2. The equation relates the radius r of a drainpipe in inches to the flow rate F of water passing through it in gallons per minute.
a. Find the radius of a pipe that can carry 600 gallons of water per minute. Round to the nearest tenth. (Let )
b. Solve the following equation for F, . Please redefine all variables. (Remember to show all work). Let and round to the nearest tenth.
600 divided by 5 (3.14)
c. What would be the flow rate of water of a drainpipe with a radius of 4 inches? Round to the nearest tenth. Show all work.
something is missing.
a. To find the radius of a pipe that can carry 600 gallons of water per minute, we need to use the given equation r = sqrt(F / (5 * pi)).
1. Substitute F with 600 in the equation: r = sqrt(600 / (5 * pi)).
2. Evaluate the expression inside the square root: r = sqrt(120 / pi).
3. Simplify the square root: r = √(120 / pi).
4. Calculate the value of r: r ≈ 6.908.
Therefore, the radius of the pipe that can carry 600 gallons of water per minute is approximately 6.9 inches when rounded to the nearest tenth.
b. To solve the equation F = 600 / (5 * 3.14) for F, we can rearrange the equation as follows:
1. Multiply 5 and 3.14: F = 600 / 15.7.
2. Divide 600 by 15.7: F ≈ 38.22.
Therefore, when rounded to the nearest tenth, the value of F is approximately 38.2 gallons per minute.
c. To find the flow rate of water for a drainpipe with a radius of 4 inches, we can again use the equation r = sqrt(F / (5 * pi)).
1. Substitute r with 4 in the equation: 4 = sqrt(F / (5 * pi)).
2. Square both sides of the equation to isolate F: 16 = F / (5 * pi).
3. Multiply both sides by (5 * pi): F = 16 * (5 * pi).
4. Calculate the value of F: F ≈ 251.33.
Therefore, when rounded to the nearest tenth, the flow rate of water for a drainpipe with a radius of 4 inches is approximately 251.3 gallons per minute.