Question

Eden just bought a trough in the shape of a rectangular prism for her horses. She needs to know what volume of water to add to the trough. She knows that the height of the trough is 13 inches shorter than the width, and that the length is 33 inches longer than the width.
The volume of the trough, V(w), can be modeled by a polynomial function, where w is the width of the trough. Which of the following correctly models the situation and gives the rate of change of the volume over a width of 38 inches to 53 inches?
A. V(w)= w^3 + 20w^2 - 429w
Rate of Change: 2167 cubic inches per inch


B. V(w)= w^3 + 20w^2 - 429w
Rate of Change: 7658 cubic inches per inch



C. V(w)=w^2 + 429w
Rate of Change: 520 cubic inches per inch


D. v(w) = w^2 + 20w - 429
Rate of Change: 111 cubic inches per inch

Answer 1

The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

Let w represent the width, hence:

length = w + 33, height = w - 13

Volume (V) = w(w + 33)(w - 13) = w³ + 20w² - 429w

V(w) = w³ + 20w² - 429w

Rate of change = dV/dw = 3w² + 40w - 429

When w = 38, dV/dw = 3(38)² + 40(38) - 429 = 5423

When w = 53, dV/dw = 3(53)² + 40(53) - 429 = 10118

Rate = 10118 - 5423 = 4695 in³/in

The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in

Find out more on equation at: brainly.com/question/2972832

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