A construction worker pulls a five-meter plank up the side of a building under c

Question

A construction worker pulls a five-meter plank up the side of a building under construction by means of a rope tied to one end of the plank (see figure). Assume the opposite end of the plank follows a path perpendicular to the wall of the building and the worker pulls the rope at a rate of 0.20 meter per second. How fast is the end of the plank sliding along the ground when it is 1.3 meters from the wall of the building? (Round your answer to two decimal places.)

A point is moving along the graph of the given function at the rate

dx/dt.

Find dy/dt for the given values of x.

y = 4x2 + 9; dx/dt = 5 cm per sec

a. x = -1 ____

b. x = 0 (0)

c x=1 = ____

Explanation / Answer

for doing the top question you need to provide me the figure

I will solve the 2nd question for you as I am allowed to solve only 1 question at a time

y = 4x^2 + 9

differentiate with respect to t,
dy/dt = 8x * dx/dt

a)
for x=-1
dy/dt = 8*(-1)*dx/dt
5 = -8*dx/dt
dx/dt = -5/8 cm/s
Answer: -5/8 cm/s

b)
for x=0
dy/dt = 8*(0)*dx/dt
5 = 0*dx/dt
dx/dt = infiity cm/s
Answer: not defined

c)
for x=1
dy/dt = 8*(1)*dx/dt
5 = 8*dx/dt
dx/dt = 5/8 cm/s
Answer: 5/8 cm/s

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