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3 years ago

The question is in the screenshot attached. Thank you!

Mathematics

1 answer:

Rzqust [24]3 years ago

7 0

Answer:

Domain: -4 < x < 4

Zeros: (-2, 0), (0, 0) and (2, 0)

The function is positive if: 0 < x < 2

The function is negative if: -4 < x < 0 and 2 < x < 4

Step-by-step explanation:

Domain of the function are those x values where the function is defined, For this case, -4 < x < 4

Zeros of a function are those x values where y = 0, that is, the graph intersect x-axis. For this case, the points are: (-2, 0), (0, 0) and (2, 0)

The function is positive if the graph o the function is above x-axis. For this case, the function is positive at the interval (0, 2)

The function is negative if the graph o the function is below x-axis. For this case, the function is negative at the intervals (-4, 0) and (2, 4)

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<h3>Answer: See attached image below</h3>

Explanation:

The law of sines is

$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

This is the same as writing

$\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$

Because we apply the reciprocal to each side to keep things balanced

Note how the 'a's stick together on one side, so do the 'b's and 'c's.

For something like $\frac{a}{b}\sin B$ we can see the $\frac{\sin B}{b}$ portion, but now there's an 'a' in there. This is from multiplying both sides of the equation below by 'a'

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The summary is that the 'a' pairs with sin(A) and that's what matches with expression number 1.

--------------

For expression number 2, we'll have it pair with sin(B). This is because the 'c's already are taken care of (they are paired up) and there's an extra b all by itself. The working/steps will basically look like what is shown in the section above, though you'll use the equation $\frac{\sin B}{b} = \frac{\sin C}{c}$

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The other expressions will match in similar fashion. The filled out answers are shown in the attached image below.

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