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nirvana33 [79]
3 years ago
15

Write the standard form of the equation of the circle with center (-5,-7) that passes through the point (7,5).

Mathematics
1 answer:
shutvik [7]3 years ago
4 0

Answer:

(x + 5)² + (y + 7)² = 288

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

The radius is the distance from the centre (- 5, - 7) to the point on the circle (7, 5)

Use the distance formula to calculate r

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 5, - 7) and (x₂, y₂ ) = (7, 5)

r = \sqrt{(7+5)^2+(5+7)^2} = \sqrt{12^2+12^2} = \sqrt{288}

Hence

(x - (- 5))² + (y - (- 7))² = (\sqrt{288})², that is

(x + 5)² + (y + 7)² = 288

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Answer:

A. 1

General Formulas and Concepts:

<u>Pre-Algebra</u>

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Step-by-step explanation:

<u>Step 1: Define</u>

-5x - 1 ≤ -9

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Add 1 to both sides:                    -5x ≤ -8
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A baseball is thrown with an upward velocity of 32 feet per second. The equation h=-16t^2+32t gives the height of the ball t sec
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Answer:

The function of height has a maximum value.

Step-by-step explanation:

Maximum or Minimum:

A given function f(x).

  1. Find out f'(x) and f''(x)
  2. Then set f'(x)=0 which gives x=a.
  3. f''(a) > 0 , then at x=a , f(x) has minimum value.
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Given that, a baseball is thrown with with an velocity of 32 feet per second.

The equation of height is

h=-16t^2+32t

Differentiating with respect to t

h'=-32 t+32

Again differentiating with respect to t

h''=-32

Next, we set h'=0

-32 t+32=0

\Rightarrow 32t=32

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Now h''|_{t=1}=-32

Since at t=1, h''<0.

The function of height has a maximum value.

The maximum of h is = -16.(1)²+32

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