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3 years ago

What is x? A. 0.75 B. 1.25 C. 1.67 D. 1.33

Mathematics

1 answer:

Nikolay [14]3 years ago

3 0

Answer:

D. 1.33

Step-by-step explanation:

$\because \: x = tan (\theta) \\ \\ tan (\theta) = \frac{4}{3} \\ \\ tan (\theta) = 1.33 \\ \\ \implies \: x = 1.33$

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A top-loading washing machine has a cylindrical basket that rotates about a vertical axis. The basket of one such machine starts

damaskus [11]

Answer:

$n_{tot}=44rev$

Step-by-step explanation:

In order to solve this problem we can make use of the following formula:

$\theta=(\frac{\omega_{f}+\omega_{0}}{2})t$

where θ is the total angle the basket has turned, ω is the angular velocity and t is the time.

Generally theta is written in radians and omega is written in radians per second. Now, since the revolutions are directly related to the radians and they want us to write our answer in revolutions, we can directly use the provided speeds in the formula, so we can rewrite it as:

$n=(\frac{f_{f}+f_{0}}{2})t$

where n represents the number of revolutions and f is the frequency at which the basket is turning.

The movement of the cylindrial basket can be split in two stages, when it accelerates and when it decelerates. So let's analye the first stage:

$n=(\frac{4rev/s+0}{2})(9s)=18rev$

and now let's analyze the second stage, where it decelerates, so we get:

$n=(\frac{0rev/s+4rev/s}{2})(13s)=26rev$

So now that we know how many revolutions the cylindrical basket will take as it accelerates and as it decelerates we can add them to get:

n=18rev+26rev=44rev

So the basket will turn a total of 44 revolutions during this 22s interval.

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2 years ago

What is the value of the sum of all the terms of the geometric series 300, 60, 12, …?

ruslelena [56]

<h3>Answer: 375</h3>

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

Work Shown:

a = 300 = first term

r = 60/300 = 0.2 = common ratio

We multiply each term by 0.2, aka 1/5, to get the next term.

Since -1 < r < 1 is true, we can use the infinite geometric sum formula below

S = a/(1-r)

S = 300/(1-0.2)

S = 300/0.8

S = 375

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As a sort of "check", we can add up partial sums like so

300+60 = 360
300+60+12 = 360+12 = 372
300+60+12+2.4 = 372+2.4 = 374.4
300+60+12+2.4+0.48 = 374.4+0.48 = 374.88

and so on. The idea is that each time we add on a new term, we should be getting closer and closer to 375. I put "check" in quotation marks because it's probably not the rigorous of checks possible. But it may give a good idea of what's going on.

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Side note: If the common ratio r was either r < -1 or r > 1, then the terms we add on would get larger and larger. This would mean we don't approach a single finite value with the infinite sum.

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2 years ago