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2 years ago

HELP PICTURE IS SHOWN

Mathematics

1 answer:

Vedmedyk [2.9K]2 years ago

4 0

The answer is c) 45 times PI cubed.

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Find all solutions of each equation on the interval 0 ≤ x < 2π.

Korvikt [17]

Answer:

$x = 0$ or $x = \pi$ .

Step-by-step explanation:

How are tangents and secants related to sines and cosines?

$\displaystyle \tan{x} = \frac{\sin{x}}{\cos{x}}$ .

$\displaystyle \sec{x} = \frac{1}{\cos{x}}$ .

Sticking to either cosine or sine might help simplify the calculation. By the Pythagorean Theorem, $\sin^{2}{x} = 1 - \cos^{2}{x}$ . Therefore, for the square of tangents,

$\displaystyle \tan^{2}{x} = \frac{\sin^{2}{x}}{\cos^{2}{x}} = \frac{1 - \cos^{2}{x}}{\cos^{2}{x}}$ .

This equation will thus become:

$\displaystyle \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} \cdot \frac{1}{\cos^{2}{x}} + \frac{2}{\cos^{2}{x}} - \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} = 2$ .

To simplify the calculations, replace all $\cos^{2}{x}$ with another variable. For example, let $u = \cos^{2}{x}$ . Keep in mind that $0 \le \cos^{2}{x} \le 1 \implies 0 \le u \le 1$ .

$\displaystyle \frac{1 - u}{u^{2}} + \frac{2}{u} - \frac{1 - u}{u} = 2$ .

$\displaystyle \frac{(1 - u) + u - u \cdot (1- u)}{u^{2}} = 2$ .

Solve this equation for $u$ :

$\displaystyle \frac{u^{2} + 1}{u^{2}} = 2$ .

$u^{2} + 1 = 2 u^{2}$ .

$u^{2} = 1$ .

Given that $0 \le u \le 1$ , $u = 1$ is the only possible solution.

$\cos^{2}{x} = 1$ ,

$x = k \pi$ , where $k\in \mathbb{Z}$ (i.e., $k$ is an integer.)

Given that $0 \le x < 2\pi$ ,

$0 \le k$ .

$k = 0$ or $k = 1$ . Accordingly,

$x = 0$ or $x = \pi$ .

8 0

2 years ago

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Rita started the day with r apps. then she deleted 5 apps and still had twice as many apps as Cora has. write an equation that r

lianna [129]

Answer:

Rita had r apps as the start of the day

After she deleted 5 apps,

equation for apps of cora = (r-5)

Equation for apps of Rita = 2 (r-5)

Step-by-step explanation:

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2 years ago

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Cottontail rabbits are found in California. Recently, the cottontail's predator, the coyote, has been disappearing due to human

azamat

Answer:

Step-by-step explanation:

my cat ate my dog s

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2 years ago

The first five terms of a sequence are 2, 5/3, 3/2, 7/5 and 4/3. what is the explicit formula?

katen-ka-za [31]

Answer:

an = (n+3)/(n+1)

Step-by-step explanation:

The sequence can be written as ...

4/2, 5/3, 6/4, 7/5, 8/6, ...

where the first numerator is n+3 and the first denominator is n+1. Each numerator and denominator increase by 1 from term to term, so the explicit formula can be written

an = (n+3)/(n+1)

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What are2 continents that are made completely out of desert??

laiz [17]

Antarctica and asia

I hope this helps

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