I need help solving these Precalculus questions in the variation chapter.

Write an equation describing the relationships of the given variables. y varies directly as a: and when a: = 5, y = 40. Preview Write an equation describing the relationships of the given variables. {y varies inversely as a: and when a: = 2, y = 3. Preview Write an equation describing the relationships of the given variables. y varies inversely as the square root of x and when x = 16, y = 8. Preview'y varies directly as the square root of 3:. When :1: = 16, then y = 12. Find y when a: = 25. y = Preview Use Kepler's Law, which states that the square of the time, T, required for a planet to orbit the Sun varies directly with the cube of the mean distance, a, that the planet is from the Sun. Using Earth's time of 1 year and a mean distance of 93 million miles, the equation relating T (in years) and a (in million miles) is 804375T2 = a3. Use that relation equation to determine the time required for a planet with mean distance of 267 million miles to orbit the Sun. Round to 2 decimal places. years The distance .5 that an object falls varies directly with the square of time, t, of the fall. If an object falls 16 feet in one second, how long for it to fall 256 feet? seconds The rate of vibration of a string under constant tension varies inversely with the length of the string. If a string is 384 inches long and vibrates 8 timers per second, what is the length of a string that vibrates 32 thnespersecond? inches The weight of an object above the surface of the Earth varies inversely with the square of the distance from the center of the Earth. If a body weighs 90 pounds when it is 3960 miles from the Earth's center. What would it weight if it were 3970 miles from the Earth's center? Round to 2 decimal places. pounds