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andrezito [222]
3 years ago
14

Write the equation of a circle with center (4,5) and a Circumference = 16 pi

Mathematics
2 answers:
3241004551 [841]3 years ago
8 0

Answer:

The required equation in standard form is (x-4)^2+(y-5)^2=64

Step-by-step explanation:

The equation of a circle with center (h,k) an radius, r units is given by the formula;

(x-h)^2+(y-k)^2=r^2

The given circle has center (4,5) and the radius can be calculated from the given circumference, which is C=16\pi

2\pi r=16\pi

\implies r=8

We substitute these values into the formula to obtain;

(x-4)^2+(y-5)^2=8^2

We simplify to get;

(x-4)^2+(y-5)^2=64

jasenka [17]3 years ago
5 0

Answer:

Equation of the circle : (x - 4)² + (y - 5)² = 64

Step-by-step explanation:

Equation of the circle

(x - x₁)² + (y - y₁)² = r²

Where (x₁, y₁) be the coordinates of center and r is the radius of circle.

<u>To find the radius</u>

It is given that circumference of circle = 16π

Circumference 2πr = 16

r = 16π/2π= 8

<u>To find the equation of the circle</u>

Center = (4, 5)

(x - x₁)² + (y - y₁)² = r²

(x - 4)² + (y - 5)² = 8²

(x - 4)² + (y - 5)² = 64

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A hardware store clerk mixed nuts worth $1.32 per kilogram with bolts worth $1.20 per kilogram. If he made 108 kilograms of a mi
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Answer:

the way to work these types of problems is to create a table. The table will have three rows and three columns.

The table:

Let x represent the kilograms of nuts, then 138 - x will represent the kilograms of bolts.

Product     Amount        Cost            Total

--------------------------------------------------------

  Nuts          x               .60         .60 * x

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Step-by-step explanation:

The equation:

The nuts plus the bolts must equal the mix or:

.60 * x + .66 * (138 - x) = .65 * 138

I do not like to work with decimals, so multiply each term by 100:

60 * x + 66 * (138 - x) = 65 * 138

Remove the parenthesis and combine like terms:

-6x = -66 * 138 + 65 * 138

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Divide both sides by -6:

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Solution:

The mixture contains 23 kilograms of nuts.

The mixture contains 138 - 23, or 115 kilograms of bolts.

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