I eliminate a variable or change the equation so I that I can answer the question? Thanks.
Answered by Penny Nom.
Related rates 2007-10-15
From Alexis:
Example 1. An observer is tracking a small plane flying at an altitude of 5000 ft. The plane flies directly over the observer on a horizontal path at the fixed rate of 1000 ft/min. Find the rate of change of the distance from the plane to the observer when the plane has flown 12,000 feet after passing directly over the observer.
Answered by Stephen La Rocque.
Area of a quadrilateral 2007-10-10
From Courtney:
how would i find the area of a quadrilateral..
the sides are a (/) is 6cm, b (—) is 9 cm, and c (\) is 7 cm..
the angle between a and b is 140 degrees and b and c is 115 degrees..

Answered by Stephen La Rocque.
A convex quadrilateral 2007-09-24
From alex:
if a convex quadrilateral ABCD is set up so that angles b and c are fixed (for example angle b= 73 and angle c =150), and sides AB and CD are congruent; can angles a and b vary, or are they also fixed
Answered by Brent Michelson.
Water flowing into a tank 2007-09-21
From andrew:
Hi, I've been having real trouble visualizing this problem as apposed to a conical tank. It says the base of a pyramid-shaped tank is a square with sides of length 12 feet. The vertex of the pyramid is 10 feet above the base. The tank is filled to a depth of 4 feet, water is flowing into the tank at the rate of 2 cubic feet per minute. Find the rate of change of the depth of water in the tank.
Answered by Harley Weston.
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?

Answered by Harley Weston.
A quadrilateral problem 2007-08-29
From James:
The sides BC and AD of a quadrilateral ABCD are parallel. X is the midpoint of AB. The area of ABCD is Y. Find the area of the triangle CXD in the terms of Y.
Answered by Harley Weston.
Three points on the circumference of a circle 2007-07-30
From Bharathi:
given a circle with radius r and a point x,y on its circumference,output two other points x1,y1 and x2,y2 on the circle so thar all 3 points form a equilateral triangle.
Answered by Stephen La Rocque.
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?

Answered by Stephen La Rocque.
The area of a quadrilateral 2007-06-10
From Lucy:
Calculate the area of the quadrilateral ABCD. AB= 4.1cm, BC = 7.6cm, AD= 5.4 cm, CD= ? Angle ABC = 117, Angle ADC = 62. Give your answer correct to 3 significant figures.
Answered by Stephen La Rocque and Penny Nom.
The area of equilateral triangle 2007-06-05
From solomon:
describe the area of equilateral triangle in terms of its side? solve in two ways.
Answered by Stephen La Rocque.
A circular blob of molasses 2007-05-28
From Julie:
A circular blob of molasses of uniform thickness has a volume of 1 m^3. The thickness of the molasses is decreasing at a rate of 0.1 cm/hour. At what rate is the radius of the molasses increasing when the radius is 8 m?

