91Ó°ÊÓ

Finding Parallel and Perpendicular Lines In Exercises \(57-62\) , write the general forms of the equations of the lines that pass through the point and are (a) parallel to the given line and (b) perpendicular to the given line. \(\left(\frac{5}{6},-\frac{1}{2}\right) \quad 7 x+4 y=8\)

Finding Points of Intersection Using Technology In Exercises \(63-66\) , use a graphing utility to find the points of intersection of the graphs of the equations. Check your results analytically. \(y=x^{3}-2 x^{2}+x-1\) \(y=-x^{2}+3 x-1\)

Rate of Change In Exercises 63 and \(64,\) you are given the dollar value of a product in 2016 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value \(V\) of the product in terms of the year t. Let \(t=0\) represent \(2010 .\)) \(\$ 17,200 \quad \$ 1600\) decrease per year

Finding Composite Functions In Exercises \(63-66,\) find the composite functions \(f^{\circ} g\) and \(g \circ f\) . Find the domain of each composite function. Are the two composite functions equal? $$\begin{array}{l}{f(x)=\frac{3}{x}} \\ {g(x)=x^{2}-1}\end{array}$$

Ripples A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius (in feet) of the outer ripple is given by \(r(t)=0.6 t,\) where \(t\) is the time in seconds after the pebble strikes the water. The area of the circle is given by the function \(A(r)=\pi r^{2} .\) Find and interpret \((A \circ r)(t) .\)

Tangent Line Find an equation of the line tangent to the circle \(x^{2}+y^{2}=169\) at the point \((5,12)\)

Think About It How do the ranges of the cosine function and the secant function compare?

Temperature Conversion Find a linear equation that expresses the relationship between the temperature in degrees Celsius \(C\) and degrees Fahrenheit \(F .\) Use the fact that water freezes at \(0^{\circ} \mathrm{C}\left(32^{\circ} \mathrm{F}\right)\) and boils at \(100^{\circ} \mathrm{C}\left(212^{\circ} \mathrm{F}\right) .\) Use the equation to convert \(72^{\circ} \mathrm{F}\) to degrees Celsius.

Symmetry A graph is symmetric with respect to one axis and to the origin. Is the graph also symmetric with respect to the other axis? Explain.

Ferris wheel. The model for the height \(h\) of a Ferris wheel car is \(h=51+50 \sin 8 \pi t\) where \(t\) is measured in minutes. (The Ferris wheel has a radius of 50 feet.) This model yields a height of 51 feet when \(t=0\) . Alter the model so that the height of the car is 1 foot when \(t=0\) .