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

--- equation

--- focus

--- directrix

---- focal width

Step-by-step explanation:

Given

Required

The equation of parabola

The depth represents the y-axis. So:

The diameter represents how the parabola is evenly distributed across the x-axis.

We have:

-2 to 2 is 4 units.

So:

So, the coordinates of the parabola is:

The equation of the parabola is calculated using:

Substitute (-2,2) for (x,y)

Divide by 8

So, the equation is:

The defining features

(a) Focus

The focus is located at:

(b) Directrix (y)

(c) Focal width

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step-by-step explanation:

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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