Thanks,
Julia

Answered by Penny Nom.
More on quadrilateral shape names 2007-05-26
From Don:
If North Americans call a quadrilateral with no parallel sides a trapezium, is a kite merely a special type of trapezium? Can a rhombus be a kite?
Answered by Walter Whiteley and Penny Nom.
Lateral area of a right cone 2007-05-17
From Crystal:
In my homework the question says the lateral area of a right cone is 226.08 cm cubed. the slant hieght is 12 cm. Find the total surface area. How do I do that?
Answered by Stephen La Rocque.
Area of an equilateral triangle 2007-05-09
From Diana:
how do i find the area of an equilateral triangle when they give us the base?
Answered by Penny Nom.
A growing heap of sand: related rates 2007-04-23
From Charles:
Sand falls on to a horizontal ground at the rate of 9m ^ 3 per second and forms a heap in the shape of a right circular cone with vertical angle 60. Show that 10 seconds after the sand begins to fall, the rate at which the radius of the pile is increasing is 3 ^ (1/3) * (4/pi) ^ (1/3) m per minute.
Answered by Stephen La Rocque and Penny Nom.
Liquid is being poured into the top of a funnel 2007-04-19
From neroshan:
Liquid is being poured into the top of a funnel at a steady rate of 200cm^3/s. The funnel is in the shape of an inverted right circular cone with a radius equal to its height. It has a small hole at the bottom where the liquid is flowing out at a rate of 20 cm^3/s. How fast is the height of the liquid changing when the liquid in the funnel is 15 cm deep? At the instant when the height of the liquid is 25cm, the funnel becomes clogged at the bottom and no more liquid flows out. How fast does the height of the liquid change just after this occurs?
Answered by Penny Nom.
Water is being pumped into a trough 2007-04-09
From Michael:
Water is being pumped into a trough that is 4.5m long and has a cross section in the shape of an equilateral triangle 1.5m on a side. If the rate of inflow is 2 cubic meters per minute how fast is the water level rising when the water is 0.5m deep?
Answered by Stephen La Rocque.
A regular quadrilateral 2007-03-13
From Jackie:
How can the measure of each angle of a regular quadrilateral be determined?
Answered by Haley Ess.
Can the triangle be called both an acute triangle and an equilateral triangle? 2007-03-10
From Jane:
If all sides of a triangle are the same length and all angles are 60 degrees, can the triangle be called both an acute triangle and an equilateral triangle?
Answered by Walter Whiteley.
At what rate is the area of the triangle changing? 2007-02-24
From mac:
two sticks 3.5 feet long are hinged together and are stood up to form an isosceles triangle with the floor. The sticks slide apart, and at the moment when the triangle is equilateral, the angle is increasing at the rate of 1/3 radian/sec. At what rate is the area of the triangle increasing or decreasing at that moment?
Mac

Answered by Penny Nom.
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?
Answered by Penny Nom.
Water in a triangular trough 2007-01-30
From Trina:
the trough is 5 feet long and its vertical cross sections are inverted isosceles triangles with base 2 feet and height 3 feet. water is draining out of the trough at a rate of 2 cubic feet per minute. at any time t, let h be the depth and v be the volume of water in the trough.
a. find the volume of water in the trough when it is full
b. what is the rate of change in h at the instant when the trough is .25 full by volume?
c. what is the rate of change in the area of the surface of the water at the instant when the trough is .25 full by volume?

Answered by Penny Nom.
I have to design a lettering on corrugated plate 2006-11-29
From Tim:
For a client of mine I have to design a lettering on corrugated plate. The lettering has to appear "normal" when viewed from the front (100%) I am so far now to consider the shape of the plate to be two halves of an oval/ellipse. What I would like to know is a way to calculate the percentage in which I have to "stretch" my design in order to let it appear "normal".
Answered by Stephen La Rocque and Penny Nom.
How many licence plates are possible? 2006-11-24
From Naomi:
The state of New York has licence plates with five numbers followed by either a letter A or a letter B (eg. 36457A ,59972B ). How many licence plates are possible?
Answered by Penny Nom.
A cyclic quadrilateral 2006-11-20
From Namrata:
If two sides of a cyclic quadrilateral are parallel, prove that
(1) remaining two sides are equal,
(2) both diagonals are equal.

Answered by Penny Nom.
Wheat is poured on a conical pile 2006-11-17
From Rachel:
wheat is poured through a chute at the rate of 10 cubic feet per minute and falls in a conical pile whose bottom radius is always half the altitude. how fast will the circumference of the base be increasing when the pile is 8 feet high?
Answered by Penny Nom.
The name of a shape 2006-11-11
From Valentina:
I have a shape of 4 sides 3 are the same length (2cm each) and the other smaller (1.5cm)
Answered by Chris Fisher.
A melting snowball 2006-11-06
From Jay:
A snowball melts at a rate proportional to its surface area. Show that its radius shrinks at a constant rate. If it melts to 8/27 of its original volume in 20 minutes, how long will it take to melt completely? Please I need your help.
Answered by Stephen La Rocque.
The area of a quadrilateral 2006-10-31
From Georgina:
I would really like to know and be shown how to figure out the area of a quadrilateral. I already know that it is side x matching height but i need to be shown what to do. Could you please help?
Answered by Penny Nom.
Water is being pumped into the pool 2006-10-24
From Jon:
A swimming pool is 12 meters long, 6 meters wide, 1 meter deep at the shallow end, and 3 meters deeps at the deep end. Water is being pumped into the pool at 1/4 cubic meters per minute, an there is 1 meter of water at the deep end.

a) what percent of the pool is filled?

b) at what rate is the water level rising?

