91Ó°ÊÓ

Change each rational number to a decimal by performing long division. \(\frac{11}{13}\)

Draw the graphs of $$ y=\arcsin x \quad \text { and } \quad y=\arctan \left(x / \sqrt{1-x^{2}}\right) $$ using the same axes. Make a conjecture. Prove it.

A right triangle has a fixed hypotenuse of length \(h\) and one leg that has length \(x\). Find a formula for the area \(A(x)\) of the triangle.

Find the solution sets of the given inequalities. $$ |4 x+5| \leq 10 $$

In Problems 35-38, find the slope and \(y\)-intercept of each line. \(6-2 y=10 x-2\)

Draw the graph of \(y=\pi / 2-\arcsin x\). Make a conjecture. Prove it.

The Acme Car Rental Agency charges \(\$ 24\) a day for the rental of a car plus \(\$ 0.40\) per mile. (a) Write a formula for the total rental expense \(E(x)\) for one day, where \(x\) is the number of miles driven. (b) If you rent a car for one day, how many miles can you drive for \(\$ 120\) ?

In Problems 31-38, plot the graphs of both equations on the same coordinate plane. Find and label the points of intersection of the two graphs (see Example 4). $$ \begin{aligned} &y-3 x=1 \\ &x^{2}+2 x+y^{2}=15 \end{aligned} $$

Change each repeating decimal to a ratio of two integers \(0.123123123 \ldots\)

Draw the graph of \(y=\sin (\arcsin x)\) on \([-1,1]\). Then draw the graph of \(y=\arcsin (\sin x)\) on \([-2 \pi, 2 \pi]\). Explain the differences that you observe.