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4 years ago

I need help on this question plz

Mathematics

1 answer:

kramer4 years ago

6 0

90° clockwise will go from (x, y) to (y, -x)

180° counterclockwise and clockwise will go from (x, y) to (-x,-y)

270° clockwise will go from (x, y) to (-y, x)

1. (5 ,2) 90° will become (2, -5)

2. (5, 2) 180° will become (-5, -2)

3. (5, 2) 270° will become (-2, 5)

4. (-5, 2) 90° will become (2, 5)

5. (-5, 2) 180° will be come (5, -2)

6. (-5, 2) 270° will be come (-2, -5)

7. (-2, 5) 90° will become (-5, -2)

8. (5, -2) 180° will become (-5, 2)

Hope this helps! Mark as brainliest please! :)))

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How to integrate 1/(1-y)^2

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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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makkiz [27]

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tatiyna

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