Answered by Stephen La Rocque.
A problem involving a quadrilateral 2006-10-13
From Jeff:
In the quadrilateral above, AB=AC=AD. If angle BCA = 65, then x=???
Answered by Penny Nom.
The area of a quadrilateral 2006-09-14
From A student:
How can i find the area of a quadrilateral?
Answered by Penny Nom.
How fast is the water level rising 2006-08-12
From Erin:
Water runs into a conical tank at the rate of 9ft3/min. The tank stands point down and has a height of 10 ft. and a base radius of 5 ft. How fast is the water level rising when the water is 6 ft. deep? (V=1/3 pi r2 h).
Answered by Penny Nom.
School bus reliability - a probability question 2006-04-27
From Peggy:
The school bus arrives at Janet's stop on time on 75% of school mornings. What is the probability it will arrive on time each day in a 5-day week?
Answered by Stephen La Rocque.
Can an equilateral triangle have an obtuse angle? 2006-03-26
From Chris:
Can an equilateral triangle have an obtuse angle?

I'm thinking not, because all sides must be equal, but
does that also imply that all angles are equal?


Answered by Stephen La Rocque.
Three towns are located at the vertices of an equilateral triangle 2006-03-20
From A student:
three towns are located at the vertices of an equilateral triangle. The towns are 8, 5, and 3 miles, respectively, from a store. How far apart are the towns?
Answered by Chris Fisher.
An equilateral triangle and a regular hexagon 2006-02-28
From Trevor:
An equilateral triangle and a regular hexagon have equal length perimeters. What is the ratio of their areas?
Answered by Penny Nom and Stephen La Rocque.
Translate and magnify a triangle 2006-02-19
From A student:
Triangle CAT has vertices located at C(-2,5), A(-5,1), T(1,1)

Translate triangle CAT 4 units right and magnify the triangle by 3. List the new coordinates and explain the process of computing the new coordinates.

Graph triangle CAT and the new triangle form part A on the same coordinate plane....

Will the area of the new triangle be 3 times as large as the original?? Explain why or why not

Answered by Penny Nom.
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.


Answered by Penny Nom.
An irregular quadrilateral 2006-02-04
From Christopher:
Is there such a shape as an irregular quadrilateral with 4 equal sides?
Answered by Penny Nom.
Two related rates problems 2005-12-29
From Shimaera:

#1. A manufacturer determines that the cost of producing x of an item is C(x)=0.015x2+12x+1000 and the price function is p(x)=250+2x/10. Find the actual and marginal profits when 500 items are produced.

#2. At 9 a.m a car is 10km directly east of Marytown and is traveling north at 100 km/h. At the same time, a truck leaves Marytown traveling east at 70 km/h. At 10 a.m, how is the distance between the car and the truck changing?


Answered by Penny Nom.
One car leaves a spot traveling at 100 km per hour 2005-12-28
From Jason:
One car leaves a spot traveling at 100 km per hour. The second car leaves the same spot 15 minutes later and traveling at 120 km per hour. How long does it take for the second car to catch up to the first car?
Answered by Penny Nom.
Constructing a quadrilateral 2005-10-07
From Jayasri:

Can we construct a unique quadrilateral with the following information:

The lenghts of all the sides of a quadrilateral are known.

The angle between one of the sides and the X-axis is known.


