A 4 cm x 6 cm rectangle sits inside a circle with radius with 11 cm. What is the area of the shaded region?

Mathematics

1 answer:

Novosadov [1.4K]3 years ago

4 0

Answer:

The area of the shaded region is $(121\pi -24)\ cm^{2}$

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the circle minus the area of the rectangle

$A=\pi r^{2} -bh$

we have

$r=11\ cm$

$b=4\ cm$

$h=6\ cm$

substitute the values

$A=\pi (11^{2}) -(4)(6)$

$A=(121\pi -24)\ cm^{2}$ ----> exact value of the shaded area

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Please help find domain and range

Oxana [17]

<h3>Answer: Choice A</h3>

Domain: x > 4
Range: y > 0

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Explanation:

We want to avoid having a negative number under the square root. Solving $x-4 \ge 0$ leads to $x \ge 4$

So it appears the domain could involve x = 4 itself; however, if we tried that x value, then we'd get a division by zero error.

So in reality, the domain is x > 4.

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The range of y = sqrt(x) is the set of positive real numbers. So y > 0 is the range for this equation. Shifting left and right does not affect the range, so the range of y = sqrt(x-4) is also y > 0.

We are dividing a positive number (3) over some positive number in the denominator. Overall, the expression $\frac{3}{\sqrt{x-4}}$ is positive because positive/positive = positive.

Therefore, the range of the given equation is y > 0

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The graph is shown below. We have a vertical asymptote at x = 4 and a horizontal asymptote at y = 0. The green curve is fenced in the upper right corner (northeast corner).