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Soloha48 [4]
3 years ago
13

Write the equation of the circle whose center is (-4,8) and has a diameter of 18

Mathematics
1 answer:
svetoff [14.1K]3 years ago
6 0

Answer:

(x + 4)^2 + (y - 8)^2 = 81

or

(x + 4)^2 + (y - 8)^2 = 9^2 depending on how your teacher wants it written.

Step-by-step explanation:

The standard form for a circle is

(x + h)^2 + (y + k)^2 = r^2

r is the radius.

You are given the diameter

r = d/2

r = 18/2

r = 9

So you already have the right hand side of the equation

(x + h)^2 + (y + k)^2 = 9*2

(x + h)^2 + (y + k)^2 = 81

You basically have h and k as well. They come from the center point.

h = 4

k = - 8

So the equation of the circle (and the answer) is

(x + 4)^2 + (y - 8)^2 = 81

One question remains. Why do the x and y values change signs? If you know what the distance formula is, then what you are finding is the distance r of all points on the circle from the center of the circle.

It is the distance formula that is actually the formula for the circle.

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Answer:

See below.

Step-by-step explanation:

D(t) = 3260 - 55t

The function that shows their distance from home as a function of time shows that they started 3260 miles from home and are driving at 55 miles per hour.

part a:

D(12) = 3260  55(12)

D(12) = 3260 - 660

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Interpretation: After 12 hours of driving home, they are 2600 miles from home.

part b:

D(t) = 2490

3260 - 55t = 2490

-55t = -770

t = 14

Interpretation: When they are 2490 miles from home, they have driven for 14 hours.

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