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3 years ago

Solve for x in the figure below. Show your work.

Mathematics

2 answers:

ololo11 [35]3 years ago

7 0

Answer:

Step-by-step explanation:

The square represents a right angle, 90 degrees, so all you do is subtract the 22 from 90. which is 68. 68 then is subtracted by 11, and you're left with 57. You then divide 57 by 3, because you have 3 x and you want to find x. And you get 19

Bad White [126]3 years ago

3 0

X equals 19. Detailed calculation is provided in the attachment.

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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

PLZ ANSWER QUICKLY Write an equation that represents the line. Use exact numbers.

denpristay [2]

.......................

5 0

3 years ago

Two sides of a triangle are as follows: 2 centimeters and 5 centimeters. Describe the possible lengths of the third side

Elden [556K]

Answer:

3cm < Third side < 7cm

Thus third side can take any value between 3cm and 7 cm

(note: excluding 3 cm and 7 cm)

If the value are integral then possible values of third side are

4cm, 5cm,6cm

Step-by-step explanation:

This question can be solved using given by Triangle Inequality Theorem Given below.

Sum of two sides is always greater than value of third side
Difference of two sides is always less than value of third side

Given two sides are 2cm, 5cm

Sum of two sides = (2+5)cm = 7 cm

Difference of two sides = (5-2) = 3 cm

Let the third side be X

thus according to Triangle Inequality Theorem

X < Sum of two sides of given triangle

X < 7cm -----1

X > Difference of two sides

X > 3cm ----1

combining expression 1 and 2 we have

3cm < X < 7cm

Thus third side can take any value between 3cm and 7 cm

(note: excluding 3 cm and 7 cm)

If the value are integral then possible values are

4c, 5cm,6c

7 0

3 years ago

Order the decimals in each from least to greatest .178 .084 .009 .2

nignag [31]

.009 , .084, .178, .2

3 0

3 years ago

Read 2 more answers

Find the smallest natural number that is a multiple of 45 and where all of its digits are zeros and ones.

Sergio039 [100]

Answer:

1111111110

Step-by-step explanation:

45 is 9, and 5.

9 divisibility rule: Digits have to add up to 9.

We know this has to be 1's and 0's.

So there has to be 9 1's.

111111111.

5 divisibility rule: Last digit has to be 0 or 5.

1111111110 will be our final answer.

Wait- let's check if it's divisible. Using a calculator, this determines it does work.

Enjoy.

6 0

3 years ago