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Roman55 [17]
3 years ago
8

25 penalties decreased by 32% is __penalties.

Mathematics
2 answers:
d1i1m1o1n [39]3 years ago
8 0
The answer is 8 becuase 25 time .32 becuase 32%=.32
jekas [21]3 years ago
3 0
If you decrease something by 32%, you are left with 68%

0.68(25) = 17
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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)}


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\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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Answer:

The correct answer is B buddy.

I hope i have been useful buddy.

good luck ♥️♥️♥️♥️♥️.

3 0
3 years ago
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