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stealth61 [152]
3 years ago
7

A graduated cylinder is filled with 36\pi36π36, pi cm^3 3 start superscript, 3, end superscript of liquid. The liquid is poured

into a different cylinder that has a radius of 333 cm. What will the height of the liquid be in the new cylinder?
Mathematics
1 answer:
barxatty [35]3 years ago
8 0
The height will be 4 cm.

Explanation
<u />The volume of a cylinder is given by the formula V=πr²h.  For a volume of 36π cm³ and a radius of 3 cm,

36π = π(3²)h
36π = 9πh

Divide both sides by 9π:
36π/9π = 9πh/9π
4 = h
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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:

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

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7 0
3 years ago
Step 3: Multiply by the scalar (1 over the determinant): Aâ’1 = a11 a12 a21 a22 a11 = a12 = a21 = a22 =
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Answer:

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