Answered by Chris Fisher.
Constructing figures 2005-09-20
From Kim:
I would like to know how to draw different shapes:
Regular Octagon with sides of length, 1 unit
Equilateral Triangles, with sides of length 1 unit
Regular Hexagons, with sides of length 1 unit
Isoseles Triangles, with hypotenuse of length 1 unit

Answered by Penny Nom.
A point is moving on the graph of x^3 + y^2 = 1 in such a way that 2005-09-17
From Gina:
A point is moving on the graph of x3 + y2 = 1 in such a way that its y coordinate is always increasing at a rate of 2 units per second. At which point(s) is the x coordinate increasing at a rate of 1 unit per second.
Answered by Penny Nom.
At what rate is the circumference of the circle increasing? 2005-08-08
From John:

A mathematics professor is knitting a sweater. The main part of the sweater is knit in a large spiral, ending up with a diameter of 30 inches. She knits at a constant rate of 6/7 square inches per minute.

1. At what rate is the circumference of the circle increasing when the diameter is 2 inches?

2. How long will it take her to finish this piece of the sweater?


Answered by Penny Nom.
A lighthouse is located on a small island,... 2005-07-14
From Brittnee:
A lighthouse is located on a small island, 3 km away from the nearest point P on a straight shoreline, and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?
Answered by Penny Nom.
Area of a region on a map 2005-04-28
From Balachandar:
Pl. find the attached map.

1. Can u pl. find out the total square are of WLMZ
2. Can u pl .find out the total square are of WXYZ -- { A }
3. Can u pl .find out the total square are of XLMY -- { B }

Pl .help me to find out the above.

.....


Answered by Chris Fisher and Penny Nom.
The area of a quadrilateral 2005-02-27
From Jonathan:
I want to know how to find the area of a quadrilateral.
Answered by Penny Nom.
Are the vetices of this quadrilateral concyclic? 2005-01-30
From A student:
Show that the peints A(-2,0),B(6,6),C(-1,7) and D(-2,6) are concyclic. Also find its circum radius.
Answered by Chris Fisher.
The area of a quadrilateral 2004-08-25
From Rich:
I would like to know how to measure the area (the formula) of a quadrilateral.
Answered by Penny Nom.
Related rates and baseball 2004-04-26
From Bethany:
A baseball diamond is the shape of a square with sides 90 feet long. A player running from second to third base at a speed of 28 feet/ second is 30 feet from second base. At what rate is the player's distance from home plate changing?
Answered by Penny Nom.
A changing rectangle 2004-04-03
From A student:
The width x of a rectangle is decreasing at 3 cm/s, and its length y is increasing at 5 cm/s. At what rate is its area A changing when x=10 and y=15?
Answered by Penny Nom.
Some calculus problems 2004-04-01
From Weisu:

I have questions about three word problems and one
regular problem, all dealing with derivatives.

  1. Find all points on xy=exy where the tangent line
    is horizontal.
  2. The width x of a rectangle is decreasing at 3 cm/s,
    and its length y is increasing at 5 cm/s. At what rate
    is its area A changing when x=10 and y=15?
  3. A car and a truck leave the same intersection, the
    truck heading north at 60 mph and the car heading west
    at 55 mph. At what rate is the distance between the
    car and the truck changing when the car and the truck
    are 30 miles and 40 miles from the intersection,
    respectively?
  4. The production P of a company satisfies the
    equation P=x2 + 0.1xy + y2, where x and y are
    the inputs. At a certain period x=10 units and y=8
    units. Estimate the change in y that should be made to
    set up a decrease of 0.5 in the input x so that the
    production remains the same.

If you could just give me some hints on these
questions, I'd really appreciate it. Thanks!


