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Alexxandr [17]
3 years ago
13

Find the equation of a circle with a center at (–7, –1) where a point on the circle is (–4, 3).

Mathematics
1 answer:
gogolik [260]3 years ago
8 0

Answer:

(x + 7)^2 + (y + 1)^2 = 25.

Step-by-step explanation:

The center of a circle is easy to set up. According to the formula below, the formula for the circle will be (x - a)^2 + (y - b)^2 = r^2.

In this case, a = -7 and b = -1, so we have...

(x - (-7))^2 + (y - (-1))^2 = r^2

(x + 7)^2 + (y + 1)^2 = r^2

To get the radius, we need to find the distance between the center and the point on the circle. The distance formula is d = sqrt((x2 - x1)^2 + (y2 - y1)^2).

In this case, x2 = -4, x1 = -7, y2 = 3, and y1 = -1.

sqrt((-4 - -7)^2 + (3 - -1)^2) = sqrt((-4 + 7)^2 + (3 + 1)^2) = sqrt((3)^2 + (4)^2) = sqrt(9 + 16) = sqrt(25) = plus or minus 5.

Since distance can only be positive, the distance is 5 units, meaning that the radius is 5 units.

5^2 = 25

So, your equation should be (x + 7)^2 + (y + 1)^2 = 25.

Hope this helps!

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Find the area of the shaded region. Use 3.14 as an approximation.​
MA_775_DIABLO [31]

Answer:

shaded area = 113.64 cm²

Step-by-step explanation:

To find the shaded area, subtract the area of the circle from the area of the triangle.

Area of a triangle = 1/2 x base x height

⇒ area of triangle = 1/2 x 25 x 21.4 = 267.5 cm²

Area of a circle = \pi r^2 (where r is the radius)

From inspection, we can see that the diameter of the circle = 14 cm

Therefore, as the diameter = 2r, then r = 14 ÷ 2 = 7 cm

⇒ area of circle = 3.14 x 7² = 153.86 cm²

Shaded area = area of triangle - area of circle

⇒ shaded area = 267.5 - 153.86 = 113.64 cm²

8 0
2 years ago
A prop for a school play is a sphere that will be hung from the ceiling. The surface area of the sphere is 5 024 cm'. If the sur
denis23 [38]

Answer:

The radius of the sphere, to the nearest cm:

r\approx 20 cm

Step-by-step explanation:

The surface area of a sphere is given by the formula

A = 4πr²

where r is the radius of the sphere.

Given

  • The surface area of sphere A = 5024 cm²

The radius of the sphere can be determined such as

A\:=\:4\pi r^2

r\:=\:\frac{1}{2}\sqrt{\frac{A}{\pi }}

Plug in Surface Area of sphere =  5024, π = 3.14 in the formula

\:r\:=\:\frac{1}{2}\sqrt{\frac{5024}{3.14}}\:\:

r\approx 20 cm

Therefore, the radius of the sphere, to the nearest cm:

r\approx 20 cm

3 0
2 years ago
10 in
lisabon 2012 [21]
The answer is 36in because that’s the pathagreom you need to use to find the answer
5 0
3 years ago
A Number decreased by the square of 9
grin007 [14]
X decreased by the square of nine
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Factor the expression.<br> 3x2 + 14x-5
Irina18 [472]

Answer:

(3x-1)(x+5)

Step-by-step explanation:

Find two numbers that when they multiply, you get the third term,

which is -5 in this problem. And when they add up, you get the second term,

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8 0
3 years ago
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