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Gennadij [26K]
3 years ago
9

What is the volume of the hemisphere? 583.2cm^3cm 3 291.6cm^3cm 3 6882.3cm^3cm 3 3441.1cm^3cm 3 Item at position 3

Mathematics
1 answer:
Sveta_85 [38]3 years ago
7 0

Answer:

See Explanation

Step-by-step explanation:

The question has missing details; as the radius or an attachment of the hemisphere is not given.

However, I'll solve on a general terms.

The volume of a hemisphere is: V = \frac{2}{3}\pi r^3

Take for instance

r = 14.9cm

The volume becomes:

V = \frac{2}{3} * 3.142 * 14.9^3

V = \frac{2 * 3.142 * 14.9^3}{3}

V = \frac{20787.151516}{3}

V = 6929.051cm^3

<em>So, all you need to do is plug in the value of radius in the formula.</em>

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The value of x is –7.

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Given expression:

$\left(\frac{1}{x+3}+\frac{6}{x^{2}+4 x+3}\right) \cdot \frac{x+3}{x+1}

Let us factor x^2+4x+3.

x^2+4x+3=(x+1)(x+3)

Substitute this in the fraction.

$\left(\frac{1}{x+3}+\frac{6}{(x+1)(x+3)}\right) \cdot \frac{x+3}{x+1}

To make the denominator same, multiply and divide the first term by (x +1).

$\left(\frac{(x+1)}{(x+1)(x+3)}+\frac{6}{(x+1)(x+3)}\right) \cdot \frac{x+3}{x+1}

Denominators are same, you can add the fractions.

$\left(\frac{x+1+6}{(x+1)(x+3)}\right) \cdot \frac{x+3}{x+1}

$\frac{x+7}{(x+1)(x+3)} \cdot \frac{x+3}{x+1}

Cancel the common term in the numerator and denominator.

$\frac{x+7}{x+1} \cdot \frac{1}{x+1}

Multiply the fractions.

$\frac{x+7}{(x+1)^2}

$\frac{x+7}{x^2+2x+1}

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Suppose the expression is equal to 0.

$\frac{x+7}{x^2+2x+1}=0

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Any number or variable multiplied by 0 gives 0.

${x+7}=0

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