1. Math 4R Test10A Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(1) A satellite dish is made in the shape of a paraboloid of
revolution. The dish is 10 ft across at its opening and is 4 ft deep at
its center.
(1a) Let (h,k) = (0,0) and graph the parabolic cross-section.
(1b) Find the equation of this parabola.
(1c) Where should you place the receiver?
a:TEST10A.4Rt
2. Math 4R Test10A Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(2) The mean distance of the Earth from the Sun is 93 million
miles. The aphelion of the Earth is 94.5 million miles.
(2a) Let (h,k) = (0,0) and find the perihelion.
(2b) Find a, b and c for this elliptical orbit.
(2c) What is the equation of this ellipse?
(2d) Graph the orbit labeling a,b,c,h,k, the Sun and the Earth.
a:TEST10A.4Rt
3. Math 4R Test10A Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(3) You and your friend are talking to each other in a whisper
gallery with an elliptical cross-section. Assume that you are both
about 6 ft tall, the highest point of the ceiling is 20 ft above you and
that the gallery is 50 ft across.
(3a) Make a sketch of this situation.
(3b) Let (h,k) = (0,0) and find a, b and c.
(3c) What is the equation of this ellipse?
(3d) Where should you and your friend stand to hear each other the best?
a:TEST10A.4Rt
4. Math 4R Test10A Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(4) Nolan Ryan throws a baseball with an initial speed of 145 feet
per second at an angle of 30° off the horizontal. The ball leaves his
hand at a height of 5 ft.
x(t) = 145cos(30°)t
y(t) = -16t2 + 145sin(30°)t + 5
(4a) How long is the ball in the air?
(4b) What is the horizontal range of the ball
(ie: how far is the ball when it hits the ground)?
(4c) When does the ball reach its zenith (ie: maximum height)?
(4d) Find this vertical range.
(4e) Make a graph of the entire trajectory of the ball.
a:TEST10A.4Rt
5. Math 4R Test10A Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(BONUS) The planet Mercury travels around the Sun in an orbit
approximated by:
3.442 ⋅ 107
r(θ) = 1 – 0.206cos(θ)
where r is measured in miles and the Sun is at the pole.
(4a) Make a complete graph of this orbit (use polar and radian mode
with θmin=0 and θmax=2π and zoom fit).
(4b) Find the aphelion.
(4c) Find the perihelion.
(4d) What is the eccentricity of this orbit and what does it mean?
(4e) Rewrite this equation in standard form.
a:TEST10A.4Rt
