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3 years ago

9

Simplify:

[3]{a {}^{6} } " alt=" \sqrt[3]{a {}^{6} } " align="absmiddle" class="latex-formula">

1 answer:

PtichkaEL [24]3 years ago

4 0

Answer:

$a^2$

Step-by-step explanation:

$\sqrt[3]{a^6}\\\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a}=a^{\frac{1}{n}}\\\left(a^6\right)^{\frac{1}{3}}\\a^{6\cdot \frac{1}{3}}\\a^2$

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Answer:

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3 years ago

A triangle has two sides measuring 16 and 21. The included angle is 116°. What is the length of the side opposite the 116° angle

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Answer:

Length of the side opposite to angle $116^{\circ}$ is 31.49

Step-by-step explanation:

Included angle can be defined as the angle in between two sides of the triangle.

So angle $116^{\circ}$ is in between sides 16 and 21.

Refer to the attachment for triangle diagram.

To find the length of opposite side, use cosine rule as follows

$a^{2}=b^{2}+c^{2}-2\:b\:c\cos\left(A\right)$

From the diagram, $b = 21,c = 16,\angle A=116^{\circ}$

Substituting the values in the formula,

$a^{2}=\left(21\right)^{2}+\left(16\right)^{2}-2\left(21\right)\left(16\right)\cos\left(116\right)$

Simplifying,

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Taking square root on both sides,

$\sqrt{a^{2}}=\sqrt{991.59}$

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3 years ago

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