Implicit Diff Story probs
Sorry if this causes any trouble but could someone check my answers for these problems?: 1. A point is moving along the graph of the function so that dx/dt is 2 cm/s. Find dy/dt for the indicated values of x. The function is y=sinx. The values are a)x= Pi/6 b)x= pi/4 c) x=pi/3 and d) x=pi/2. After finding these values tind the rate of change of the distanse between the origin and the moving point on the graph of the function. (x and y are functions of time).
I got a) the square root of 3 b) the square root of 2 c) 1 and d) 0.
for the rate of change part i had some ridiculous numbers and was lost. I got 2pie/(the square root of (pi squared +4)).
The second problemis: find the rate of change of the volume of a cone if dr/dt is 2 inches/min and h=3r when a) r=6 inches and b)r=24 inches. I got a) 216*pie and b) 576*pie
The third problem is: A conical tank (with vertex down), is 10 feet across the top and 12 ft deep. if water is flowing into the tank at the rate of 10 cubic feet per minute, find the rate of change f the depth of the water the instant it is 8 ft deep. I got 2.7/pi in/min for the answer.
The fourth problem is that a trough is 12 ft long and 3 ft across the top. its ends are isosceles triangles with an altitude of 3 ft. water is being pumped into the trough at 2 cubic feet per minute. How fast is the water level rising when it is 1 foot deep? i got 2 ft/min
The fifth and final problem is: a construction worker pulls a 16-foot plank up the side of a building under construcion by means of a rope tied to the end of the plank. assume the opposite end of the plank follows a path perpendicular to the wall of the building and the worker pulls the rope at the rate of .5 ft/s. how fast is the end of the plank sliding along the ground when it is 8 ft from the wall of the building. i got .5 ft/s for that one
Thanks for any help at all.