Purchase Solution

Rate of change and the chain rule

Not what you're looking for?

Ask Custom Question

A rocket ship is speeding away from the sun. In convenient units, the radiation R inside the ship is given by
R = 1/x^2, where x is the distance to the sun. This distance x, as a function of time t in hours, is given by x = 12t+ 2.

How far is the ship from the sun when the radiation level is decreasing at a rate of 3 units per hour, when dR/dt =-3?
What does x=___?

Purchase this Solution

Solution Summary

Given the distance to the sun of a rocket as a function of time, and the radiation inside the ship as a function of the distance to the sun, we find the distance to the sun when the radiation level is decreasing at a rate of 3 units per hour

Solution Preview

Use the chain rule here:
dR/dt=dR/dx dx/dt.

Now, with dR/dx=-2/x^3 and dx/dt=12, then we have the following:
dR/dt=-24/x^3

When dR/dt=-3, we see ...

Purchase this Solution


Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.