What temperature is 23 degrees above freezing in fahrenheit

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(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

1. One box of cereal is 16 ounces and costs $3. A smaller box of The same cereal is 11.5 ounces and costs $2. Which box of cerea

pav-90 [236]

1. The 1.5 oz box for $2 is best because if you make $3 into $6 then the box is 32 oz. And if you change $2 to $6, the box is 34..5 oz which is better because its bigger.

6 0

3 years ago

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Ella is a landscape photographer. One weekend at her gallery she sells a total of 52 prints for a total of $2,975. A small paint

rosijanka [135]

<h2>Answer:37 paintings of $50 and 15 paintings of $75</h2>

Step-by-step explanation:

Let $x$ be the number of paintings Ella sells for $ $50$ .

Let $y$ be the number of paintings Ella sells for $ $75$ .

Profit made through $ $50$ paintings is $50x$

Profit made through $ $75$ paintings is $75y$

So,total profit is given by $50x+75y$

It is given that total profit is $ $2975$

So, $50x+75y=2975$ ..(i)

Given that the total number of prints is $52$

So, $x+y=52$ ..(ii)

using (i) and (ii),

$50x+75(52-x)=2975\\50x+3900-75x=2975\\25x=925\\x=37$

$y=52-x=52-37=15$

7 0

3 years ago

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Find q if p = -12 and the quotient p/q = -3.

s2008m [1.1K]

The quotient to p/q = -3 is 4

3 0

3 years ago

HELP PLZ WILL GIVE BRAINLIEST! find the arrithmetic means in the given sequence<br> -3,?,?,?,93

pav-90 [236]

Answer:

Step-by-step explanation:

The standard form of an arithmetic sequence is

aₙ = a₁ + d(n - 1)

where aₙ is the number of the term in the sequence (in order from first term where n = 1, to second term where n = 2, to third term where n = 3, etc) a₁ is the the first term in the sequence, and d is the arithmetic difference or means. This is what we are looking to solve for.

In our sequence we have the first term, -3 (where n = 1) and the fifth term, 93 (where n = 5). If we fill in what we have, the only unknown is d, our arithmetic difference (means) between each number in the sequence.

Because we have the fifth term, we can write our standard form to fit our needs:

a₅ = a₁ + d(n-1). Therefore,

93 = -3 + d(5 - 1) and

93 = -3 + d(4) so

96 = 4d and

d = 24

Our arithmetic difference (means) is 24. Let's test it on a few values of n. Let's look for the second, third, and 4th terms, and then try it out for n = 5 to make sure the 5th term, using our arithmetic sequence with d = 24 works and we do, in fact, find the fifth term to be 93.

Testing n = 2

a₂ = -3 + 24(2 - 1) so

a₂ = -3 + 24(1) and

a₂ = 21. Second term is 21 (Notice that difference between -3 and 21 is 24)

Testing n = 3

a₃ = -3 + 24(3 - 1) so

a₃ = -3 + 24(2) and

a₃ = 48 - 3 and

a₃ = 45 (Notice the difference between 21 and 45 is 24)

Testing n = 4

a₄ = -3 + 24(4 - 1) so

a₄ = -3 + 24(3) and

a₄ = 72 - 3 and

a₄ = 69 (Notice the difference between 45 and 69 is 24)

Testing n = 5 (and it better come out as 93 or we did something wrong!)

a₅ = -3 + 24(5 - 1) and

a₅ = -3 + 24(4) so

a₅ = 96 - 3 so

a₅ = 93 (Phew!) ; )

5 0

3 years ago

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