PLEASE HELP IM STUCK PLS

Mathematics

2 answers:

tankabanditka [31]1 year ago

6 0

Answer:

y is equal to -16

Elis [28]1 year ago

4 0

Answer:

y = 8

Step-by-step explanation:

We can use proportions for this question since y varies directly with x. This means that if x changes, y changes along with the x, and vice versa.

When y = -8, x = 4, so the proportion will be -8 : 4.

We need to find the y when x is 4, so our equation will be:

-8 : 4 = y : -4

Since the proportion will be the same.

Next, we multiply the inner two numbers, and the outer two numbers, saying that the values are the same.

4y = 32

y = 8

So y = 8 will be our answer!

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If sin(x) = 5/13, and x is in quadrant 1, then tan(x/2) equals what?

Rufina [12.5K]

$x$ is in quadrant I, so $0$ , which means $0$ , so $\dfrac x2$ belongs to the same quadrant.

Now,

$\tan^2\dfrac x2=\dfrac{\sin^2\frac x2}{\cos^2\frac x2}=\dfrac{\frac{1-\cos x}2}{\frac{1+\cos x}2}=\dfrac{1-\cos x}{1+\cos x}$

Since $\sin x=\dfrac5{13}$ , it follows that

$\cos^2x=1-\sin^2x\implies \cos x=\pm\sqrt{1-\left(\dfrac5{13}\right)^2}=\pm\dfrac{12}{13}$

Since $x$ belongs to the first quadrant, you take the positive root ( $\cos x>0$ for $x$ in quadrant I). Then

$\tan\dfrac x2=\pm\sqrt{\dfrac{1-\frac{12}{13}}{1+\frac{12}{13}}}$

$\tan x$ is also positive for $x$ in quadrant I, so you take the positive root again. You're left with

$\tan\dfrac x2=\dfrac15$