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loris [4]
3 years ago
7

Help Me Pleaseeee A square is cut out of a circle whose diameter is approximately 14 feet. What is the approximate area (shaded

region) of the remaining portion of the circle in square feet? ( where )
Mathematics
1 answer:
Setler [38]3 years ago
6 0

Answer:

(4\pi -2)49

Step-by-step explanation:

let radius of the circle be r = 14 feet.

then side of the square would be \sqrt{2}r

therefore area of the square = 2r^{2}

area of remaining circle = area of circle - area of square

                                        4\pi r^2-2r^{2}

                                        =(4\pi -2)49

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What is the product? x^2-16/2x+8 multiplied by x^3-2x^2+x/x^2+3x-4
Contact [7]

Answer:

(x (x - 4) (x - 1))/(2 (x + 4))

Step-by-step explanation:

Simplify the following:

((x^2 - 16) (x^3 - 2 x^2 + x))/((2 x + 8) (x^2 + 3 x - 4))

The factors of -4 that sum to 3 are 4 and -1. So, x^2 + 3 x - 4 = (x + 4) (x - 1):

((x^2 - 16) (x^3 - 2 x^2 + x))/((x + 4) (x - 1) (2 x + 8))

Factor 2 out of 2 x + 8:

((x^2 - 16) (x^3 - 2 x^2 + x))/(2 (x + 4) (x + 4) (x - 1))

x^2 - 16 = x^2 - 4^2:

((x^2 - 4^2) (x^3 - 2 x^2 + x))/(2 (x + 4) (x + 4) (x - 1))

Factor the difference of two squares. x^2 - 4^2 = (x - 4) (x + 4):

((x - 4) (x + 4) (x^3 - 2 x^2 + x))/(2 (x + 4) (x + 4) (x - 1))

Factor x out of x^3 - 2 x^2 + x:

(x (x^2 - 2 x + 1) (x - 4) (x + 4))/(2 (x + 4) (x + 4) (x - 1))

The factors of 1 that sum to -2 are -1 and -1. So, x^2 - 2 x + 1 = (x - 1) (x - 1):

(x (x - 1) (x - 1) (x - 4) (x + 4))/(2 (x + 4) (x + 4) (x - 1))

(x - 1) (x - 1) = (x - 1)^2:

(x (x - 1)^2 (x - 4) (x + 4))/(2 (x + 4) (x + 4) (x - 1))

((x - 4) (x + 4) x (x - 1)^2)/(2 (x + 4) (x + 4) (x - 1)) = (x + 4)/(x + 4)×((x - 4) x (x - 1)^2)/(2 (x + 4) (x - 1)) = ((x - 4) x (x - 1)^2)/(2 (x + 4) (x - 1)):

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Cancel terms. ((x - 4) x (x - 1)^2)/(2 (x + 4) (x - 1)) = ((x - 4) x (x - 1)^(2 - 1))/(2 (x + 4)):

(x (x - 4) (x - 1)^(2 - 1))/(2 (x + 4))

2 - 1 = 1:

Answer: (x (x - 4) (x - 1))/(2 (x + 4))

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