Explanation:
The 3.5% saltwater means that for every 100 gallons of saltwater, there are 3.5 gallons of salt and 96.5 gallons of purified water. Therefore, to find the number of gallons of salt mix that Julian should add to 30 gallons of purified water, we can set up the following proportion:
3.5 gallons of salt / 100 gallons of saltwater = x gallons of salt / 30 gallons of purified water
Simplifying this proportion, we get:
x = (3.5 gallons / 100 gallons) * 30 gallons / 96.5 gallons
x = 0.01078 gallons of salt mix
To find the number of pints of aquarium salt mix that Julian should use, we can set up another proportion:
1 gallon of salt mix / 8 pints of salt mix = 0.01078 gallons of salt mix / y pints of salt mix
Simplifying this proportion, we get:
y = (0.01078 gallons of salt mix / 1 gallon of salt mix) * (8 pints of salt mix / 1 gallon of salt mix)
y = 0.0862 pints of aquarium salt mix
Rounding to the nearest tenth, Julian should use approximately 0.1 pints of aquarium salt mix for 30 gallons of purified water.
Shiv S. Goswami
Water flows at a rate of 6500 cubic inches per minute into a cylindrical tank. The tank has a diameter of 120 inches and a height of 72 inches. What is the height, in inches, of the water in the tank after 5 minutes? Round your answer to the nearest tenth.
The volume of the cylindrical tank can be calculated using the formula:
V = πr^2h
where r is the radius (half the diameter) of the tank, and h is the height of the tank.
The radius of the tank is 120/2 = 60 inches, and the height is 72 inches. Therefore, the volume of the tank is:
V = π(60)^2(72) ≈ 9,678,696.12 cubic inches
Water flows into the tank at a rate of 6500 cubic inches per minute. Therefore, after t minutes, the volume of water in the tank will be:
Vw = 6500t cubic inches
The height of the water in the tank after t minutes can be calculated by rearranging the formula for the volume of a cylinder:
V = πr^2h
to solve for h:
h = V / (πr^2)
Substituting the values we know, we get:
h = (V + Vw) / (πr^2)
After 5 minutes, the volume of water in the tank will be:
Vw = 6500 * 5 = 32,500 cubic inches
So the total volume of water in the tank after 5 minutes will be:
V + Vw = 9,678,696.12 + 32,500 = 9,711,196.12 cubic inches
Substituting these values into the formula for the height of the water, we get:
h = (9,711,196.12) / (π(60)^2) ≈ 82.2 inches
Therefore, the height of the water in the tank after 5 minutes is approximately 82.2 inches (rounded to the nearest tenth).