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=___?
SOLUTION This solution is FREE courtesy of BrainMass!
Use the chain rule here:
Now, with dR/dx=-2/x^3 and dx/dt=12, then we have the following:
When dR/dt=-3, we see that -3=-24/x^3, so in x^3=8 form, where x=2.
Alternatively, one can write R in terms of t, by replacing the expression for x:
Then dR/dt=-24/(12t+2)^3, so dR/dt=-3 implies that -24/(12t+2)^3=-3, or equivalently (12t+2)^3=8.
Solving for t gives only one value, t=0. Replacing the value of t in the expression for x gives x=2.
Note that the method that uses the chain rule is faster. You may consider that when solving problems of the same kind.© BrainMass Inc. brainmass.com December 24, 2021, 10:54 pm ad1c9bdddf>