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.

DA/dt   = 37 / 18

Step-by-step explanation:

We have the following information:

Sides of the rectangle    L = length     w = width

Area of the rectangle  is :   A = L* w

the rate of growing of the length ( as function of time ) 1 mile in 6 years

we can express that as :

DL/dt   = 1 /6

And the rate  of growing of the width ( as function of time ) 1 mile in 9 years

Dw/dt  = 1/9

In 1995  dimensions of the rectangle were

L = 5 miles   and  w = 9 miles

Then:

A = L * w          Taking derivatives

DA/dt   =  L * Dw/dt  +  w * DL/dt

DA/dt   = 5 * (1/9) + 9 * (1/6)     ⇒   DA/dt   =  5/9  + 9/6

DA/dt   =  111 / 54      ⇒    DA/dt   = 37 / 18

6,250

step-by-step explanation:

to get the area, multiply 360 by 160.(57,600)

to find out how many bags of fertilizer it will take, first figure out how many square feet one bag can hold. divide 1000 by 8(125) to get the unit rate(how many square feet one pound of fertilizer can hold)and multiply it by 50(6250). if i haven't made a mistake, that is the answer.