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3 years ago

Which of the following could be the number shown on the number line?

Mathematics

1 answer:

sladkih [1.3K]3 years ago

4 0

Answer: Choice A. $\sqrt{35}$

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Explanation:

Recall that 36 is a perfect square

36 = 6^2

Or in other words, $\sqrt{36} = \sqrt{6^2} = 6$

The point marked on this number line is some value smaller than 6, so the number under the square root must be smaller than 36.

That could apply to either choices A or B.

Using a calculator shows that

$\sqrt{35} \approx 5.916\\\\\sqrt{30} \approx 5.477\\\\$

Choice A is the better answer as it's much closer to 6 than choice B is.

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Read 2 more answers

For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va

Black_prince [1.1K]

Answer:

3 solutions:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is $tan(\frac{\theta}{2})$ so let's focus on that part of the equation first.

We know that:

$tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}$

therefore:

$cos(\frac{\theta}{2})\neq0$

so we need to find the angles that will make the cos function equal to zero. So we get:

$cos(\frac{\theta}{2})=0$

$\frac{\theta}{2}=cos^{-1}(0)$

$\frac{\theta}{2}=\frac{\pi}{2}+\pi n$

$\theta=\pi+2\pi n$

we can now start plugging values in for n:

$\theta=\pi+2\pi (0)=\pi$

if we plugged any value greater than 0, we would end up with an angle that is greater than $2\pi$ so, that's the only angle we cannot include in our answer set, so: