2. The reflector of a satellite dish is in the shape of a parabola with a diameter of 4 feet and a depth of 2 feet. To get the maximum reception we need to place the antenna at the focus.

a. Write the equation of the parabola of the cross section of the dish, placing the vertex of the parabola at the origin. Convert the equation into standard form, if necessary. What is the defining feature of the equation that tells us it is a parabola?
b. Describe the graph of the parabola. Find the vertex, directrix, and focus.
c. Use the endpoints of the latus rectum to find the focal width.
d. How far above the vertex should the receiving antenna be placed?

Step-by-step explanation:

Assume the dish opens upwards. The cross-section through the vertex is a parabola. You know three points on the parabola: (0,0), (2,2), and (-2,2). Plug the points into y = ax² + bx + c to get a system of three equations where a=0.5, b=c=0.

Equation of parabola: y = 0.5x²

Vertex (0,0)

Focal length = 1/(4×0.5) = 0.5

Focus (0,0+0.5) = (0, 0.5)

Directrix y = 0-0.5 = -0.5

At endpoints of latus rectum, y = 0.5

x = ±√0.5 = ±√2/2

Focal width = 2×√2/2 = √2

Place antenna at focus, (9,2)

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step-by-step explanation:

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere