## A city is in the shape of a rectangle. In 1995 the width of the city was 9 miles and the length of the city was 5 miles. The width of the ci

Question

A city is in the shape of a rectangle. In 1995 the width of the city was 9 miles and the length of the city was 5 miles. The width of the city is growing at a rate of 1 mile in 9 years. The length of the city is growing at a rate of 1 mile in 6 years. Use the product rule to find how quickly the area of the city is growing in 1995.

in progress
0

Math
3 weeks
2021-12-27T08:14:08+00:00
2021-12-27T08:14:08+00:00 1 Answer
0 views
0
## Answers ( )

Answer:DA/dt = 37 / 18Step-by-step explanation:We have the following information:Sides of the rectangle L = length w = widthArea of the rectangle is : A = L* wthe rate of growing of the length ( as function of time ) 1 mile in 6 yearswe can express that as :DL/dt = 1 /6And the rate of growing of the width ( as function of time ) 1 mile in 9 yearsDw/dt = 1/9In 1995 dimensions of the rectangle wereL = 5 miles and w = 9 milesThen:A = L * w Taking derivativesDA/dt = L * Dw/dt + w * DL/dtDA/dt = 5 * (1/9) + 9 * (1/6) ⇒ DA/dt = 5/9 + 9/6DA/dt = 111 / 54 ⇒ DA/dt = 37 / 18