Mathematics, 23.01.2021 09:20 codysaucier2823

Hi everyone, so I was doing some math homework and I got stuck. Please help me with these two questions (numbers 7 and 8). Thank you! I'll also try my hardest to help you in return!

Hi everyone, so I was doing some math homework and I got stuck. Please help me with these two quest

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Answer from: park7497

7). x = 6, $\frac{14}{3}$

8). x = 2

Step-by-step explanation:

7). Area of a circle = πr²

Here 'r' = radius of the circle

Area of the shaded region of the circle = Area of the large circle - Area of the small circle

= π(x)² - $\pi (\frac{x}{2})^2$

= $\pi x^{2} -\pi (\frac{x^2}{4})$

= $\pi x^{2}(1-\frac{1}{4})$

= $\frac{3\pi x^{2} }{4}$ in²

If area of the shaded region is (8πx - 21π) in²

$\frac{3\pi x^{2} }{4}=8\pi x - 21\pi$

$\frac{3x^2}{4}=8x-21$

3x² = 32x - 84

3x²- 32x + 84 = 0

3x² - 14x - 18x + 84 = 0

x(3x - 14) - 6(3x - 14) = 0

(x - 6)(3x - 14) = 0

x = 6, $\frac{14}{3}$

8). Area of the shaded region = Area of the largest circle - Area of the smaller semicircle - Area of the smallest semicircle

Area of the largest circle = π(2x + 2x)²

= 16πx²

Area of the smaller semicircle = $\frac{1}{2}\pi (3x)^{2}$

= 4.5(πx²)

Area of the smallest semicircle = $\frac{1}{2}\pi (2x)^{2}$

= 2πx²

Now area of he shaded region = 16πx² - [4.5(πx²) + 2πx²]

= 16πx² - 6.5πx²

= 9.5πx² mm²

If the area of the shaded region = 12πx + 14π

12πx + 14π = 9.5πx²

12x + 14 = 9.5x²

9.5x² - 12x - 14 = 0

19x² - 24x - 28 = 0

19x² - 38x + 14x - 28 = 0

19x(x - 2) + 14(x - 2) = 0

(19x + 14)(x - 2) = 0

x = $-\frac{14}{19},2$

But the radius o a circle can't be negative.

Therefore, x = 2 will be the answer.

Answer from: Quest

the amount you'd have after the work is $1.55

step-by-step explanation:

you subtract 95% from $31.

Answer from: Quest

step-by-step explanation:

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