91Ó°ÊÓ

Express as a quotient. $$X^{-1 / 2}-X^{3 / 2}$$

Simplify the expression, and rationalize the denominator when appropriate. $$\sqrt[4]{\left(5 x^{5} y^{-2}\right)^{4}}$$

The temperature \(T\) within a cloud at height \(h\) (in feet) above the cloud base can be approximated using the equation \(T=B-\left(\frac{3}{1000}\right) h,\) where \(B\) is the temperature of the cloud at its base. Determine the temperature at \(10,000\) feet in a cloud with a base temperature of \(55^{\circ} \mathrm{F}\) and a base height of 4000 feet.

Simplify the expression, and rationalize the denominator when appropriate. $$\sqrt[6]{\left(7 u^{-3} v^{4}\right)^{6}}$$

Archeologists can determine the height of a human without having a complete skeleton. If an archeologist finds only a humerus, then the height of the individual can be determined by using a simple linear relationship. (The humerus is the bone between the shoulder and the elbow.) For a female, if \(x\) is the length of the humerus (in centimeters), then her height \(h\) (in centimeters) can be determined using the formula \(h=65+3.14 x\). For a male, \(h=73.6+3.0 x\) should be used. (a) A female skeleton having a 30 -centimeter humerus is found. Find the woman's height at death. (b) A person's height will typically decrease by 0.06 centimeter each year after age \(30 .\) A complete male skeleton is found. The humerus is 34 centimeters, and the man's height was 174 centimeters. Determine his approximate age at death.

Express as a quotient. $$X^{-2 / 3}+X^{7 / 3}$$

The distance that a car travels between the time the driver makes the decision to hit the brakes and the time the car actually stops is called the braking distance. For a certain car traveling \(v \mathrm{mi} / \mathrm{hr},\) the braking distance \(d\) (in feet) is given by \(d=v+\left(v^{2} / 20\right)\). (a) Find the braking distance when \(v\) is \(55 \mathrm{mi} / \mathrm{hr}\). (b) If a driver decides to brake 120 feet from a stop sign, how fast can the car be going and still stop by the time it reaches the sign?

Simplify the expression, and rationalize the denominator when appropriate. $$\sqrt[5]{\frac{8 x^{3}}{y^{4}}} \sqrt[5]{\frac{4 x^{4}}{y^{2}}}$$

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

Simplify the expression, and rationalize the denominator when appropriate. $$\sqrt{5 x y^{2}} \sqrt{15 x^{3} y^{3}}$$