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Delicious77 [7]
3 years ago
10

June made 18 liters of fruit punch,one third is orange juice.and 4 liters of pinespple juice.the rest is club soda.how may liter

s if club soda use
Mathematics
1 answer:
Katyanochek1 [597]3 years ago
6 0
You have 8 liters of club soda
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Answer:

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Step-by-step explanation:

To reflect the rectangle over the x-axis, think of it as flipping it over the x-axis. On the graph, count the units from V to S, it's 6 units. So, from the x-axis, count 6 units up from V. S would lie on -6, 6. Do the same for W to T. T would lie on (2, 6). The remaining coordinates U and V don't change because it is <em>already </em>on the x-axis. <em> </em>

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If you're using the app, try seeing this answer through your browser:  brainly.com/question/2822772

_______________


Evaluate the indefinite integral:

\mathsf{\displaystyle\int\! \frac{cos\,x}{sin^2\,x}\,dx}\\\\\\&#10;=\mathsf{\displaystyle\int\! \frac{1}{(sin\,x)^2}\cdot cos\,x\,dx\qquad\quad(i)}


Make the following substitution:

\mathsf{sin\,x=u\quad\Rightarrow\quad cos\,x\,dx=du}


and then, the integral (i) becomes

=\mathsf{\displaystyle\int\! \frac{1}{u^2}\,du}\\\\\\&#10;=\mathsf{\displaystyle\int\! u^{-2}\,du}


Integrate it by applying the power rule:

\mathsf{=\dfrac{u^{-2+1}}{-2+1}+C}\\\\\\&#10;\mathsf{=\dfrac{u^{-1}}{-1}+C}\\\\\\&#10;\mathsf{=-\,\dfrac{1}{u}+C}


Now, substitute back for u = sin x, so the result is given in terms of x:

\mathsf{=-\,\dfrac{1}{sin\,x}+C}\\\\\\&#10;\mathsf{=-\,csc\,x+C}


\therefore~~\boxed{\begin{array}{c}\mathsf{\displaystyle\int\! \frac{cos\,x}{sin^2\,x}\,dx=-\,csc\,x+C} \end{array}}\qquad\quad\checkmark


I hope this helps. =)


Tags:  <em>indefinite integral substitution trigonometric trig function sine cosine cosecant sin cos csc differential integral calculus</em>

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