coffee maker has the shape of a cone 10cm high with a radius of 6 cm at the top. The coffee maker is filled with water, and the water is allowed to drain out the bottom of the cone. Water is flowing out of the filter at a rate of 5 cubic centimerters per second. At what rate is the water level in the cone falling when it is 5cm from the bottom of the cone.

the rate of the water level in the cone falling when it is 5cm from the bottom of the cone is -0.1768 cm/sec

Step-by-step explanation:

Given the data in the question;

H/h = R/r

10/5 = 6/r

r 1 = 30/10 = 3

Also

10/h = 6/r

r2 = 6h/10 = 3/5 × h

Volume = 1/3πr²h

V = 1/3 × π × (3/5 × h)² × h

V =  1/3 × π × 9/25 × h³

V = 3π/25 × h³

Now

dv/dt = 3π/25 × 3 × h² × dh/dt

-5 = 3π/25 × 3 × 25 × dh/dt

-5 = 3π × 3 × dh/dt

-5 = 9π × dh/dt

dh/dt = -5/9π

dh/dt = -0.1768 cm/sec

therefore, the rate of the water level in the cone falling when it is 5cm from the bottom of the cone is -0.1768 cm/sec

1.30

step-by-step explanation:

168

step-by-step explanation:

first off, we know that he drove 3.5 hours at a rate of 48 mph.

knowing that, we want to see how many miles he drove all-together.

in this case, we can just multiply 48 by 3.5.

48 * 3.5 = 168