Water is being pumped into an inverted conical tank at a rate of 9.4 cubic meters per min. The tank has height 13 meters and the diameter at the top is 5 meters. Find the rate at which the water level is rising when the height of the water is 1.5 meters.

dh/dt = 35.96 m/min

Step-by-step explanation:

Volume of a cone is given as;

V = (1/3)πr²h

Now, we need to find a relationship between dV/dt and dh/dt

Now, if we imagine the cone, at the height of 1.5m where the water level is rising, let's call the radius there r.

We are told the height of the cone is 13m and the radius of top is 5/2 =2.5m

Thus,by similar triangles;

r/h = 2.5/13

r = 2.5h/13

So,let's put this in the volume equation;

V = (1/3)π(2.5h/13)²h

V = (1/3)π(2.5²h³/169)

Since we need to find a relationship between dV/dt and dh/dt, thus;

dV/dt = π(2.5²h²/169) dh/dt

From the question, dV/dt = 9.4m³/min and h = 1.5m. so,

9.4 = π(2.5²•1.5²/169) dh/dt

9.4 = 0.2614 dh/dt

dh/dt = 9.4/0.2614 = 35.96 m/min

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: