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8. What's the circumference of a circle with a radius of 7 in? Round your answer to the neares
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O A. 41 in.
O B. 14 in.
O C.21
O D.44 in.
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The circumference of the given circle is D. 44 inches.

Step-by-step explanation:

Step 1:

From the given question, the radius of the given circle is 7 inches.

The circumference of any given circle is calculated by multiplying 2π with the radius. The radius of this circle is 7 inches and π = 3.14159.

Step 2:

The circumference for the given circle = 2π × r = 2 × 3.14159 × 7 inches,

                                                  = 6.28318 × 7 inches = 43.98226 inches.

Rounding this off to the nearest inch, 43.98226 inches, the circumference equals 44 inches which is option D.

f(x) = + 2x³ - 4x² - 6x + 3

Step-by-step explanation:

Note that radical zeros occur in conjugate pairs, thus

- 1 + is a zero then - 1 - is also a zero

is a zero then - is also a zero

Thus the corresponding factors are

(x - (- 1 + ) ), (x - (- 1 - ) ), (x - ), (x - (- )), that is

(x + 1 - ), (x + 1 + ), (x - ), (x + )

The polynomial is then the product of the roots

f(x) = (x + 1 - )(x + 1 + )(x - )(x + )

     = ((x + 1)² - ()²)((x² - ()²)

     = (x² + 2x + 1 - 2)(x² - 3)

     = (x² + 2x - 1)(x² - 3) ← distribute

     = - 3x² + 2x³ - 6x - x² + 3

     = + 2x³ - 4x² - 6x + 3