Carlos is the last person to board a Ferris wheel that has a radius of 52 feet. The counterclockwise arc swept out by Carlos is measured from where he got on, at the bottom of the Ferris wheel. Since Carlos is the last one to board, the Ferris wheel starts up and doesn't stop again unit the ride is over. a. Draw a diagram that show's Carlos's location and the angle swept out by Carlos at an arbitrary moment in time. b. Define a function f that relates Carlos's vertical distance above the center of the Ferris wheel (measured in feet) as a function of the measure of the angle (in radians) swept out by Carlos. Over what interval of input will Carlos complete one revolution? c. Define a function g that relates Carlos's horizontal distance to the right of the center of the Ferris wheel (measured in feet) as a function of the measure of the angle (in radians) swept out by Carlos Over what interval of input will Carlos complete one revolution? d. Suppose Carlos's cart is traveling 0.3 radii per second on a circular path as the wheel rotates. Define a function h that relates Carlos's horizontal distance to the right of the center of the Ferris wheel (measured in feet) as a function of the time since beginning the ride (measured in seconds). How long will it take for Carlos to complete one revolution? e. Marilyn claimed that she saw Carlos's cart travel at a speed of 3.5 radii per second. Is that possible? Explain. (Hint: Determine the cart's speed in miles per hour. f. Suppose that Carlos's cart traveled at 0.4 radii per second. Define a function j that relates Carlos's horizontal distance to the right of the center of the Ferris wheel (measured in feet) as a function of the time since beginning the ride (measured in seconds). How long will it take for Carlos to complete one revolution? g. Suppose Carlos's cart is traveling 0.2 radii per second. Define a function k that relates Carlos's horizontal distance to the right of the center of the Ferris wheel (measured in feet) as a function of the time since beginning the ride (measured in seconds). How long will it take for Carlos to complete one revolution? h. Sketch a graph of each function defined in parts (d)-(g). Label your axes. Identify the interval of input over which Carlos completes one revolution.

Lucia boards a Ferris wheel with a radius of 42.5 feet. When Lucia boards, the Ferris wheel is at the bottom of its rotation. The angle swept out as Lucia rotates is measured from the 6 o'clock position. a. Make a drawing of the situation and illustrate the quantities. b. Graph Lucia's vertical distance above the ground (measured in feet) as a function of the measure of the angle (in radians) swept out by Lucia from the bottom of the Ferris wheel. (Define your variables and label your axes.) c. Define a function f that relates Lucia's vertical distance above the ground (measured in feet) as a function of the measure of the angle (in radians) swept out by Lucia from the bottom of the Ferris wheel. (Define variables to represent the values the quantities assume (include units). d. Suppose that the Ferris wheel travels at a constant rate of 7.5 feet per second and makes no stops. Express the distance traveled by Lucia (in feet) as a function of the number of seconds since the Ferns wheel began to turn. e. Define a function g that relates Lucia's vertical distance above the ground (measured in feet) as a function of the number of seconds elapsed since the Ferris wheel began to turn. How many seconds will it take for Lucia to complete one revolution? f. Sketch a graph of the function you defined in part (e). On your graph, identify the interval of input values on which the function values complete one full cycle (i.e., the interval of t for which Lucia completes one revolution)

If a patient takes a does of D units of a particular drug, the amount of the dosage that remains in the patient's bloodstream after t days is

$$D e ^ { - k t },$$

where k is a positive constant depending on the particular drug. Show that if the patient takes a dose D every day for an extended period, the amount of drug in the bloodstream approaches

$$R = \frac { D e ^ { - k } } { 1 - e ^ { - k } }.$$

A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at the focus. If the dish is $12$ feet across at its opening and $4$ feet deep at its center, where should the receiver be placed?

A 450.0-mL sample of a 0.257-M solution of silver nitrate is mixed with 400.0 mL of 0.200 M calcium chloride. What is the concentration of $\mathrm{Cl}^{-}$ in solution after the reaction is complete?

Explain why you agree or disagree with the following statements. Assume other things equal.
a. A country that grows faster than its major trading partners can expect the international value of its currency to depreciate.
b. A nation whose interest rate is rising more rapidly than interest rates in other nations can expect the international value of its currency to appreciate.
c. A country’s currency will appreciate if its inflation rate is less than that of the rest of the world.

What type of statement is used to rethrow an exception?

The following model was fitted to explain the selling prices of condominiums in a sample of 815 sales:

$$\hat{y}=\underset{(0.91)}{-1264}+\underset{(515)}{48.18 x_1}+\underset{(488)}{3382 x_2}-\underset{(947)}{1859 x_3}+\underset{(768)}{3219 x_4}$$

$$+\underset{(768)}{2005 x_5} \quad \bar{R}^2=0.86$$

where

$\hat{y}=$ selling price of condo, in dollars

$x_1=$ square footage of living area

$x_2=$ size of garage, in number of cars

$x_3=$ age of condo, in years

$x_4=$ dummy variable taking the value 1 if the condo has a fireplace and 0 otherwise

$x_5=$ dummy variable taking the value 1 if the condo has hardwood floors and 0 if it has vinyl floors

a. Interpret the estimated coefficient of $x_4$.

b. Interpret the estimated coefficient of $x_5$.

c. Find a $95 \%$ confidence interval for the impact of a fireplace on selling price, all other things being equal.

d. Test the null hypothesis that type of flooring has no impact on selling price against the alternative that, all other things equal, condos with hardwood floors have a higher selling price than those with vinyl flooring.

The Day Company and the Knight Company are identical in every respect except that Day is not levered. Financial information for the two firms appears in the following table. All earnings streams are perpetuities, and neither firm pays taxes. Both firms distribute all earnings available to common stockholders immediately.

a. An investor who can borrow at 6 percent per year wishes to purchase 5 percent of Knight’s equity. Can he increase his dollar return by purchasing 5 percent of Day’s equity if he borrows so that the initial net costs of the strategies are the same?
b. Provided the two investment strategies in (a), which will investors choose? When will this process cease?

In the following exercise, determine whether at x = 1, the following function is

a) differentiable

b) continuous.

$$f(x)=1 / x$$

By inspection, decide which equation have no solution and which equation have all real number as a solution.

$$5 x-2=5 x-7$$

Which type of object is thrown by a throw statement?

Show that the function is continuous on its domain. State the domain.

$$h(x)=x e^{\sin x}$$

What will happen if the Combined Center of Gravity moves outside the stability triangle?