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Contact [7]
4 years ago
13

Lim as x approaches 2pi/3 from the right of csc x, solve by substituting csc with sin

Mathematics
1 answer:
Zielflug [23.3K]4 years ago
5 0
\bf csc(\theta)=\cfrac{1}{sin(\theta)}
\\\\
-------------------------------\\\\
\lim\limits_{x\to \frac{2\pi }{3}^+}~csc(x)\implies \lim\limits_{x\to \frac{2\pi }{3}^+}~\cfrac{1}{sin(x)}\implies \cfrac{1}{sin\left( \frac{2\pi }{3} \right)}\implies \cfrac{1}{\frac{\sqrt{3}}{2}}\implies \cfrac{\frac{1}{1}}{\frac{\sqrt{3}}{2}}

\bf -------------------------------\\\\
\cfrac{\frac{a}{b}}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\qquad thus\\\\
-------------------------------\\\\
\cfrac{1}{1}\cdot \cfrac{2}{\sqrt{3}}\implies \cfrac{1\cdot 2}{1\cdot \sqrt{3}}\implies \cfrac{2}{\sqrt{3}}
\\\\\\
\textit{and now, rationalizing the denominator, we get}\implies \cfrac{2\sqrt{3}}{3}
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If standard deviation of a given data is 5 and mean is 50 then coefficient of variation (C.V) is equal to *
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Answer:

10

Step-by-step explanation:

Coefficient of variation is a measure of dispersion, showing the variability of data in relation to the mean.

The Coefficient of variation compares the degree of variation between data points. The coefficient of variation is the ratio of mean to standard deviation. It is given by the formula:

Coefficient of variation = mean / standard deviation

Coefficient of variation = 50 / 5

Coefficient of variation = 10

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3 years ago
Water flows into a tank according to the rate F of t equals the quotient of 6 plus t and the quantity 1 plus t, and at the same
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Answer:

Step-by-step explanation:

The complete question is

Water flows into a tank according to the rate F(t)= (t+6)/(1+t), and at the same time empties out at the rate E(t)= (ln(t+2))/(t+1), with both F(t) and E(t) measured in gallons per minute. How much water, to the nearest galllon, is in the tank at time t=10 minutes.

Let C(t) be the amount of water in the tank at time t. We now that the rate of change of the tank is given by

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Unfortunately, the integral \int \frac{\ln(t+2)}{(t+1)} dt cannot be expressed using fundamental functions. So, the problem cannot have an specific function (if you are willing to know the complete answer, the integral of this function uses the  polylogarithm function with n=2).

Since you want the exact amount of water at time, you need to give C a value, that is, you need to know an initial condition for the problem. This means, you need to know the amount of water in the tank at time 0

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3 years ago
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hram777 [196]

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Step-by-step explanation:

15 min is 1/4 hr.

Working an add'l 1/4 hr brings the employee additional pay:

($14/hr)(1/4  hr)  = $7/2, or $3.50

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Do you mean y? if you did it should be 1/6 or 1.666666 repeating.

Step-by-step explanation:

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