Question

When a rocket ship gets 125 miles from the surface of the planet, it will join the Earth's orbit and not

need its rocket boosters any longer.
A rocket ship takes off from planet Earth
following the function y = - 0.5x7 + 35x
(where x is time in minutes) and y is height in miles). If the rocket burns through 31,000 gallons of fuel every
minute, how much fuel does the rocket ship need to get into the Earth's orbit.

Answer 1

To find out how much fuel the rocket ship needs to get into Earth's orbit, you can calculate the total fuel consumption by integrating the rate of fuel consumption over the time it takes to reach 125 miles.

The rate of fuel consumption is given as 31,000 gallons per minute, and the function for the height of the rocket is y = -0.5x^7 + 35x. We need to find the time it takes for the rocket to reach 125 miles.

Set y = 125 in the height function and solve for x:

125 = -0.5x^7 + 35x

Now, let's find the time it takes for the rocket to reach 125 miles by solving this equation. Unfortunately, solving this equation for x is quite complex, and it doesn't have a straightforward algebraic solution. You may need to use numerical methods or a graphing calculator to find the approximate value of x when y = 125.

Once you have an approximate value of x, you can then calculate the total fuel consumption by multiplying the rate of fuel consumption (31,000 gallons/minute) by the time it takes to reach 125 miles.

Fuel consumption = (31,000 gallons/minute) * (approximate value of x)

This will give you the amount of fuel needed for the rocket to reach Earth's orbit.

Explanation:

Have great day!