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2 years ago

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What is the domain of the exponential function shown below?

1 answer:

Phoenix [80]2 years ago

7 0

The function will exist on all real numbers. Hence the domain of the exponential function given is all real numbers

<h3>Domain of a function</h3>

The domain are independent values of an expression for which it exist. The standard exponential equation is expressed as y = ab^x

Given the exponential function as shown:

y = 5(3)^x

The function will exist on all real numbers. Hence the domain of the exponential function given is all real numbers

Learn more on domain here: brainly.com/question/26098895

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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

Crank

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,

$a^{2}=441+256-225792\left(-0.44\right)$

$a^{2}=991.59$

Taking square root on both sides,

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

$a=31.49$

Therefore length of third side is 31.49

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