Answered by Penny Nom.
Napoleon's theorem 2004-02-27
From David:
How do i prove this : For any triangle, if you make 3 equillateral triangles using the sides of the the original triangle, the central points of the 3 tringles another triangle that is equillateral.z
Answered by Chris Fisher and Penny Nom.
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.)
Answered by Harley Weston.
Area of an equilateral triangle 2003-11-25
From Jared:
Can you help me understand why the area of a equilateral triangle is the square root of 3 divided by 4 times the lenght of the side squared?
Answered by Penny Nom.
The height of an equilateral triangle 2003-04-06
From Rosa:
If Each side of an equilateral triangle is 10 m. What is the height?
Answered by Penny Nom.
An equilateral triangle 2003-03-17
From Shirley:
An equilateral triangle is one in which all three sides are of equal length. If two vertices of an equilateral triangle are (0,4) and (0,0), find the third vertex. How many of these triangles are possible?
Answered by Penny Nom.
An equalateral polygon inscribed within an ellipse 2002-06-30
From Steven:
How would you calculate the length of one of the sides of an equalateral polygon (of n sides) inscribed within an ellipse ( of any eccentricity ) where all of the vertices exactly touch the perimeter of the ellipse?

I know that when the eccentricity is zero ( i.e a circle ) the formula: r * (sin(180/n) * 2) will suffice. But what about when the eccentricity is greater than zero?


Answered by Chris Fisher.
An equilateral triangle 2002-06-11
From Sarah:
Hi. My name is Sarah. I'm a secondary student taking a Math 30C course by correspondence. The question has two parts.

The first part is: Draw an equilateral triangle XYZ. Draw the altitude from X to YZ. Choose any point P inside the triangle or on the triangle. Draw perpendiculars from P to the sides of the triangle. The Second part is:

Measure the altitude h and the 3 perpendiculars s, t, and u to the nearest mm. Repeat as many time as is necessary until you can state a generalization concerning h, s, t, and u. If you could help me, it would be greatly appreciated.

Answered by Penny Nom.
3 = -2x 2002-05-05
From Timothy:
My question is 3 = -2x

How do I isolate the variable here?


Answered by Penny Nom.
Solving for x 2002-04-19
From Susan:
I'm having a little trouble solving these equations for x. I can't seem to separate x fully from the other numbers. Please help! Here are the problems:

(2x-1)/(x-2)(x 2+3) = 0 and

y/(x+1)=z/x
Answered by Penny Nom.

Moving a triangle 2002-04-18
From A student:
find the verticles of a triangle after it is translated 2 units to the left and then is reflected across the graph of y=x+2. The original verticles of the triangle are (2,0), (3,2), and (6,2).
Answered by Peny Nom.
Related rates 2002-04-17
From Molly:
A tanker spilled 30 ft cubed of chemicals into a river, causing a circular slick whose area is expanding while its thickness is decreasing. If the radius of the slick expands at the rate of 1 foot per hour, how fast is them thickness of the slick decreasing when the area is 100 feet squared?
Answered by Penny Nom.
A quadrilateral with 0 sets of parallel sides 2001-12-12
From Jess:
Ok well for quadrilaterals a parallelogram is a 4 sided figure with 2 sets of parallel sides and a trapezoid is a 4 sided figure with 1 set of parallel sides.

So is there a name for a quadrilateral with 0 sets of parallel side?


Answered by Chris Fisher.
A lighthouse and related rates 2001-11-29
From Melissa:
A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline, and its light makes 4 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?
Answered by Penny Nom.
Translated by the vector (-5,2) 2001-11-19
From Jennifer:
Give the image of (p,q) when translated by the vector (-5,2).
Answered by Penny Nom.
Isoscles and scalene 2001-04-17
From Autumn:
explain where the term isoscles and scalene came from?
Answered by Chris Fisher.
Constructing an equilateral triangle 2001-04-14
From Peggy:
Please send directions to make an equilateral triangle in plane geometry. I want each student to draw two, cut them out, and place them together to form a Jewish Star.
Answered by Penny Nom.
How can you prove a quadrilateral to be a parallelogram? 2001-03-16
From Joy:
How can you prove a quadrilateral to be a parallelogram?
Answered by Walter Whiteley.
Equilateral 2001-01-25
From A student:
I AM 9 YEARS OLD AND I HAVE HOMEWORK. I WOULD LIKE TO KNOW IF THERE IS SUCH A THING AS A EQUILATERAL SQUARE.
Answered by Penny Nom.
Related Rates 2000-05-07
From Derek:
How can you show that if the volume of a balloon is decreasing at a rate proportional to its surface area, the radius of the balloon is shrinking at a constant rate.
Answered by Harley Weston.
An equilateral triangle in a circle 2000-03-11
From Michael Setlik:
An equilateral triangle is drawn within a circle such that all three points of the triangle just touch the inside of the circle. Given the diameter of the cicle as six inches what is the length of the sides of the triangle?
Answered by Harley Weston.
Two calculus problems 2000-03-03
From Tara Doucet:
  1. The height of a cylinder with a radius of 4 cm is increasing at rate of 2 cm per minute. Find the rate of change of the volume of the cylinder with respect to time when the height is 10 cm.

