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Mandarinka [93]

2 years ago

10

Draw a number line to show that 2/8 and 1/4 are equivalent fraction

1 answer:

solniwko [45]2 years ago

8 0

1/4 2/8 3/12 4/16 5/20 6/24

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600 millimeters of rain fell in 30 minutes what is the unit rate for millimeters per minute

sleet_krkn [62]

600 mm of rain / 30 min = 50 mm of rain per minute

3 0

3 years ago

PLZ HELP ILL GIVE BRAINLIEST I HAVE AN F IN MATH

kumpel [21]

the answer is 144,36,9

5 0

2 years ago

What is the antiderivative of 3x/((x-1)^2)

Maslowich

Answer:

$\int \:3\cdot \frac{x}{\left(x-1\right)^2}dx=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)+C$

Step-by-step explanation:

Given

$\int \:\:3\cdot \frac{x}{\left(x-1\right)^2}dx$

$\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx$

$=3\cdot \int \frac{x}{\left(x-1\right)^2}dx$

$\mathrm{Apply\:u-substitution:}\:u=x-1$

$=3\cdot \int \frac{u+1}{u^2}du$

$\mathrm{Expand}\:\frac{u+1}{u^2}:\quad \frac{1}{u}+\frac{1}{u^2}$

$=3\cdot \int \frac{1}{u}+\frac{1}{u^2}du$

$\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx$

$=3\left(\int \frac{1}{u}du+\int \frac{1}{u^2}du\right)$

as

$\int \frac{1}{u}du=\ln \left|u\right|$ ∵ $\mathrm{Use\:the\:common\:integral}:\quad \int \frac{1}{u}du=\ln \left(\left|u\right|\right)$

$\int \frac{1}{u^2}du=-\frac{1}{u}$ ∵ $\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1$

so

$=3\left(\ln \left|u\right|-\frac{1}{u}\right)$

$\mathrm{Substitute\:back}\:u=x-1$

$=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)$

$\mathrm{Add\:a\:constant\:to\:the\:solution}$

$=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)+C$

Therefore,

$\int \:3\cdot \frac{x}{\left(x-1\right)^2}dx=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)+C$

4 0

3 years ago

Find the value of x in isosceles trapezoid ABCD<br> Given AC=3x-16 and BD=10x-86

Nastasia [14]

X = 10
(WORK SHOWN BELOW)

7 0

2 years ago

M ∠4 = 2x°, m ∠2 = (4/3)x°, m ∠3 = 20°, find x.

anygoal [31]

The answer is c, b/c...

20+(4/3)x=2x

-(4/3)x -(4/3)x

20=(2/3)x

20/(2/3)=(2/3)x/(2/3)

A: 30=x

7 0

3 years ago