91Ó°ÊÓ

Solve \(8-6(x-4) \leq 2(x-5)-4(2 x-1)\)

Find the equation and sketch the graph for each function. A quadratic function with \(x\) -intercepts \((3,0)\) and \((-6,0)\) and \(y\) -intercept \((0,-5)\)

Find the equation and sketch the graph for each function. A cubic function with \(x\) -intercepts \((1,0),(-1 / 2,0),\) and \((1 / 4,0)\) and \(y\) -intercept \((0,2)\)

Find the additive inverse and multiplicative inverse of \(-8 i\).

Find the equation and sketch the graph of each function. A rational function that passes through \((-1,2),\) has the line \(y=-2\) as a horizontal asymptote, and has the line \(x=-3\) as its only vertical asymptote

Find the equation and sketch the graph of each function. A rational function that passes through \((3,3),\) has \(y=x-2\) as an oblique asymptote, and has \(x=-5\) as its only vertical asymptote

Solve the problem. Renting a Car The cost of renting a car for one day is 39 dollar plus 30 cents per mile. Write the average cost per mile \(C\) as a function of the number of miles driven in one day \(x .\) Graph the function for \(x>0 .\) What happens to \(C\) as the number of miles gets very large?

An engineer is designing a cylindrical metal tank that is to hold \(500 \mathrm{ft}^{3}\) of gasoline. a. Write the height \(h\) as a function of the radius \(r\) Hint: The volume is given by \(V=\pi r^{2} h\) b. Use the result of part (a) to write the surface area \(S\) as a function of \(r\) and graph it. Hint: The surface area is given by \(S=2 \pi r^{2}+2 \pi r h\) c. Use the minimum feature of a graphing calculator to find the radius to the nearest tenth of a foot that minimizes the surface area. Ignore the thickness of the metal. d. If the tank costs 8 dollar per square foot to construct, then what is the minimum cost for making the tank?