How many terms are in the expression shown below?

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

AVprozaik [17]

Answer:

D

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(2x).

Note that since x 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(x) = -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 x 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

Help me Please!!!!!!!

Murljashka [212]

Answer:

$\boxed{Option \ C}$

Step-by-step explanation:

$Sin \ Y = \frac{Opposite }{Hypotenuse } = \frac{XZ}{XY}$

$Cos \ Y = \frac{Adjacent}{Hypotenuse} = \frac{YZ}{XY}$

$Tan Y = \frac{opposite}{adjacent} = \frac{XZ}{ZY}$

7 0

3 years ago

Read 2 more answers

The cost to rent a jet ski is $80 per hour. in addition there also includes fee for a lesson on how to use the jet ski. Steve re

melomori [17]

Answer:

$y=80x+25$

Step-by-step explanation:

Let

x ----> the number of hours

y ---> the total cost of renting a jet ski in dollars

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value

In this problem we have

The slope is equal to

$m=\$80\ per\ hour$

we have the ordered pair (3,265)

substitute in the linear equation

$265=80(3)+b$

solve for b

$265=240+b$

$b=265-240$

$b=\$25$ ----> fee for a lesson on how to use the jet ski

substitute

$y=80x+25$

8 0

2 years ago

What is the average rate of change

algol [13]

The average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.

6 0

3 years ago

What is the simplified form of 30 times x to the sixth power over 14 times y to the fifth power times the fraction 7 times y-squ

Sonbull [250]

If we convert the given in its mathematical form, we have,

(30x⁶/14y⁵)(7y²/6x⁴)
It can be observed that the numerator of the first and the denominator of the second have a common factor of 6x⁴. Also, the denominator of the first and the numerator of the second expression have a common factor of 7y².

((6x⁴)(5x²)/(7y²)(2y³))(7y²/6x⁴)

Cancellation of the common terms will give us an answer of,

5x²/2y³

Therefore, the simplified version of the involved operation is 5x²/2y³.

6 0

3 years ago