91Ó°ÊÓ

Solve. Geometry. A rectangle has an area of 20 in \(^{2}\) and a perimeter of 18 in. Find its dimensions.

Solve. Investments. A certain amount of money saved for 1 year at a certain interest rate yielded 125 dollars in simple interest. If $625 more had been invested and the rate had been 1% less, the interest would have been the same. Find the principal and the rate.

The standard form for equations of horizontal or vertical hyperbolas centered at \((h, k)\) are as follows: $$ \frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1 $$ (Graph can't copy) $$ \frac{(y-k)^{2}}{b^{2}}-\frac{(x-h)^{2}}{a^{2}}=1 $$ The vertices are as labeled and the asymptotes are $$ y-k=\frac{b}{a}(x-h) \text { and } y-k=-\frac{b}{a}(x-h) $$ For each of the following equations of hyperbolas, complete the square, if necessary, and write in standard form. Find the center, the vertices, and the asymptotes. Then graph the hyperbola. $$ \frac{(x-5)^{2}}{36}-\frac{(y-2)^{2}}{25}=1 $$

The standard form for equations of horizontal or vertical hyperbolas centered at \((h, k)\) are as follows: $$ \frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1 $$ (Graph can't copy) $$ \frac{(y-k)^{2}}{b^{2}}-\frac{(x-h)^{2}}{a^{2}}=1 $$ The vertices are as labeled and the asymptotes are $$ y-k=\frac{b}{a}(x-h) \text { and } y-k=-\frac{b}{a}(x-h) $$ For each of the following equations of hyperbolas, complete the square, if necessary, and write in standard form. Find the center, the vertices, and the asymptotes. Then graph the hyperbola. $$ 4 x^{2}-y^{2}+24 x+4 y+28=0 $$

Simplify. $$16^{-1 / 2}$$

Simplify. $$\log 10,000$$

Simplify. $$\sqrt{500}$$

The equation \(x^{2}+y^{2}=\frac{81}{4},\) where \(x\) and \(y\) represent the number of meters from the center, can be used to draw the outer circle on a wrestling mat used in International, Olympic, and World Championship wrestling. The equation \(x^{2}+y^{2}=16\) can be used to draw the inner edge of the red zone. Find the area of the red zone. (IMAGE CANNOT COPY)