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The reflector of a flashlight is in the shape of a parabolic surface. The casting has a diameter of 4 inches and a depth of 1 inch. How far from the vertex should the light bulb be placed?

The reflector of a flashlight is in the shape of a parabolic surface. The casting has a diameter of 8 inches and a depth of 1 inch. How far from the vertex should the light bulb be placed?

How can you distinguish an ellipse from a hyperbola by looking at their equations?

The towers of the Golden Gate Bridge connecting San Francisco to Marin County are 1280 meters apart and rise 160 meters above the road. The cable between the towers has the shape of a parabola and the cable just touches the sides of the road midway between the towers. What is the height of the cable 200 meters from a tower? Round to the nearest meter. (IMAGES CANNOT COPY).

The towers of a suspension bridge are 800 feet apart and rise 160 feet above the road. The cable between the towers has the shape of a parabola and the cable just touches the sides of the road midway between the towers. What is the height of the cable 100 feet from a tower? (IMAGES CANNOT COPY).

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I graphed a hyperbola centered at the origin that was symmetric with respect to the \(x\) -axis and also symmetric with respect to the \(y\) -axis.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If one branch of a hyperbola is removed from a graph, then the branch that remains must define \(y\) as a function of \(x\).

A baseball player throws a ball with an initial velocity of 140 feet per second at an angle of \(22^{\circ}\) to the horizontal. The ball leaves the player's hand at a height of 5 feet. a. Write the parametric equations that describe the ball's position as a function of time. b. Use a graphing utility to obtain the path of the baseball. c. Find the ball's maximum height and the time at which it reaches this height. Round all answers to the nearest tenth. d. How long is the ball in the air? e. How far does the ball travel?

The plane curve described by the parametric equations \(x=3 \cos t \quad\) and \(\quad y=3 \sin t, \quad 0 \leq t<2 \pi, \quad\) has \(\quad\) a counterclockwise orientation. Alter one or both parametric equations so that you obtain the same plane curve with the opposite orientation.

Use the exponential decay model, \(A=A_{0} e^{k t},\) to solve this exercise. The half-life of aspirin in your bloodstream is 12 hours. How long, to the nearest tenth of an hour, will it take for the aspirin to decay to \(60 \%\) of the original dosage? (Section \(3.5,\) Example 2 )