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natali 33 [55]
2 years ago
12

The equation is. -0.5p-2=p how do I solve this?? And show my work

Mathematics
1 answer:
ASHA 777 [7]2 years ago
3 0
-0.5p-2=p

Add 0.5 to both sides which would equal
-2=1.5p

Then divide -2 by 1.5p
P=-1.33333333

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How to integrate 1/(1-y)^2
Akimi4 [234]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/866966

_______________


Evaluate the indefinite integral:

\mathsf{\displaystyle\int\!\dfrac{1}{(1-y)^2}\,dy}\\\\\\ =\mathsf{\displaystyle\int\!\dfrac{-1}{(1-y)^2}\cdot (-1)\,dy}\\\\\\ =\mathsf{\displaystyle- \int\!(1-y)^{-2}\cdot (-1)\,dy\qquad\quad(i)}


Substitution:

\begin{array}{lcl} \mathsf{1-y=u}&\quad\Rightarrow\quad&\mathsf{y=1-u}\\\\ &&\mathsf{dy=-1\,du} \end{array}


So the integral \mathsf{(i)} becomes

=\mathsf{\displaystyle -\int\! u^{-2}\,du}\\\\\\ =\mathsf{-\,\dfrac{u^{-2+1}}{-2+1}+C}\\\\\\ =\mathsf{-\,\dfrac{u^{-1}}{-1}+C}\\\\\\ =\mathsf{u^{-1}+C}\\\\\\ =\mathsf{\dfrac{1}{u}+C}

=\mathsf{\dfrac{1}{1-y}+C}\\\\\\\ \therefore~~\boxed{\begin{array}{c}\mathsf{\displaystyle\int\!\dfrac{1}{(1-y)^2}\,dy=\dfrac{1}{1-y}+C} \end{array}}\qquad\quad\checkmark


I hope this helps. =)


Tags:  <em>indefinite integral fraction rational substitution power differential calculus</em>

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