# Trapezoidal trough related rates problem

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Answer to: A water trough is 10 \ m long and a cross-section has the shape of an isosceles trapezoid that is 30 \ cm wide at the bottom, 80 \ cm...

Calculus Related Rates Problem: How fast is the water level falling as water drains from the cone? An inverted cone is 20 cm tall, has an opening radius of 8 cm, and was initially full of water. which gives that x  3. Thus, dy dt y2.  500 3 2 250 3. Our conclusion is that the distance of the plane from the radar station is increasing at a rate of 250 3 433 miles per hour at the instant when the plane is two miles from the radar station. A water trough is 4 m long and its cross-section is an isosceles trapezoid which is 80 cm wide at the bottom and 120 cm wide at the top, and the height is 40 cm. The trough is not full. Give an expression for V, the volume of water in the trough in cm3, when the depth of the water is d cm. Solve more elaborate problems with related rates. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Problem 05 A triangular trough is 10 ft long, 6 ft wide across the top, and 3 ft deep. If water flows in at the rate of 12 ft 3 /min, find how fast the surface is rising when the water is 6 in deep. A "related rates'' problem is a problem in which we know one of the rates of change at a given instant—say, $\ds \dot x = dx/dt$—and we want to find the other rate $\ds \dot y = dy/dt$ at that instant.

Jul 27, 2010 · This problem is very similar to filling a pool but with an added consideration. This is a very typical related rates problem for a Calculus 1 class. You may find a problem like this on a test or exam. A water trough is 9 m long and has a cross-section in the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 70 cm wide at the top, and has height 40 cm. If the trough is being filled with water at the rate of 0.2 m3/min how fast is the water level rising when the water is 20 cm deep? Here is a set of practice problems to accompany the Approximating Definite Integrals section of the Applications of Integrals chapter of the notes for Paul Dawkins Calculus II course at Lamar University.

The number in parenthesis indicates the number of variations of this same problem. Re-clicking the link will randomly generate other problems and other variations. All answers must be numeric and accurate to three decimal places, so remember not to round any values until your final answer. Also, remember NOT to use an approximation for π! Use ... Related Rates Calculus Problem (water trough)? Question is: A water trough is 10m long and a cross section has the shape of a isosceles trapezoid that is 30cm wide at the bottom, 80 cm wide at the top, and has a height of 50 cm.

Calculus Related Rates Problem: How fast is the water level falling as water drains from the cone? An inverted cone is 20 cm tall, has an opening radius of 8 cm, and was initially full of water. Oct 28, 2017 · In this video we solve a related rates problem involving a triangular trough that has isosceles triangles as its ends. This is a common AP Calculus problem. Feb 07, 2003 · A trough is 10 feet long. Each end is a trapezoid of height 2 ft with bottom base 2 ft and top base 6 ft. Water is flowing into the trough at a rate of 5 cubic feet per minute. let A represent the area of the top surface of the water, let h represent the depth of the water in the trough, and let V represent the volume of water in the trough.

A water trough is 10m long and a cross-section has the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 80 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of 0.2 m 3 /min, how fast is the water level rising when the water is 30 cm deep? Answer to: A water trough is 10 \ m long and a cross-section has the shape of an isosceles trapezoid that is 30 \ cm wide at the bottom, 80 \ cm...

Let's review related rates again. In related rates, you're going to take a relationship that you know. In one problem it is my height as a function of the distance the fire truck is away from the ... Let's review related rates again. In related rates, you're going to take a relationship that you know. In one problem it is my height as a function of the distance the fire truck is away from the ... You have a rate of change of volume and want to know the corresponding rate of change of depth at a particular depth. This problem can be solved in three steps: The first step is to find an equation that relates water depth to volume. The second step is to take the derivative of both sides of the equation with respect to time.

You have a rate of change of volume and want to know the corresponding rate of change of depth at a particular depth. This problem can be solved in three steps: The first step is to find an equation that relates water depth to volume. The second step is to take the derivative of both sides of the equation with respect to time. Dec 16, 2012 · Math help -- Calculus related rates problems? 1. A trough is a right trapezoidal prism; the cross section is an isoceles trapezoid. The lower base is 1 foot wide and ... Time Rates If a quantity x is a function of time t, the time rate of change of x is given by dx/dt. When two or more quantities, all functions of t, are related by an equation, the relation between their rates of change may be obtained by differentiating both sides of the equation with respect to t. 8 Related Rate “Word Problems” U n i v ersit a s S a sk atchew n e n s i s DEO ET PAT-RIÆ 2002 Doug MacLean Example 4: A trough is ten metres long and its ends have the shape of isosceles trapezoids that are 80 cm across at the top and 30 cm across at the bottom, and has a height of 50 cm. If the trough is ﬁlled with water at a rate of 0 ...

Water is pumped into an empty trough which is $200{\rm{ cm}}$ long at the rate of $33000{\rm{ c}}{{\rm{m}}^3}/s$. The uniform cross section of the trough is an isosceles trapezium with the dimensions shown: Find the rate at which the depth of the water is increasing at the instant when the depth is 20cm. A helpful strategy I've found with related rates is to conjure a relationship between two variables, take the derivative with respect to time and you're done. The only thing left to do is to substitute the rate of change one of the quantitys is changing at.

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Dec 11, 2017 · Homework Statement A trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 80 cm wide at the top, and has a height of 50 cm. If the trough is being filled with water at the rate of 0.2m3/min, how fast is the water level rising when the... Problem 13 A trapezoidal trough is 10 ft long, 4 ft wide at the top, 2 ft wide at the bottom and 2 ft deep. If water flows in at 10 ft 3 /min, find how fast the surface is rising, when the water is 6 in deep. Solution 13 Answer to: A water trough is 10 \ m long and a cross-section has the shape of an isosceles trapezoid that is 30 \ cm wide at the bottom, 80 \ cm...

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Oct 23, 2009 · Related Rates Homework Problem? A water trough is 8 m long and has a cross-section in the shape of an isosceles trapezoid that is 40 cm wide at the bottom, 90 cm wide at the top, and has height 50 cm.

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Water is leaking from a trough at the rate of 0.8 l/s. The trough has a trapezoidal cross section, where the width at the bottom is 55 cm, at the top i How do I do this calculus related rates problem? A water trough is 9 m long and has a cross-section in the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 70 cm wide at the top, and has height 40 cm. If the trough is being filled with water at the rate of 0.2 m3/min how fast is the water level rising when the water is 20 cm deep?