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3 years ago

The center of a circle is at (−3, 1) and its radius is 9. What is the equation of the circle?

Mathematics

1 answer:

jek_recluse [69]3 years ago

7 0

If a circle has center (a,b) and radius r, the equation is

$(x-a)^2+(y-b)^2=r^2$

So, you have

$(x+3)^2+(y-1)^2=81$

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How do you solve this using substitution method 17x+7y=20 Y=20x-42

Nutka1998 [239]

Answer:

17 x + 7 y = 20

y =20x - 42

17 x + 7(20x - 42) = 20

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3 years ago

4, Find a number x such that x = 1 mod 4, x 2 mod 7, and x 5 mod 9.

olchik [2.2K]

4, 7 and 9 are mutually coprime, so you can use the Chinese remainder theorem.

Start with

$x=7\cdot9+4\cdot2\cdot9+4\cdot7\cdot5$

Taken mod 4, the last two terms vanish and we're left with

$x\equiv63\equiv64-1\equiv-1\equiv3\pmod4$

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$x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5$

Taken mod 7, the first and last terms vanish and we're left with

$x\equiv72\equiv2\pmod7$

which is what we want, so no adjustments needed here.

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Taken mod 9, the first two terms vanish and we're left with

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so we don't need to make any adjustments here, and we end up with $x=401$ .

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$x\equiv401\pmod{4\cdot7\cdot9}\implies x\equiv149\pmod{252}$

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