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3 years ago

5 less than twice a number

Mathematics

2 answers:

Dmitry [639]3 years ago

6 0

Answer:

2*x - 5

Step-by-step explanation:

Twice a number = 2 multiplied by some number (call it "x").

5 less than implies to subtract 5 from that "twice a number" result.

TiliK225 [7]3 years ago

3 0

Answer:

5 less than twice a number is 9. So, twice a number is 14.

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3 years ago

Amy is scuba diving. She starts at – 15.5 m relative to the ocean surface. She swims

solniwko [45]

Answer:

-9.85

Step-by-step explanation:

-15.5 - 4.2 = -19.7

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2 years ago

How do i solve a triangles area

shusha [124]

Answer:

Area = 1/2 Base x height

Step-by-step explanation:

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6 0

3 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Maddy and Caitlin spend a certain amount of money from their money box each month to buy bracelet-making supplies.

fomenos

Solutions

We know that Function 1 shows a greater rate of change, because Maddy spends $20 each month and Caitlin spends $18.

Maddy spends 2 dollars more.

Therefore the correct answer is the last option.

8 0

3 years ago

Read 2 more answers