5· 0-m points My Notes Ask Your Teach Each side of a square is increasing at a r

Question

5· 0-m points My Notes Ask Your Teach Each side of a square is increasing at a rate of 4 cm/s. At what rate is the area of the square increasing when the area of the square is 16 cm2 cm2/s Need Help? Read It Watch It Talk to a Tutor 6. + -11 points My Notes Ask Your Teach The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of 9 cm/s. When the length is 9 cm and the width is 4 cm, how fast is the area of the rectangle increasing? cm2/s 7. -11 points My Notes Ask Your Teach At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 30 km/h. How fast is the distance between the ships changing at 4:00 PM? Need Help?Read ItTalk to a Tutor

Explanation / Answer

#5

Area of square = (side)^2

A = a^2. ----------(1)

differentiate with respect to t

dA/dt = 2a da/dt --------(2)

given A = 16 cm2 so a = 4 cm (from equation (1))

da/dt = 4 cm/s

Putting it in equation (2)

dA/dt = 4 * 4 = 16 cm2/sec

#6

Area of rectangle = length × width

A = l*w

differentiate with respect to t

dA/dt = l*(dw/dt) + (dl/dt)*w

given l =9 cm , w= 4 cm , dw/dt = 9 cm /s ,dl/dt = 6 cm/s

dA/dt = 9*9 + 6*4

=81 + 24 = 105 cm2/sec

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