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1 year ago

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A circle with radius of \greenD{5\,\text{cm}}5cmstart color #1fab54, 5, start text, c, m, end text, end color #1fab54 sits insid

e a \blueD{11\,\text{cm} \times 11\,\text{cm}}11cm×11cmstart color #11accd, 11, start text, c, m, end text, times, 11, start text, c, m, end text, end color #11accd rectangle.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.

2 answers:

Marat540 [252]1 year ago

7 0

Answer:

The area of the shaded region is 42.50 cm².

Step-by-step explanation:

Consider the figure below.

The radius of the circle is, <em>r</em> = 5 cm.

The sides of the rectangle are:

<em>l</em> = 11 cm

<em>b</em> = 11 cm.

Compute the area of the shaded region as follows:

Area of the shaded region = Area of rectangle - Area of circle

$=[l\times b]-[\pi r^{2}]\\\\=[11\times 11]-[3.14\times 5\times 5]\\\\=121-78.50\\\\=42.50$

Thus, the area of the shaded region is 42.50 cm².

bearhunter [10]1 year ago

4 0

Answer:

50.27 cm

Step-by-step explanation:

π × 5 × 5 = 25π cm
π × 3 × 3 = 9π cm
25π - 9π = 16π cm = 50.27 cm

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<u>Given:</u>

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<u>Solving the equation:</u>

To determine the extraneous solution, we shall first solve the given equation.

Applying the log rule $\log _{c}(a)+\log _{c}(b)=\log _{c}(a b)$ , we get;

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Thus, we have;

$x(x-3)=-7 x+21$

Simplifying the equation, we get;

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$x^2+4x=21$

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$(x-3)(x+7)=0$

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The extraneous solutions are the solutions that does not work in the original equation.

Now, to determine the extraneous solution, let us substitute x = 3 and x = -7 in the original equation.

Thus, we get;

$\log _{4}(3)+\log _{4}(3-3)=\log _{4}(-7 \cdot 3+21)$

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Thus, we get;

Undefined = Undefined

This is false.

Thus, the solution x = 3 does not work in the original equation.

Hence, x = 3 is an extraneous solution.

Similarly, substituting x = -7, in the original equation. Thus, we get;

$\log _{4}(-7)+\log _{4}(-7-3)=\log _{4}(-7(-7)+21)$

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1 year ago

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