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3 years ago

What is 10(b + 4c) expanded? (using the distributive property)

Mathematics

1 answer:

jeka943 years ago

8 0

Answer:

10b+40c

Step-by-step explanation:

10(b + 4c) you have to multiply 10 by each member

10b+40c

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Find ????⋅ ???? if |????|=3 , |????|=9 , and the angle between ???? and ???? is π2 radians.

mrs_skeptik [129]

Answer:

$a{\cdot}b=0$

Step-by-step explanation:

It is given that,

Magnitude of a A, $|A|=3$

magnitude of B, $|B|=9$

The angle betwern a and b is $\dfrac{\pi}{2}\ rad=90^{\circ}$

Dot product,

$a{\cdot} b=|a||b|\ \cos\theta\\\\a{\cdot} b=3\times 9\times \ \cos(90)\\\\a{\cdot} b=0$

So, a.b is equal to 0.

5 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

Write the missing power of 10 in each equation.

Mrac [35]

1. 10 or 10 to the first power
2. 10000 or 10 to the fourth power
3. 100 or 10 to the second power
4. 1000 or 10 to the third power

7 0

2 years ago

The length of a rectangular map is 15 inches and the perimeter is 50 inches. Find the width.

jonny [76]

P = 2(L + W)
P = 50
L = 15

50 = 2(15 + W)
50 = 30 + 2W
50 - 30 = 2W
20 = 2W
20/2 = W
10 = W.....so the width is 10 inches

3 0

2 years ago

Read 2 more answers

I really do need help solving this equation

strojnjashka [21]

Answer:

Step-by-step explanation:

3/5 = 0.6

75% = .75

0.8, 0.75, 0.6, 0.56

8 0

2 years ago