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3 years ago

Which of the following are solutions to the equation below?

Mathematics

1 answer:

lana66690 [7]3 years ago

8 0

Answer:

F. - 4

Hope it help

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Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and then evaluate the integra

worty [1.4K]

Answer:

$x^2+4x -\frac{1}{2} lnx + \frac{2}{13} ln(x-2) + C$

Step-by-step explanation:

Given the integrand $\int\limits{\dfrac{2x^3 - 2x + 1}{x^2-2x} } \, dx$ , before evaluating the integral function, we will need to simplify the function first by applying long division as shown in the attachment.

Hence the partial form of the function $\dfrac{2x^3 - 2x + 1}{x^2-2x} } = 2x+4 + \frac{6x+1}{x^2-2x}$

Integrating its partial sum

$\int\limits \dfrac{2x^3 - 2x + 1}{x^2-2x} }dx = \int\limits (2x+4 + \frac{6x+1}{x^2-2x})\ dx\\\\= \int\limits {2x} \, dx + \int\limits {4} \, dx + \int\limits {\frac{6x+1}{x^2-2x} \, dx\\ = \frac{2x^2}{2}+4x -\frac{1}{2} \int\limits{\frac{1}{x} } \, dx + \frac{2}{13} \int\limits{\frac{1}{x-2} } \, dx$

$= \frac{2x^2}{2}+4x -\frac{1}{2} lnx + \frac{2}{13} ln(x-2) + C$

$= x^2+4x -\frac{1}{2} lnx + \frac{2}{13} ln(x-2) + C$

NB: Find the partial sum calculation also in the attachment.

5 0

3 years ago

Karen is riding her bike at 4 miles per hour she wants to show this on a graph what should she draw

astraxan [27]

Graph needs to be labeled. I labeled it as shown on picture. It also needs a title. The title can be up to you. :) you can title it “Karen riding her bike”

6 0

3 years ago

What is greater three sets of 5-2 or two sets of 2+3? Draw diagrams

Inga [223]

Two sets of 2+3 is greater

8 0

3 years ago

Two trains leave two different stations 300 km apart; the first starts at noon and the second at 12 15 h. Travelling on parallel

alexgriva [62]

Answer:

See below

Step-by-step explanation:

From noon to 1500 is three hours

train A then travels 3x where x = speed in km/hr

train B only travels for 2.45 hours and covers

2.45 ( x + 15) where x + 15 is its speed in km/hr

these two values sum to the 300 km distance

3x + 2.45 ( x + 15) = 300

3x + 2.45 x + 36.75 = 300

x = 48.3 km/hr x+15= 63.3 km / hr

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2 years ago

Which number is halfway between 1/2 and 2/3 ?

MariettaO [177]

For example, 3/5.

3/5 = 0.6.

1/2 = 0.5
2/3 = 0.6666

0.5 -- 0.6 -- 0.66666666

8 0

4 years ago