Need help please show work. We are suppose to 1. Draw a diagram 2. Write down wh
ID: 2859602 • Letter: N
Question
Need help please show work. We are suppose to 1. Draw a diagram 2. Write down what we know in calculus notation 3. Write down what we need in calculus notation 4. Equation that relates to both rates 5. Solve 3. Gravel is being dumped from a conveyor belt at a rate of 30 cubic ft /min, and its coarseness is such that it forms a pile in the shape of a equal. How fast is the height of the pile increasing when the pile is 10 ft high? cone whose base diameter and height are always ft above the ground moves horizontally at a speed of 8 fus. At what rate is the angle 4. A kite 100 ft above the ground moves horizontally at a speed o between the string and the horizontal decreasing when 200 ft of string has been let out ?Explanation / Answer
3) The volume V of a cone is given by
V = (1/3) r² h
where r is the base radius and h is the height.
We're told that the base diameter always equals the height, so the base radius is always half of the height. Putting that in the volume formula,
V = (1/3) (h/2)² h = (1/12) h³
We know what dV/dt is. Find dh/dt when h=10 ; dh/dt= 0.3819 ft/min
4)
i think the question is assuming the height to be at 100 ft through out (but doesn't say so. anyhow that is the only way you will be able to do this problem, because the rate at which the string is let out is not given).
After you've diagrammed the scenario, you can see that a right triangle forms after 200 ft of string had been let out. Now let the angle formed between the string and the horizontal plane be (now, the hypotenuse = 200 ft, and with reference to the , opposite side = 100 ft)
so we have, sin = opp / hyp = 100/200 = 1/2
therefore, = 30
now horizontal distance travelled by the kite (again assuming the person flying the kite is still/not moving) or adjacent side = cos x hypotenuse = (cos 30) x 200 ft = 173 ft
time elapsed so far = distance / speed = 173 ft / (8 ft/s) = 21.66 secs
rate at which angle is decreasing = total angle covered / time elapsed = 30/21.66 = 1.39 degrees / sec
you may want to convert it to radians if that's what you are looking for. 1.39 degrees/sec = 1.39 x ( / 180) = 0.024 radians/sec