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3 years ago

Find the equation of the circle. With center at (-3, 1) and point on the circle= (5, -3).

Mathematics

1 answer:

patriot [66]3 years ago

3 0

Answer:

(x + 3)² + (y - 1)² = 80

Step-by-step explanation:

Circle equation: (x - h)² + (y - k)² = r²

We are given h and k, so we just plug that in:

(x + 3)² + (y - 1)² = r²

To find r, we need to use distance formula: $d = \sqrt{(x2-x1)^2+(y2-y1)^2}$ between the center of the circle and the point on the circle. We should get √80 as r. We plug that in to get our answer:

(x + 3)² + (y - 1)² = 80

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2 years ago

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4 years ago

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3 years ago

Use mathematical induction to prove the statement is true for all positive integers n. 1^2 + 3^2 + 5^2 + ... + (2n-1)^2 = (n(2n-

Charra [1.4K]

Answer:

The statement is true is for any $n\in \mathbb{N}$ .

Step-by-step explanation:

First, we check the identity for $n = 1$ :

$(2\cdot 1 - 1)^{2} = \frac{2\cdot (2\cdot 1 - 1)\cdot (2\cdot 1 + 1)}{3}$

$1 = \frac{1\cdot 1\cdot 3}{3}$

$1 = 1$

The statement is true for $n = 1$ .

Then, we have to check that identity is true for $n = k+1$ , under the assumption that $n = k$ is true:

$(1^{2}+2^{2}+3^{2}+...+k^{2}) + [2\cdot (k+1)-1]^{2} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}$

$\frac{k\cdot (2\cdot k -1)\cdot (2\cdot k +1)}{3} +[2\cdot (k+1)-1]^{2} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}$

$\frac{k\cdot (2\cdot k -1)\cdot (2\cdot k +1)+3\cdot [2\cdot (k+1)-1]^{2}}{3} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}$

$k\cdot (2\cdot k -1)\cdot (2\cdot k +1)+3\cdot (2\cdot k +1)^{2} = (k+1)\cdot (2\cdot k +1)\cdot (2\cdot k +3)$

$(2\cdot k +1)\cdot [k\cdot (2\cdot k -1)+3\cdot (2\cdot k +1)] = (k+1) \cdot (2\cdot k +1)\cdot (2\cdot k +3)$

$k\cdot (2\cdot k - 1)+3\cdot (2\cdot k +1) = (k + 1)\cdot (2\cdot k +3)$

$2\cdot k^{2}+5\cdot k +3 = (k+1)\cdot (2\cdot k + 3)$

$(k+1)\cdot (2\cdot k + 3) = (k+1)\cdot (2\cdot k + 3)$

Therefore, the statement is true for any $n\in \mathbb{N}$ .

4 0

3 years ago

What number must be added to the expression below to complete the square? X^2-7x

Yuki888 [10]

Answer:

49/4

Step-by-step explanation:

x² -7x +(7/2)²=(x-7/2)²

x²-2x·7/2+ (7/2)²=(x²-7/2)²

(7/2)²=49/4

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3 years ago