For this case we have that by definition of trigonometric relations of a rectangular triangle, that the sine of an angle is given by the opposite leg to the angle on the hypotenuse of the triangle. While the tangent of the same angle is given by the leg opposite the angle on the leg adjacent to the angle.
Then, according to the figure we have:
Answer:
Answer:
The height of the pile is increasing at the rate of
Step-by-step explanation:
Given that :
Gravel is being dumped from a conveyor belt at a rate of 20 ft³ /min
i.e
we know that radius r is always twice the diameter d
i.e d = 2r
Given that :
the shape of a cone whose base diameter and height are always equal.
then d = h = 2r
h = 2r
r = h/2
The volume of a cone can be given by the formula:
Taking the differentiation of volume V with respect to time t; we have:
we know that:
So;we have:
The height of the pile is increasing at the rate of