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Anika [276]
3 years ago
15

there are 50 people in a class out of this number 1/10 speak French only and 4/5 of the remainder speak both French and English

if the rest speak English only find number of students who speak both English and French , only English​
Mathematics
2 answers:
Flura [38]3 years ago
7 0

Answer:

36 students speak both english and french

14 students speak only english

Shtirlitz [24]3 years ago
4 0

Step-by-step explanation:

there are 50 people in a class out of this number 1/10 speak French only and 4/5 of the reminder speak both and English if the rest speak English only find number of students who speak both English and French only

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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{\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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