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3 years ago

What is the value of (StartFraction 3 Over 10 EndFraction) cubed?

Mathematics

2 answers:

ad-work [718]3 years ago

6 0

Answer:

The answer is StartFraction 27 Over 1000 EndFraction or $\\ \frac{27}{1000}$

Step-by-step explanation:

We have here a fraction. In this case, the numerator and the denominator of the fraction must be cubed, that is, both, the numerator and the denominator must be raised to the same exponent, in this case 3 (cubed).

In general, for fractions, this is the general rule that we must to follow to raise some fraction to any exponent.

In the case concerning this question, we have

$\\ (\frac{3}{10})^3$

$\\ \frac{3^3}{10^3}$

$\\ \frac{3*3*3}{10*10*10}$

$\\ \frac{27}{1000}$

So, the value of $\\ (\frac{3}{10})^3 = \frac{27}{1000}$ .

Nostrana [21]3 years ago

4 0

Answer:

27/1000

Step-by-step explanation:

i just took the test

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Integrate 1 - x / x(x2 + 1) d x by partial fractions.

solniwko [45]

Answer:

$log x-\frac{log(x^{2}+1) }{2}-tan^{-1} x$

Step-by-step explanation:

step 1:- by using partial fractions

$[tex]\frac{1-x}{x(x^{2}+1) } =\frac{A(x^{2}+1)+(Bx+C)(x }{x(x^{2}+1) }$ ......(1)

step 2:-

solving on both sides

$1-x=A(x^{2} +1)+(Bx+C)x......(2)$

substitute x =0 value in equation (2)

1=A(1)+0

A=1

comparing x^2 co-efficient on both sides (in equation 2)

0 = A+B

0 = 1+B

B=-1

comparing x co-efficient on both sides (in equation 2)

-1 = C

step 3:-

substitute A,B,C values in equation (1)

now

$\\\int\limits^ {} \, \frac{1-x}{x(x^{2}+1) } d x =\int\limits^ {} \frac{1}{x} d x +\int\limits^ {} \frac{-x}{x^{2}+1 } d x -\int\limits \frac{1}{x^{2}+1 } d x$

by using integration formulas

i) by using $\int\limits \frac{1}{x} d x =log x+c........(a)\\\int\limits \frac{f^{1}(x) }{f(x)} d x= log(f(x)+c\\$ .....(b)

$\int\limits tan^{-1}x dx =\frac{1}{1+x^{2} } +C$ .....(c)

step 4:-

by using above integration formulas (a,b,and c)

we get answer is

$log x-\frac{log(x^{2}+1) }{2}-tan^{-1} x$

6 0

3 years ago

I really need help. I've been stuck on this question for almost an hour.

S_A_V [24]

Ma=Mc is the correct answer

8 0

3 years ago

Given: y" - 2y' = 6t + 5e^2t. Find the correct form to use for y_p if the equation is solved using Undetermined coefficients. Do

const2013 [10]

Answer:

$y_p=A+Bt+Ce^{2t}$

Step-by-step explanation:

Given: $y'' - 2y' = 6t + 5e^{2t}$ .

we need to find the correct form for $y_p$ if the equation is solve using undetermined coefficients.

A first order differential equation $\frac{\mathrm{d} y}{\mathrm{d} x}=f\left ( x,y \right )$ is said to be homogeneous if $f(tx,ty)=f(x,y)$ for all t.