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Sergeu [11.5K]
3 years ago
9

–19w + 11 = –17w − 19 w= Please help, will mark brainliest to correct answer!

Mathematics
1 answer:
pychu [463]3 years ago
6 0

Answer:

w = 15

Step-by-step explanation:

We have an expression and are asked to solve for w.

-19w + 11 = -17w - 19

Subtract 11 from both sides :

-19w = -17w - 30

Add 17w to both sides :

-2w = -30

Divide -2 from both sides to isolate w :

w = 15

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Evaluate the integral, show all steps please!
zalisa [80]

Answer:

\dfrac{3}{2} \ln |x-4| - \dfrac{1}{2} \ln |x+2| + \text{C}

Step-by-step explanation:

<u>Fundamental Theorem of Calculus</u>

\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

\displaystyle \int \dfrac{x+5}{(x-4)(x+2)}\:\:\text{d}x

Take <u>partial fractions</u> of the given fraction by writing out the fraction as an <u>identity</u>:

\begin{aligned}\dfrac{x+5}{(x-4)(x+2)} & \equiv \dfrac{A}{x-4}+\dfrac{B}{x+2}\\\\\implies \dfrac{x+5}{(x-4)(x+2)} & \equiv \dfrac{A(x+2)}{(x-4)(x+2)}+\dfrac{B(x-4)}{(x-4)(x+2)}\\\\\implies x+5 & \equiv A(x+2)+B(x-4)\end{aligned}

Calculate the values of A and B using substitution:

\textsf{when }x=4 \implies 9 = A(6)+B(0) \implies A=\dfrac{3}{2}

\textsf{when }x=-2 \implies 3 = A(0)+B(-6) \implies B=-\dfrac{1}{2}

Substitute the found values of A and B:

\displaystyle \int \dfrac{x+5}{(x-4)(x+2)}\:\:\text{d}x = \int \dfrac{3}{2(x-4)}-\dfrac{1}{2(x+2)}\:\:\text{d}x

\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ax^n\:\text{d}x=a \int x^n \:\text{d}x$\end{minipage}}

If the terms are multiplied by constants, take them outside the integral:

\implies \displaystyle \dfrac{3}{2} \int \dfrac{1}{x-4}- \dfrac{1}{2} \int \dfrac{1}{x+2}\:\:\text{d}x

\boxed{\begin{minipage}{5 cm}\underline{Integrating}\\\\$\displaystyle \int \dfrac{f'(x)}{f(x)}\:\text{d}x=\ln |f(x)| \:\:(+\text{C})$\end{minipage}}

\implies \dfrac{3}{2} \ln |x-4| - \dfrac{1}{2} \ln |x+2| + \text{C}

Learn more about integration here:

brainly.com/question/27805589

brainly.com/question/28155016

4 0
2 years ago
What is the y intercept of 2y-5x=16
scoundrel [369]
To find y-intercepts, you substitute in 0 for X

2y-5x=16
2y-5(0)=16
2y-0=16
2y=16
Y=8

So the y-intercept is (0,8)
7 0
4 years ago
Read 2 more answers
Hey, guys I really need help with this sooo... if one of you smart people can help me, please Its for 8th grade math
Licemer1 [7]

Answer:

(0,-1)

Step-by-step explanation:

x point is 6, and the translation is x - 6

6 - 6 = 0

x = 0

y point is 0 and translation is y - 1

0 - 1 = -1

y = -1

Coordinates are (0,-1)

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

4 0
3 years ago
Read 2 more answers
Which expression is equivalent? Please see pictures attached!
VMariaS [17]

hey, u didn’t rlly attach anything :/

5 0
3 years ago
Please help my grade is a 68 i need a 70 at least
aleksklad [387]

Answer:

10s²-6s+9

Step-by-step explanation:

C = -3 + 5s²

B = -2s + 5

2(-3 + 5s²) = -6 + 10s²

3(-2s + 5) = -6s + 15

10s² - 6s + 9

8 0
3 years ago
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