  2. A 24 cm piece of string is cut in two pieces. One piece is used to form a circle and the other to form a square. How should the string be cut so the sum of the areas is a maximum?


Answered by Harley Weston.
A moving point on the graph of y=sinx 2000-02-22
From Veronica Patterson:
Find the rate of change of the distance between the origin and a moving point on the graph of y=sinx if dx/dt=2 centimeters per second.
Answered by Harley Weston.
Play ball 2000-02-03
From Jessie:
Here's a calc question that is probably a lot easier than I am making it. If you have a legendary "baseball problem" for the related rates section of Calc I, and you are given that the runner is running from 2nd to 3rd base at a given rate, and the umpire is standing at home plate, and you are given the distance between the bases on the field, how do you find the rate of change of the angle between the third base line (from the point of the umpire) and the runner? Here is a sample prob: Runner is moving from 2nd to 3rd base at a rate of 24 feet per second. Distance between the bases is 90 feet. What is the rate of change for the angle (theta, as described previously) when the runner is 30 feet from 3rd base?
Answered by Harley Weston.
A probability experiment 2000-01-05
From Vanessa:
Duels in the town of Discretion are rarely fatal. There, each contestant comes at a random moment between 5 a.m. and 6 a.m. on the appointed day and leaves exactly 5 minutes later, honor served, unless his opponent arrives within the time interval and then they fight. What fraction of duels lead to violence?

There must be a minimum number of 100 trials and things like graphing calculator, dice, spinners, and whatever are allowed.
Answered by Harley Weston.

A decreasing ellipsoid 1999-12-15
From A student instructor:
The volume of an ellipsoid whose semiaxes are of the lengths a,b,and c is 4/3 *pi*abc. Suppose semiaxes a is changing at a rate of A cm/s , the semiaxes b is changing at B cm/s and the semiaxes c is changing at C cm/s . If the volume of the ellipsoid is decreasing when a=b=c what can you say about A,B,C? Justify.
Answered by Harley Weston.
Two calculus problems 1999-12-13
From Alan:
I have 2 questions that are very new to me, they were included on a quiz and the material was never covered. Our teacher never explained the purpose and detailed explanation of how to solve the problem. Could you help? Thanks.

Question 1:
A ball is falling 30 feet from a light that is 50 feet high. After 1 sec. How fast is the shadow of the ball moving towards the light post. Note that a ball moves according to the formula S=16t^2

Question 2:
How many trapezoids must one use in order for the error to be less than 10^-8 if we want to find the area under the curve Y=1/X from 1 to 2. Find the exact area, Graph the function and use the trap rule for the "N" that you found.


Answered by Harley Weston.

Two calculus problems 1999-12-01
From O'Sullivan:
Question #1 Assume that a snowball melts so that its volume decreases at a rate proportional to its surface area. If it takes three hours for the snowball to decrease to half its original volume, how much longer will it take for the snowball to melt completely? It's under the chain rule section of differentiation if that any help.

I've set up a ratio and tried to find the constant but am stuck.

Question #2 The figure shows a lamp located three units to the right of the y-axis and a shadow created by the elliptical region x^2 + 4y^2 < or= 5. If the point (-5,0) is on the edge of the shadow, how far above the x axis is the lamp located?

