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seropon [69]
3 years ago
8

Clare is paid $90 for 18,000 seconds of work. At this rate, how many seconds does it take for her to earn 25 cents? It would tak

e Clare seconds to earn a quarter.
Mathematics
1 answer:
Anastaziya [24]3 years ago
5 0

Answer: 50 seconds

Step-by-step explanation:

From the question, we are informed that Clare is paid $90 for 18,000 seconds of work. This means that for Clare to get $1, she'll work for (18000/90) = 200 seconds. From the calculation $1 = 200 seconds

We should note that 100 cents = $1, therefore 25 cents = 25/100 = $0.25.

The seconds that it will take for her to earn 25 cents will be:

= 200 × 0.25

= 50 seconds

Therefore, it'll take 50 seconds for her to earn 25 cent.

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Simplify. What is your answer 8x + 9d + 3x -5d
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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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  • \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:

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  • \displaystyle x =- \frac{\pi}{3} +2\,k\, \pi.
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3 years ago
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