Skylar is designing a flashlight that uses a parabolic reflecting mirror and a light source. the shape of the mirror can be modeled by (y+5)^2=12(x+2), where x and y are measured in inches. what is the focus of the flashlight?

The focus of the flashlight= (1,-5)

Step-by-step explanation:

Given: Skylar is designing a flashlight that uses a parabolic reflecting mirror and a light source.

The shape of the mirror can be modeled by

We know that the standard form for the equation of parabola is , where focus = (h+p,k)

Rewrite the given equation in the standard form , we get

Therefore, focus of the flashlight=(-2+3,-5)=(1,-5)

18

step-by-step explanation:

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80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

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