91Ó°ÊÓ

GENERAL: Water Pressure At a depth of \(d\) feet underwater, the water pressure is \(p(d)=0.45 d+15\) pounds per square inch. Find the pressure at: a. The bottom of a 6 -foot-deep swimming pool. b. The maximum ocean depth of 35,000 feet.

$$ \begin{array}{l} \text { For each function, find and simplify }\\\ \frac{f(x+h)-f(x)}{h} . \quad(\text { Assume } h \neq 0 .) \end{array} $$ $$ \begin{array}{l} f(x)=x^{3} \\ {\left[\text { Hint: Use } \quad(x+h)^{3}=x^{3}+3 x^{2} h+3 x h^{2}+h^{3} .\right]} \end{array} $$

ECONOMICS: Does Money Buy Happiness? Several surveys in the United States and Europe have asked people to rate their happiness on a scale of \(3={ }^{\prime \prime}\) very happy," \(2=\) "fairly happy," and \(1={ }^{\prime \prime}\) not too happy," and then tried to correlate the answer with the person's income. For those in one income group (making $$\$ 25,000$$ to $$\$ 55,000$$ ) it was found that their "happiness" was approximately given by \(y=0.065 x-0.613\). Find the reported "happiness" of a person with the following incomes (rounding your answers to one decimal place). a. $$\$ 25,000$$ b. $$\$ 35,000$$ c. $$\$ 45,000$$

Simplify. $$ \left[\left(x^{3}\right)^{3}\right]^{3} $$

GENERAL: Boiling Point At higher altitudes, water boils at lower temperatures. This is why at high altitudes foods must be boiled for longer times - the lower boiling point imparts less heat to the food. At an altitude of \(h\) thousand feet above sea level, water boils at a temperature of \(B(h)=-1.8 h+212\) degrees Fahrenheit. Find the altitude at which water boils at \(98.6\) degrees Fahrenheit. (Your answer will show that at a high enough altitude, water boils at normal body temperature. This is why airplane cabins must be pressurized - at high enough altitudes one's blood would boil.)

$$ \begin{array}{l} \text { For each function, find and simplify }\\\ \frac{f(x+h)-f(x)}{h} . \quad(\text { Assume } h \neq 0 .) \end{array} $$ $$ \begin{array}{l} f(x)=x^{4} \\ \text { [Hint: Use }(x+h)^{4}=x^{4}+4 x^{3} h+6 x^{2} h^{2}+ \\ \left.4 x h^{3}+h^{4} .\right] \end{array} $$

$$ \begin{array}{l} \text { For each function, find and simplify }\\\ \frac{f(x+h)-f(x)}{h} . \quad(\text { Assume } h \neq 0 .) \end{array} $$ $$ f(x)=\frac{2}{x} $$

Simplify. $$ \frac{\left(w w^{2}\right)^{3}}{w^{3} w} $$

\(71-72 .\) GENERAL: Stopping Distance A car traveling at speed \(v\) miles per hour on a dry road should be able to come to a full stop in a distance of $$ D(v)=0.055 v^{2}+1.1 v \text { feet } $$ Find the stopping distance required for a car traveling at: \(40 \mathrm{mph}\).

$$ \begin{array}{l} \text { For each function, find and simplify }\\\ \frac{f(x+h)-f(x)}{h} . \quad(\text { Assume } h \neq 0 .) \end{array} $$ $$ f(x)=\frac{3}{x} $$