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Fed [463]
3 years ago
14

Find an equation of the circle whose diameter has endpoints , 6−2 and , −4−4 .

Mathematics
1 answer:
MrRissso [65]3 years ago
4 0
If you need just the answer, it's in bold at the bottom. Otherwise, the process for how I got there is below. 

In order to find the equation, we first find the midpoint. This will give us the center of the two endpoints. Then, we do the distance formula to find how many units there are between the endpoints and cut it in half to find the radius. After, we plug in the new information into the equation format of the circle. 

Midpoint = ( \frac{x_{1}+ x_{2} }{2},  \frac{ y_{1} + y_{2} }{2} )

So plug in the ordered pairs given to get: 

Midpoint = ( \frac{6-4}{2},  \frac{-2-4}{2})
Midpoint = ( \frac{2}{2},  \frac{-6}{2})
Midpoint = (1, - 3)

This is your center.

Now for the distance between the endpoints. 

Distance = √((X₂ - X₁)² + (Y₂ - Y₁)²)
Distance = √((-4 - 6)² + (-4 - (-2))²)
Distance = √((- 10)² + (- 2)²)
Distance = √(100 + 4)
Distance = √104 which simplifies to 2√26

So the distance between the two endpoints (the diameter) is 2√26 units long. We divide this by 2 and get the measurement of the radius. The radius is √26 units long. 

Now we plug in to the equation of a circle:

(x - h)² + (y - k)² = r² 

The center of the circle is represented by the ordered pair (h, k) and the radius is represented by r. 

So your equation becomes:
(x - 1)² + (y + 3)² = (√26)²

Which simplifies to your final answer:

(x - 1)² + (y + 3)² = 26

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3 years ago
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Please help and show work
gladu [14]

Answer:

A

Step-by-step explanation:

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2 1/2 —> 2.5

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With this equation I know that one bag lasts 23 full days.

This is almost a month, and so it would not make sense for the answers to be B, C, or D.

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2 years ago
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There were 166 paid admissions to a game. The price was $2 for adults and $.75 for children. The amount of data taken in was $29
JulijaS [17]

Answer:the number of adults that attended the game is 135.

the number of children that attended the game is 31

Step-by-step explanation:

Let x represent the number of adults that attended the game.

Let y represent the number of children that attended the game.

There were 166 paid admissions to a game. This means that

x + y = 166

The price was $2 for adults and $.75 for children. The amount of data taken in was $293.25. This means that

2x + 0.75y = 293.25 - - - - - - - - - - 1

Substituting x = 166 - y into equation 1, it becomes

2(166 - y) + 0.75y = 293.25

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\cos(2x)  =  \cos(x)

Solution (1)

2x = x + 2k\pi

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x = 2k\pi

for k=0 / for k=1 / for k=-1

x=0 / x=2π / x=-2π

acc / acc / rej

solution (2)

2x =  - x  + 2k\pi

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