Related rates(calculus)the radius of a sphere is increasing at a rate of  4  mm/s. how fast is the volume increasing when the diameter is  100  mm?

The volume increases at a rate of

Step-by-step explanation:

The rate of change of the radius with respect to time is 4 mm / s.

So:

Now we must find a relationship between the volume of a sphere and its radius.

The equation of the volume of a sphere is:

So:

The diameter of the sphere is 100 mm. Therefore its radius is 100/2 = 50 mm.

So:

The volume increases at a rate of :

40000 π mm ^ 3 / s = 125663.71 mm^3/s

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

this is false ^.^ lol