The picture shows an x and y axis with only the points -5 and 3 written on the x axis. the lamp is on the upper right quadrant shining down diagonally to the left. There's an ellipse around the origin creating the shadow. It's formula is given as x^2 + 4y^2=5.


Answered by Harley Weston.
Area of a quadrilateral 1999-11-19
From Zane Cram:
I need the formula to calculate the area of an irregular sided rectangle. Each side has a different measurement or length.
Answered by Walter Whiteley.
Clockwise or Counterclockwise? 1999-10-27
From Tim:
A particle moves around the circle x2 + y2 = 1 with an x-velocity component dx/dt = y
  1. Find dy/dt

  2. Does the particle travel clockwise or counterclockwise around the circle? Why?

Answered by Harley Weston.
Isosceles triangles 1999-10-12
From Amber:
In defining the types of triangles, our class was stumped by a question asked by one of the student. Maybe you could help. The definition of an equilateral triangle is a triangle with three congruent sides. The definiton of an isosceles triangle is a triangle with at LEAST two congruent sides. The question is, if an isosceles triangle only requires at Least two of the sides to be congruent, could an equilateral triangle be called an isosceles triangle?
Answered by Penny Nom, Walter Whiteley and Chris Fisher.
A circle in a square 1999-05-26
From Jose V Peris:
A circle is inscribed in a square. The circumference of the circle is increasing at a constant rate of 6 inches per second. As the circle expands, the square expands to maintain the condition of tangency.

find the rate at which the perimeter of the square is increasing.

find the rate of increase in the area enclosed between the circle and the square at the instant when the area of the circle is 25(pi) square inches.
Answered by Harley Weston.

Related rates 1999-05-13
From Tammy:
The sides of a rectangle increase in such a way that dz/dt=1 and dx/dt=3*dy/dt. At the instant when x=4 and y=3, what is the value of dx/dt? (there is a picture of a rectangle with sides x and y, and they are connected by z, which cuts the rectangle in half)
Answered by Harley Weston.
An equilateral triangle on a square 1999-04-26
From Ed:
My Grade 8 class and I were discussing the solution to the following problem:

What is the area of the largest equilateral triangle that can be drawn on a 5 cm square.

We used 5 cm as the base of our triangle and then drew the other two legs of 5 cm each to make the equilateral triangle. We then drew an altitude from the upper vertex to the base of the triangle. Using the law of Pythagoras with side a of 2.5 and side c of 5 we calculated side b to be 4.3 cm (the altitude). Therefore the area of the triangle would be 5 x 4.3 divided by 2 or 10.75 square cm.

The answer key to this resource says I am wrong.

What do you think? Have we interpreted the question incorrectly?
Answered by Chris Fisher and Harley Weston.

A Kite 1998-10-07
From Paul Scott:
What is the mathematical term for the kite shape?
Answered by Walter Whiteley.
A Tightrope Walker. 1998-02-19
From Amy Zitron:
A tightrope is stretched 30 feet above the ground between the Jay and the Tee buildings, which are 50 feet apart. A tightrope walker, walking at a constant rate of 2 feet per second from point A to point B, is illuminated by a spotlight 70 feet above point A....
Answered by Harley Weston.
Area of a triangle. 1998-02-01
From Jodi Blucher:
Is there a formula for the area of an equilateral triangle knowing the length of the sides?
Answered by Chris Fisher and Harley Weston.
Un triangle équilatéral 2002-10-27
From Un eleve:
Soit ABC un triangle équilatéral construit dans le sens direct. Le point D est symétrique de A par rapport à la droite (BC), et le point E est symétrique de B par rapport au point C. L'intersection des droites (AD) et (BC)est notée H. On pose AB=a.
  1. Je dois calculer les longueurs AD et AE en fonction de a.

  2. Je dois montrer que le triangle ADE est équilatéral. J'arrive a prouver qu'il est isocèle en E mais j'aimerai trouver que AD=DE.

Answered by Claude Tardif.
 
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