1.The length of a rectangle is increasing at a rate of 8 cm/s and its width is i

Question

1.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 11 cm and the width is 7 cm, how fast is the area of the rectangle increasing?

_______cm^2/s

2.Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV = C, where C is a constant. Suppose that at a certain instant the volume is 400 cm3, the pressure is 200 kPa, and the pressure is increasing at a rate of 30 kPa/min. At what rate is the volume decreasing at this instant?

_____cm^3/min

3.Two sides of a triangle have lengths 13 m and 19 m. The angle between them is increasing at a rate of 2°/min. How fast is the length of the third side increasing when the angle between the sides of fixed length is 60°? (Round your answer to three decimal places.)

_____m/min

Explanation / Answer

A = LW.
(d/dt)(A) = (d/dt)(LW)
==> dA/dt = W(dL/dt) + L(dW/dt).

Substituting in L = 11, W = 9, dL/dt = 3, and dW/dt = 8 gives

dA/dt =9*3+11*8

=27+88

=115 cm^2/s

2.

C = PV = 400 cm^3 / 200 kPa = 2 cm^3/kPa

(30 kPa/min) x (4 cm^3 / kPa) = 120 cm^3/min

3.

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