91Ó°ÊÓ

Let \(f(x)=4 x^{3}+16 x^{2}-3 x-45 .\) Find \(f(-3)\) and then solve the equation \(f(x)=0\)

The formula \(A=\frac{2 T t+Q q}{2 T+Q}\) gives a student's average \(A\) after \(T\) tests and Q quizzes, where each test counts as 2 quizzes. \(t\) is the test average, and \(q\) is the quiz average. Solve for \(Q\).

A local bus travels 7 mph slower than the express. The express travels \(45 \mathrm{mi}\) in the time that it takes the local to travel 38 mi. Find the speed of each bus.

Simplify. If possible, use a second method or evaluation as a check. $$ \frac{a^{-1}+b^{-1}}{a^{-3}+b^{-3}} $$

Divide and check. $$ \left(2 x^{4}-2 x^{3}+3 x^{2}-2 x+1\right) \div\left(x^{2}+1\right) $$

Perform the indicated operations. Simplify when possible $$ \frac{x}{x^{2}+11 x+30}-\frac{5}{x^{2}+9 x+20} $$

The formula \(L=\frac{d R}{D-d}\) where \(D\) is the diameter of the sun, \(d\) is the diameter of the earth, \(R\) is the earth's distance from the sun, and \(L\) is some fixed distance, is used in calculating when lunar eclipses occur. Solve for \(D .\)

Cameron's moped travels \(8 \mathrm{km} / \mathrm{h}\) faster than Ellia's. Cameron travels \(69 \mathrm{km}\) in the same time that Ellia travels \(45 \mathrm{km} .\) Find the speed of each person's moped.

Solve. If no solution exists, state this. $$ \frac{n+2}{n-3}=\frac{n+1}{n-2} $$

Write simplified form for each of the following. Be sure to list all restrictions on the domain, as in Example 5. $$ g(t)=\frac{16-t^{2}}{t^{2}-8 t+16} $$