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3 years ago

Find the value of each variables

Mathematics

1 answer:

kompoz [17]3 years ago

7 0

Answer:

Step-by-step explanation:

Two similar triangles.

10/26 = y/13

y = 5

x² = 13² - y² = 144

x = 12

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Suppose cos(x)= -1/3, where π/2 ≤ x ≤ π. What is the value of tan(2x). EDGE

AVprozaik [17]

Answer:

Step-by-step explanation:

We are given that:

$\displaystyle \cos x = -\frac{1}{3}\text{ where } \pi /2 \leq x \leq \pi$

And we want to find the value of tan(2<em>x</em>).

Note that since <em>x</em> is between π/2 and π, it is in QII.

In QII, cosine and tangent are negative and only sine is positive.

We can rewrite our expression as:

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

Using double angle identities:

$\displaystyle \tan(2x)=\frac{2\sin x\cos x}{\cos^2 x-\sin^2 x}$

Since cosine relates the ratio of the adjacent side to the hypotenuse and we are given that cos(<em>x</em>) = -1/3, this means that our adjacent side is one and our hypotenuse is three (we can ignore the negative). Using this information, find the opposite side:

$\displaystyle o=\sqrt{3^2-1^2}=\sqrt{8}=2\sqrt{2}$

So, our adjacent side is 1, our opposite side is 2√2, and our hypotenuse is 3.

From the above information, substitute in appropriate values. And since <em>x</em> is in QII, cosine and tangent will be negative while sine will be positive. Hence:

<h2> $\displaystyle \tan(2x)=\frac{2(2\sqrt{2}/3)(-1/3)}{(-1/3)^2-(2\sqrt{2}/3)^2}$ </h2>

Simplify:

$\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{(1/9)-(8/9)}$

Evaluate:

$\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{-7/9} = \frac{4\sqrt{2}}{7}$

The final answer is positive, so we can eliminate A and B.

We can simplify D to:

$\displaystyle \frac{2\sqrt{8}}{7}=\frac{2(2\sqrt{2}}{7}=\frac{4\sqrt{2}}{7}$

So, our answer is D.

7 0

3 years ago

If the simple interest on $6,000 for 9 years is $4,320, then what is the interest rate?

MaRussiya [10]

Answer:

6.48%

Step-by-step explanation:

the rule of the simple interest is:

I=PRT

but here we want the rate, and we have I and P and T

so put the rate on 1 side, and all the given numbers in other side

the rule will be like this:

R=I/PT

R=4320/6000×9

R=6.48%

4 0

3 years ago

ASSIGNMENT: Show that the correct solution to the following system of equations is (-2, 0). Upload a photo of your work or neatl

ki77a [65]

Answer:

Step-by-step explanation:

5 0

3 years ago

A basketball team is giving a signed basketball to their coach. The ball has a diameter of 14 inches. How much room is there on

Aliun [14]

Answer: 153.9 inches sq

Step-by-step explanation: The area of a circle is A= 3.14 times radius squared. Assuming we are finding area, we use this formula. The diameter is 14 so the radius is 7. Seven squared is 49, so we would do 3.14 times 49. This equals 153.86, then rounded is 153.9. I hope that I helped you out a bit!

3 0

4 years ago

Plz help me! I don’t get it

34kurt

Y= -3.5/1x + 4 because

3 0

3 years ago

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Find the value of each variables​

Find the value of each variables