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2 years ago

If the diameter of a circle is 50 yards ,the radius is

Mathematics

2 answers:

Inessa05 [86]2 years ago

6 0

Answer: 25 yards

Explanation:

Your radius is half the diameter

Inga [223]2 years ago

3 0

If the diameter of a circle is 50 yards the radius must be 25 yards.

This is because the radius is always half the diameter of the circle. Since we know the diameter is 50 yards, half of 50 is 25 so the radius must be 25 yards.

Have a great day!

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What is the partial fraction decomposition of StartFraction 8 x + 19 Over (x + 8) (x minus 1) EndFraction? StartFraction 3 Over

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The partial fraction decomposition is $\frac{8x + 19}{(x + 8)(x - 1)} = \frac{5}{x + 8} + \frac{3}{x - 1}$

<h3>How to determine the decomposition?</h3>

The fraction is given as:

$\frac{8x + 19}{(x + 8)(x - 1)}$

Split the fraction as follows:

$\frac{8x + 19}{(x + 8)(x - 1)} = \frac{A}{x + 8} + \frac{B}{x - 1}$

Take the LCM

$\frac{8x + 19}{(x + 8)(x - 1)} = \frac{Ax -A + Bx + 8B}{(x + 8)(x -1)}$

Cancel the common factors

8x + 19 = Ax - A + Bx + 8B

By comparison, we have:

Ax + Bx = 8x

-A + 8B = 19

This gives

A + B = 8

-A + 8B = 19

Add both equations

9B = 27

Divide by 9

B = 3

Substitute B = 3 in A + B = 8

A + 3 = 8

Solve for A

A = 5

So, we have:

$\frac{8x + 19}{(x + 8)(x - 1)} = \frac{5}{x + 8} + \frac{3}{x - 1}$

Hence, the partial fraction decomposition is $\frac{8x + 19}{(x + 8)(x - 1)} = \frac{5}{x + 8} + \frac{3}{x - 1}$

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