Solving an Equation for an Unknown Function Suppose that
Find a function
Use the same sort of reasoning to find a function g such that
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College Algebra
- Polynomial Inequalities Solve the inequality. (x1)(x+2)(x3)(x+4)0arrow_forwardAdding Functions A certain function f is the sum of two temperatures, one given by t2+3, and the other given by tt2+1. Find a formula for f in terms of t.arrow_forwardRevenue A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function R(x)=80x0.4x2, where the revenue R(x) is measured in dollars. What is the maximum revenue? and how many units should be manufactured to obtain this maximum?arrow_forward
- The function f graphed below is defined by a polynomial equation of degree 4 .use the graph to solve the exercises. (a) if f is increasing on an interval then the y-values of the point on the graph _______ as the x-values increase. From the graph of f we see that f is increasing on the interval _______and ________. (b) If f is decreasing on an interval, then the y-values of the points on the graph_____ as the x-values increases. From the graph of f we see that f is decreasing on the interval_____ and______.arrow_forwardRadius of a Shock Wave An explosion produces a spherical shock wave whose radius R expands rapidly. The rate of expansion depends on the energy E of the explosion and the elapsed time t since the explosion. For many explosions, the relation is approximated closely by R=4.16E0.2t0.4. Here R is the radius in centimeters, E is the energy in ergs, and t is the elapsed time in seconds. The relation is valid only for very brief periods of time, perhaps a second or so in duration. a. An explosion of 50 pounds of TNT produces an energy of about 1015 ergs. See Figure 2.71. How long is required for the shock wave to reach a point 40 meters 4000 centimeters away? b. A nuclear explosion releases much more energy than conventional explosions. A small nuclear device of yield 1 kiloton releases approximately 91020 ergs. How long would it take for the shock wave from such an explosion to reach a point 40 meters away? c. The shock wave from a certain explosion reaches a point 50 meters away in 1.2 seconds. How much energy was released by the explosion? The values of E in parts a and b may help you set an appropriate window. Note: In 1947, the government released film of the first nuclear explosion in 1945, but the yield of the explosion remained classified. Sir Geoffrey Taylor used the film to determine the rate of expansion of the shock wave and so was able to publish a scientific paper concluding correctly that the yield was in the 20-kiloton range.arrow_forwardMultiplying Functions A certain function f is the product of weight, given by t+1t, and height, given by t2. Find a formula for f in terms of t.arrow_forward
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