Sand falls from a conveyor belt at a rate of 15 startfraction m cubed over min endfraction onto the top of a conical pile. the height of the pile is always three-eighths of the base diameter. how fast are the height and the radius changing when the pile is 5 m high?

dh/dt = 0.107m/min

dr/dt = 0.1435m/min

Explanation:

The volume of a cone is given by:

The relationship between height and radius is:

h = 3/8 * (2*r) = 3/4 * r

Replacing this value into the volume formula:

If we derive this equation:

  Solving for dr/dt and knowing that dV/dt=15m^3/min

With the relation between height and radius:

dh/dt=3/4*dr/dt = 0.107m/min

emily ruth's annual premium is $1058.50

step-by-step explanation:

emily ruth is a female of 27 years age purchasing 20 year endowment insurance with face value $25000.

from the given table,

for females, the age of a male 3 years younger should be used.

so, we have to check for 24 year male for 20 year endowment.

it is 42.34 for every $1000 face value.

for a face value of $25000,

it is 25 * 42.34 = $1058.50

∴ emily ruth's annual premium is $1058.50