Find f'(x) for the following and factor the answer completely, if possible: 1. f(x) = (3x - 1)*e-x*

Find the unknown value. y varies inversely as the square of x and when x=3,y=2. Find y if x=1.

The half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14 remaining as a function of time, measured in years.

If y varies inversely with x and y=11 when x=3 find the equation that relates x and y.

bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.

The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?

The windchill index announced during the winter by the weather bureau measures how cold it "feels" for a given temperature t (in degrees Fahrenheit) and wind speed w (in miles per hour). It is calculated by the formula C(t, w) = 35.74 + 0.6215t - 35.75w 0.16 + 0.4275tw0.16 + '.+ If the temperature is 31 degrees and the wind speed is 10 miles per hour, estimate the change in the windchill temperature if the wind speed increases by 4 miles per hour and the temperature drops by 5 degrees. (Round your answer to two decimal places.)

The function f(x) = 4(2)x models the length of an image in centimeters after it has been enlarged by 100% x times. Which of these is the length of the image after it has been enlarged 3 times?