Question

In: Math

The radius of a melting snowball is decreasing at a rate of 1 centimeter per minute,...

The radius of a melting snowball is decreasing at a rate of 1 centimeter per minute, then

(a) How fast is the volume of the snowball changing when its radius is 3 centimeters?

(b) How fast is the surface area of the snowball changing when its radius is 2 centimeters?

Solutions

Expert Solution


Related Solutions

A spherical snowball is melting in such a way that its radius is decreasing at rate...
A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.1 cm/min. At what rate is the volume of the snowball decreasing when the radius is 14 cm. (Note the answer is a positive number). When air expands adiabatically (without gaining or losing heat), its pressure PP and volume VV are related by the equation PV1.4=CPV1.4=C where CC is a constant. Suppose that at a certain instant the volume is 310310 cubic centimeters...
A spherical snowball is melting. The radius after ? hours is 1−? meters. (Remember that the...
A spherical snowball is melting. The radius after ? hours is 1−? meters. (Remember that the volume of a sphere of radius ?R is 4?3?/34R3π/3.) a) What fraction of the initial mass of the snowball remains after half an hour? b) What fraction of the initial mass of the snowball remains after half an hour? (cubic cm per hour)
A solenoid (coil) of radius R has 10 turns per centimeter. It is 10cm long, and...
A solenoid (coil) of radius R has 10 turns per centimeter. It is 10cm long, and the coiled wire carries a current I. In addition to the coil of wire, a second wire runs right down the central axis of the solenoid, carrying a current of 2I. (The solenoid wire doesn't intersect this second wire, because the former wraps around the latter, always a distance R away.) A) Find the magnitude of the total magnetic field at a distance R/2...
Measure heart rate in beats per minute, respiration rate in breaths per minute and blood pressure...
Measure heart rate in beats per minute, respiration rate in breaths per minute and blood pressure as systolic/diastolic (these measurements should look like 120/70). Your pulse rate should be measured for at least 15 seconds and your respiration rate should be measured for at least 30 seconds. Try taking your blood pressure as quickly as you can. Perform the following experiments and enter your data on the Report Page. 1. While you are resting, either or sitting or lying down,...
A machine is set to turn out ball bearings having a radius of 1 centimeter. A...
A machine is set to turn out ball bearings having a radius of 1 centimeter. A sample of 10 ball bearings produced by this machine has a mean radius of 1.004 centimeters with a standard deviation of 0.003 centimeters. Is there any reason to suspect the machine is turning out ball bearings having a mean radius different than 1 centimeter?
On a highway, vehicles pass according to a Poisson process with rate 1 vehicle per minute....
On a highway, vehicles pass according to a Poisson process with rate 1 vehicle per minute. Suppose that 25% of the vehicles are trucks and 75% of the vehicles are cars. Let NC(t) and NT(t) denote the number of cars and trucks that pass in t minutes, respectively. Then N(t) = NC(t) + NT(t) is the number of vehicles that pass in t minutes. Find E[N(10) | NT(10)=2] Find P[NC(10)=14 | N(10)=15]
1. Calculate the number of atoms per cubic centimeter of lead given that the density of...
1. Calculate the number of atoms per cubic centimeter of lead given that the density of lead is 11.3 ?/??3 and its atomic weight is 207.21. 2. Calculate the ionization potential of a singly ionized ?? 4 atom. 3. (a) How much energy would be released if 1 g of deuterium were fused to form helium according to the equation 2? + 2? → ?? 4 + ?? (b) How much energy is necessary to drive the two deuterium nuclei...
A Medication is infusing at the rate of 1.2 ml per minute. how much of the...
A Medication is infusing at the rate of 1.2 ml per minute. how much of the Medication will be infused after 8 hours?
The area of a square is increasing at a rate of 2 square feet per minute....
The area of a square is increasing at a rate of 2 square feet per minute. How fast is the perimeter changing in feet per minute when the area of the square is 64 square feet?
A machine pumps cleanser into a process at a rate of 7 gallons per minute.
A machine pumps cleanser into a process at a rate of 7 gallons per minute. Upon inspection, it is learned that the machine pumps cleanser at a rate described by the uniform distribution over the interval 6.5 to 7.5 gallons per minute. a. What is the mean of this distribution? The standard deviation? Answer: mean = 7, standard deviation = 0.29 b. Find the probability that the machine pumps less than 7 gallons during a randomly selected minute. Answer: 0.5
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT