1) 2) 3) Suppose xy = -4 and dy/dt = -4. Find dx/dt when X = -4. A rock is throw

Question

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Suppose xy = -4 and dy/dt = -4. Find dx/dt when X = -4. A rock is thrown into a still pond and causes a circular ripple. If the radius of the ripple is increasing at a rate of 2 feet per second, how fast is the circumference changing when the radius is 20 feet? Change in circumference = A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.3 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 17 cm? (Note the answer is a positive number). Rate =

Explanation / Answer

1.) xy = -4

when x=-4 then y = 1

so x ( dy/dt) + y (dx/dt) = 0

or (-4) (-4) + 1 ( dx/dt) = 0

so dx/dt = -16

2.)circumference C = 2 pi r

so dC / dt = 2pi ( dr/dt)

= 2(pi)(2)

= 12.56 feet/sec

3.) v = (4/3)(pi)(r^3)

= (1/6)(pi)d^3

so dv/dt = (1/2) pi d^2 (d d/dt)

= (1/2) pi(d^2)(d d/dt)

= 0.5 (pi) (17)^2 (0.3)

= 136.19 cm^3 / min

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