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3 years ago

This is very important

1 answer:

3 0

1. 1650 / 55 = 330 / 11 = 30
2. 5634 / 18 = 939 / 3 = 313
3. 6440 / 28 = 920 / 4 = 230
4. 5256 / 52 = 2628 / 26 = 1314 / 13 = 101.07
5. 1955 / 85 = 391 / 17 = 23

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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

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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>

3 0

3 years ago

WILL GIVE BRAINLIST PLEASE HELP

Harlamova29_29 [7]

Good evening ,

______

Answer:

12×11×10×9×8×7= 665 280 ways

___________________

Step-by-step explanation:

The first inquiry has 12 ways

The 2nd inquiry has 11 ways

The 3rd inquiry has 10 ways

The 4th inquiry has 9 ways

The 5th inquiry has 8 ways

The 6th inquiry has 7 ways

8 0

3 years ago

Sam can mow 2 lawns in 3/4 hour.

MrRa [10]

Answer:

5 lawns is the answer don't forget to mark as brainliest!

6 0

3 years ago

Look at the picture

gladu [14]

Answer:

Step-by-step explanation:

- π can be added to π to get a rational number

π + (-π) = 0

0 is a rational number

6 0

3 years ago

You pay $10 to play the following game of chance. there is a bag containing 12 balls: three are red, five are green, and the res

Bogdan [553]

Answer:

$ -2.08 expected to lose

Step-by-step explanation:

3 25.0% $15.00 $5.00 $1.25

5 41.7% $10.00 $- $-

4 33.3% $- $(10.00) $(3.33)

$(2.08) expected to lose

7 0

3 years ago