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3 years ago

Convert 6 liters to quarts

Mathematics

2 answers:

maksim [4K]3 years ago

4 0

Answer:

6.34013 quarts

Step-by-step explanation:

i looked it up

stellarik [79]3 years ago

4 0

6 liters makes exactly 6.34013 quarts

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How do I solve: 2 sin (2x) - 2 sin x + 2√3 cos x - √3 = 0

ziro4ka [17]

Answer:

$\displaystyle x = \frac{\pi}{3} +k\, \pi$ or $\displaystyle x =- \frac{\pi}{3} +2\,k\, \pi$ , where $k$ is an integer.

There are three such angles between $0$ and $2\pi$ : $\displaystyle \frac{\pi}{3}$ , $\displaystyle \frac{2\, \pi}{3}$ , and $\displaystyle \frac{4\,\pi}{3}$ .

Step-by-step explanation:

By the double angle identity of sines:

$\sin(2\, x) = 2\, \sin x \cdot \cos x$ .

Rewrite the original equation with this identity:

$2\, (2\, \sin x \cdot \cos x) - 2\, \sin x + 2\sqrt{3}\, \cos x - \sqrt{3} = 0$ .

Note, that $2\, (2\, \sin x \cdot \cos x)$ and $(-2\, \sin x)$ share the common factor $(2\, \sin x)$ . On the other hand, $2\sqrt{3}\, \cos x$ and $(-\sqrt{3})$ share the common factor $\sqrt[3}$ . Combine these terms pairwise using the two common factors:

$(2\, \sin x) \cdot (2\, \cos x - 1) + \left(\sqrt{3}\right)\, (2\, \cos x - 1) = 0$ .

Note the new common factor $(2\, \cos x - 1)$ . Therefore:

$\left(2\, \sin x + \sqrt{3}\right) \cdot (2\, \cos x - 1) = 0$ .

This equation holds as long as either $\left(2\, \sin x + \sqrt{3}\right)$ or $(2\, \cos x - 1)$ is zero. Let $k$ be an integer. Accordingly:

$\displaystyle \sin x = -\frac{\sqrt{3}}{2}$ , which corresponds to $\displaystyle x = -\frac{\pi}{3} + 2\, k\, \pi$ and $\displaystyle x = -\frac{2\, \pi}{3} + 2\, k\, \pi$ .
$\displaystyle \cos x = \frac{1}{2}$ , which corresponds to $\displaystyle x = \frac{\pi}{3} + 2\, k \, \pi$ and $\displaystyle x = -\frac{\pi}{3} + 2\, k \, \pi$ .

Any $x$ that fits into at least one of these patterns will satisfy the equation. These pattern can be further combined:

$\displaystyle x = \frac{\pi}{3} + k \, \pi$ (from $\displaystyle x = -\frac{2\,\pi}{3} + 2\, k\, \pi$ and $\displaystyle x = \frac{\pi}{3} + 2\, k \, \pi$ , combined,) as well as
$\displaystyle x =- \frac{\pi}{3} +2\,k\, \pi$ .

7 0

3 years ago

A total of 428 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student t

aalyn [17]

321 adult tickets were sold use the formula to solve
108 student tickets were sold

6 0

3 years ago

PLEASE NEED CORRECT ANSWERS NOW1 WILL MARK BRAINLIEST!!!!!!!!!!!

Natasha_Volkova [10]

Answer:

7.7ft

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

How do I find out the perimeter of a L shape polygon

antoniya [11.8K]

Treat the polygon like to different polygons. In an L it most likely with be a square and a rectangle that you will be taking apart from the polygon

5 0

3 years ago

HI CAN SOMEONE PLZ HELP ME I HAVE NO CLUE HOW TO DO THIS SOS. THANKS SM!!!❤️❤️❤️

Kitty [74]

Problem 1)

This question is incomplete. It asks us to find something, but doesn't say what to find. It's literally blank after the word "find" which suggests your teacher made a typo. Please get back to me on this. Thanks.

===================================

Problem 2)

Angles GAR and GAT are supplementary because they are a linear pair. They form a straight angle. So we add up the expressions of x for each of these angles, solve for x, and use this to find angle GAR.

(angle GAR) + (angle GAT) = 180

(5x) + (3x+4) = 180

8x+4 = 180

8x+4-4 = 180-4

8x = 176

8x/8 = 176/8

x = 22

Note: now that I reached this point I realize that this might be the answer to problem 1; however, I'm not 100% sure because of the incomplete problem.

Use this x value to find angle GAR

angle GAR = 5*x

angle GAR = 5*22

angle GAR = 110

Unfortunately this answer isn't listed. I'm thinking your teacher made another typo.

===================================

Problem 3)

Answer: angle GAR and angle ABQ are corresponding angles.

Thankfully this answer is listed. Corresponding angles are angles that are on the same side of the transversal line and they are either both above or below the parallel lines they are next to. In this case, they are both above the parallel line counerparts.

===================================

Problem 4)

Corresponding angles are congruent as long as we have a set of parallel lines. So that means angle ABQ is equal to angle GAR. So angle ABQ is also 110 degrees

===================================

Problem 5)

angle BAT = angle GAR, because they are vertical angles

angle BAT = 110

angle BAT = (angle BAD) + (angle DAT)

(angle BAD) + (angle DAT) = angle BAT

(100) + (angle DAT) = 110

angle DAT = 110-100

angle DAT = 10

angle ADB = angle DAT, because they are alternate interior angles

angle ADB = 10

--------

Final Answer: 10 degrees

5 0

4 years ago