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1 year ago

Help me with this for 50 points.

Mathematics

1 answer:

inn [45]1 year ago

6 0

Answer:

1/2 or 1:2

Step-by-step explanation:

3 circles to 6 squares

3/6 simplified is 1/2

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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

Read 2 more answers

What are the common multipls of 2 and 3 between 2 and 25

Colt1911 [192]

Answer:

6, 12, 18, and 24

Step-by-step explanation:

Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24. Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24. Common multiples of 2 and 3 include 6, 12, 18, and 24.

4 0

3 years ago

What factors of 48 are multiples of 4

docker41 [41]

4, 8, 12, 16, and 24

8 0

3 years ago

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Given m||n, find the value of x.

USPshnik [31]

Answer:

57 degrees

Step-by-step explanation:

Same side interior angles are supplementary which means they both equal 180 degrees.

3 0

2 years ago

The rule for a pattern is ''take half the number to get the next number.'' the first number in the pattern is 16 what is the nex

vfiekz [6]

Answer:

Step-by-step explanation:

Let the next number be x

'taking half the number to get the next number. is expressed as;

1/2 of 16 = x

x = 1/2 *16

x = 16/2

x = 8

hence the next number will be 8

7 0

2 years ago