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shusha [124]
4 years ago
5

Which of the following is true about the function below?

Mathematics
1 answer:
STALIN [3.7K]4 years ago
3 0

For this case we have the following function:

f (x) = \frac {1} {\sqrt {x + 4}}

By definition, the domain of a function is given by all the values for which the function is defined. The given function is defined when the denominator is non-zero and when the argument of the root is greater than or equal to zero. So:

x + 4 = 0\\x = -4

The function is not defined in -4.

x + 4 \geq0\\x \geq-4

Thus, the domain of the function is given by all the strict major numbers to -4.

The range is the set of values that correspond to the domain.

The range is given by all y> 0.

Answer:

OPTION D

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The
stepan [7]

Answer:

Area = 129.5m^2

Perimeter = 48m

Step-by-step explanation:

Given

See attachment

Required

Determine the area and the perimeter of the garden

Calculating Area

First, we calculate the area\ of\ the\ rectangle

A_1 = L * B

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L = 20-(3.5 +3.5)

B = 7

So:

A_1 = (20 - (3.5 + 3.5)) * 7

A_1 = (20 - 7) * 7

A_1 = 13 * 7

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Next, we calculate the area of the two semi-circles.

Two semi-circles = One Circle

So:

A_2 = \pi r^2

Where

r = \frac{7}{2}

A_2 = \frac{22}{7} *  (\frac{7}{2})^2

A_2 = \frac{22}{7} *  \frac{49}{4}

A_2 = \frac{22}{1} *  \frac{7}{4}

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A_2 = \frac{154}{4}

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Calculating Perimeter

First, we calculate the perimeter of the rectangle

But in this case, we only consider the length because the widths have been covered by the semicircles

P_1 = 2 * L

Where:

L = 20-(3.5 +3.5)

So:

P_1 =2 * (20-(3.5 +3.5))

P_1 =2 * (20-7)

P_1 =2 * 13

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Two semi-circles = One Circle

So:

P_2 = 2\pi r

Where

r = \frac{7}{2}

P_2 = 2 * \frac{22}{7} * \frac{7}{2}

P_2 = \frac{2 * 22 * 7}{7 * 2}

P_2 = \frac{308}{14}

P_2 = 22

Perimeter of the garden is

Perimeter = P_1 + P_2

Perimeter = 26 + 22

Perimeter = 48m

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