91Ó°ÊÓ

The temperature \(T\) (in "C) at which water boils is related to the elevation \(h\) (in meters above sea level) by the formula $$h=1000(100-T)+580(100-T)^{2}$$ for \(95 \leq T \leq 100\). (a) At what elevation does water boil at a temperature of \(98^{\circ} \mathrm{C} ?\) (b) The elevation of Mt. Everest is approximately 8840 meters. Estimate the temperature at which water boils at the top of this mountain.

Simplify the expression. $$(6 x-5)^{3}(2)\left(x^{2}+4\right)(2 x)+\left(x^{2}+4\right)^{2}(3)(6 x-5)^{2}(6)$$

Simplify the expression. $$\left(x^{2}-4\right)^{1 / 2}(3)(2 x+1)^{2}(2)+(2 x+1)^{3\left(\frac{1}{2}\right)\left(x^{2}-4\right)^{-1 / 2}(2 x)}$$

Simplify the expression, and rationalize the denominator when appropriate. $$\sqrt[3]{3 t^{4} v^{2}} \sqrt[3]{-9 t^{-1} v^{4}}$$

Simplify the expression. $$=(3 x+2)^{1 / 3}(2)(4 x-5)(4)+(4 x-5)^{2}\left(\frac{1}{3}\right)(3 x+2)^{-2 / 3}(3)$$

Simplify the expression, and rationalize the denominator when appropriate. $$\sqrt[3]{(2 r-s)^{3}}$$

When a rock is dropped from a cliff into an ocean, it travels approximately \(16 t^{2}\) feet in \(t\) seconds. If the splash is heard 4 seconds later and the speed of sound is \(1100 \mathrm{ft} / \mathrm{sec},\) approximate the height of the cliff.

Simplify the expression. $$(3 x+1)^{6}\left(\frac{1}{2}\right)(2 x-5)^{-1 / 2}(2)+(2 x-5)^{1 / 2}(6)(3 x+1)^{5}(3)$$

When a popular brand of CD player is priced at \(\$ 300\) per unit, a store sells 15 units per week. Each time the price is reduced by \(\$ 10,\) however, the sales increase by 2 per week. What selling price will result in weekly revenues of \(\$ 7000 ?\)

Simplify the expression, assuming \(x\) and \(y\) may be negative. $$\sqrt{x^{6} y^{4}}$$