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The heat loss of a glass window varies jointly as the window's area and the difference between the outside and inside temperatures. A window 3 feet wide by 6 feet long loses 1200 Btu per hour when the temperature outside is \(20^{\circ}\) colder than the temperature inside. Find the heat loss through a glass window that is 6 feet wide by 9 feet long when the temperature outside is \(10^{\circ}\) colder than the temperature inside.

Find all zeros of the polynomial function or solve the given polynomial equation. Use the Rational Zero Theorem, Descartes's Rule of Signs, and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first zero or the first root. $$3 x^{3}-8 x^{2}-8 x+8=0$$

Solve each rational inequality and graph the solution set on a real number line. Express each solution set in interval notation. $$ \frac{x+4}{x}>0 $$

Write an equation in standard form of the parabola that has the same shape as the graph of \(f(x)=3 x^{2}\) or \(g(x)=-3 x^{2},\) but with the given maximum or minimum. Maximum \(=-7\) at \(x=5\)

During the 1980 s, the controversial economist Arthur Laffer promoted the idea that tax increases lead to a reduction in government revenue. Called supply- side economics, the theory uses functions such as $$f(x)=\frac{80 x-8000}{x-110}, 30 \leq x \leq 100$$ This function models the government tax revenue, \(f(x),\) in tens of billions of dollars, in terms of the tax rate, \(x\). The graph of the function is shown. It illustrates tax revenue decreasing quite dramatically as the tax rate increases At a tax rate of (gasp) \(100 \%\), the government takes all our money and no one has an incentive to work. With no income earned, zero dollars in tax revenue is generated. CAN'T COPY THE GRAPH a. Find and interpret \(f(40)\). Identify the solution as a point on the graph of the function. b. Rewrite the function by using long division to perform $$(80 x-8000) \div(x-110)$$ Then use this new form of the function to find \(f(40) .\) Do you obtain the same answer as you did in part (a)? c. Is \(f\) a polynomial function? Explain your answer.

Show incomplete graphs of given polynomial functions. a. Find all the zeros of each function. b. Without using a graphing utility, draw a complete graph of the function. $$f(x)=2 x^{4}+2 x^{3}-22 x^{2}-18 x+36$$ (GRAPH CANT COPY)

The equations in Exercises \(72-75\) have real roots that are rational. Use the Rational Zero Theorem to list all possible rational roots. Then graph the polynomial function in the given viewing rectangle to determine which possible rational roots are actual roots of the equation. $$2 x^{3}-15 x^{2}+22 x+15=0 ;[-1,6,1] \text { by }[-50,50,10]$$

The perimeter of a rectangle is 50 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 114 square feet.

Use a graphing utility to obtain a complete graph for each polynomial function in Exercises \(79-82 .\) Then determine the number of real zeros and the number of imaginary zeros for each function. $$f(x)=3 x^{5}-2 x^{4}+6 x^{3}-4 x^{2}-24 x+16$$

What is a rational inequality?