The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 6 cm/s. When the length is 7 cm and the width is 4 cm, how fast is the area of the rectangle increasing?

Given :

The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 6 cm/s. When the length is 7 cm and the width is 4 cm .

To find :-

how fast is the area of the rectangle increasing?

Solution :-

As we know that :-

A = lb

To find the rate :-

d(A)/dt = d(lb)/dt .

Differenciate :-

dA/dt = l (db/dt ) + b (dl/dt )

Substitute :-

dA/dt = 6*7 + 4* 8 dA/dt = 42 + 32 cm²/s dA/dt = 74 cm²/s

A) for the n row: 22+(n-1)×6therefore,b) 100-22=78that means (n-1)×6=7878÷6=1313+1=1414th row has 100 seats