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Zanzabum
3 years ago
8

I need some help with math

Mathematics
1 answer:
Irina18 [472]3 years ago
5 0

Answer:

(y-7)^2+(x-2)^2=16

and

(x+2)^2+(y-15)^2 = 9

Step-by-step explanation:

The standard equation of a circle is (x-h)^2+(y-k)^2=r^2 where the coordinate (h,k) is the center of the circle.  

Second Problem:

  1. We can start with the second problem which uses this info very easily.
  2. (h,k) in this problem is (-2,15) simply plug these into the equation. (x--2)^2+(y-15)^2=r^2 .
  3. We can also add the radius 3 and square it so it becomes 9. The equation.
  4. This simplifies to (x+2)^2+(y-15)^2 = 9.

First Problem:

  1. The first problem takes a different approach it is not in standard form. But we can convert it to standard form by completing the square.
  2. y^2-14y+x^2-4x+37=0 first subtract 37 from both sides so the equation is now y^2-14y+x^2-4x=-37.
  3. y^2-14y+x^2-4x+37=0 by adding (-\frac{b}{2a} )^2 to both the x and y portions of this equation you can complete the squares. (-\frac{b}{2a})^2=(-\frac{-14}{2(1)})^2 and (-\frac{-4}{2(1)})^2 which equals 49 and 4.
  4. Add 49 and 4 to both sides and the equation is now:y^2-14y+49+x^2-4x+4=-37+49+4 You can simplify the y and x portions of the equations into the perfect squares or factored form (y-7)^2 and (x-2)^2.
  5. Finally put the whole thing together. (y-7)^2+(x-2)^2=16.

I hope this helps!

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Nonamiya [84]

Answer:

5

Step-by-step explanation:

To find the prime factorization of a number, start by dividing the number by each prime number that you can divide by as many times as possible, starting with the smallest prime number and moving up. Then move on to the next prime number. The last division must give a quotient of 1. Then the prime factorization is the product of all the prime factors you divided the number by.

Here's how you use this method with 180.

Here are the first 10 prime numbers:

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Start by trying to divide by 2. 180 is divisible by 2.

180/2 = 90       90 is divisible by 2.

90/2 = 45         45 is not divisible by 2, so now try 3.

45/3 = 15          15 is divisible by 3.

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5/5 = 1              The divisors in bold are the prime factors of 180.

180 = 2 × 2 × 3 × 3 × 5

180 = 2² × 3² × 5

Answer: 5

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