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Katena32 [7]
3 years ago
10

Write the standard form of the equation of a circle with a radius of 2 and center at (4,-5)

Mathematics
2 answers:
Veronika [31]3 years ago
7 0

center-radius form of the circle  (x – h)^2 + (y – k^)2 = r^2

(x-4)^2 + (y--5)^2 = 2^2

(x-4)^2 +(y+5)^2 = 4

yaroslaw [1]3 years ago
6 0

<u>Answer:</u>

(x-4)^2+(y+5)^2=4

<u>Step-by-step explanation:</u>

We are given a circle with a radius of 2 with a center at the point (4, -5).

Assuming x and y to be the coordinates of any point on the circle, we can find the equation of the circle by using the following distance formula:

r=\sqrt{(x_1-x)^2+(y_1-y)^2}

Putting the given values to get:

2=\sqrt{(x-4)^2+(y+5)^2}

Taking square on both sides to get:

4=(x-4)^2+(y+5)^2

Therefore, the equation of the given circle with radius 2 and center at (4, -5) is (x-4)^2+(y+5)^2=4.

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The length of a rectangle is four times its width. If the area of the rectangle is 324m^2, find its perimeter.
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Answer:

perimeter=90

Step-by-step explanation:

We know that the length is four times the width, so:

l=4w

We also know the area, which is 324 m². The formula for area:

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Solve for w. Simplify by removing parentheses:

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Divide 4 from both sides to isolate the variable:

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Find the square root of both sides:

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Solve for l. Divide both sides by 9:

\frac{324}{9}=\frac{l*9}{9}\\\\  l=36

The length of the rectangle is 36. (You can check: 4 times 9 is 36)

Now find the perimeter:

P=2l+2w

Insert values:

P=2(36)+2(9)\\\\P=72+18\\\\P=90

The perimeter is 90 m.

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