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3 years ago

What is the relationship between multiplying and factoring?

Mathematics

2 answers:

HACTEHA [7]3 years ago

7 0

Answer:

In multiplication the numbers you multiply are called factors; the answer is called the product. In division the number being divided is the dividend, the number that divides it is the divisor, and the answer is the quotient.

Step-by-step explanation:

muminat3 years ago

6 0

Answer:

3x + 12

Step-by-step explanation:

Factoring straddles the line between multiplying and dividing. Let's take a look at the following expression:

3x + 12

Both 3x and 9 have a three in common, so we can factor out that three:

3x ÷ 3 = x

12 ÷ 3 = 4

Now that 3 has been factored out, we set it aside what's left:

3(x + 4)

We can get our original expression by distributing (by multiplying) that 3 back in:

x * 3 = 3x

4 * 3 = 12

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Suppose we want to write 2/5

Basile [38]

Answer:

you must multiply the numerator and denominator by 6

Step-by-step explanation:

because 5 x 6 = 30

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3 years ago

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3 years ago

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Find $\int \dfrac{x}{\sqrt{1-x^4}}$ Please, help

ki77a [65]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2867785

_______________

Evaluate the indefinite integral:

$\mathsf{\displaystyle\int\! \frac{x}{\sqrt{1-x^4}}\,dx}\\\\\\ \mathsf{=\displaystyle\int\! \frac{1}{2}\cdot 2\cdot \frac{1}{\sqrt{1-(x^2)^2}}\,dx}\\\\\\ \mathsf{=\displaystyle \frac{1}{2}\int\! \frac{1}{\sqrt{1-(x^2)^2}}\cdot 2x\,dx\qquad\quad(i)}$

Make a trigonometric substitution:

$\begin{array}{lcl}
\mathsf{x^2=sin\,t}&\quad\Rightarrow\quad&\mathsf{2x\,dx=cos\,t\,dt}\\\\
&&\mathsf{t=arcsin(x^2)\,,\qquad 0\ \textless \ x\ \textless \ \frac{\pi}{2}}\end{array}$

so the integral (i) becomes

$\mathsf{=\displaystyle\frac{1}{2}\int\!\frac{1}{\sqrt{1-sin^2\,t}}\cdot cos\,t\,dt\qquad\quad (but~1-sin^2\,t=cos^2\,t)}\\\\\\
\mathsf{=\displaystyle\frac{1}{2}\int\!\frac{1}{\sqrt{cos^2\,t}}\cdot cos\,t\,dt}$

$\mathsf{=\displaystyle\frac{1}{2}\int\!\frac{1}{cos\,t}\cdot cos\,t\,dt}\\\\\\
\mathsf{=\displaystyle\frac{1}{2}\int\!\f dt}\\\\\\
\mathsf{=\displaystyle\frac{1}{2}\,t+C}$

Now, substitute back for t = arcsin(x²), and you finally get the result:

$\mathsf{\displaystyle\int\! \frac{x}{\sqrt{1-(x^2)^2}}\,dx=\frac{1}{2}\,arcsin(x^2)+C}$ ✔

________

You could also make

x² = cos t

and you would get this expression for the integral:

$\mathsf{\displaystyle\int\! \frac{x}{\sqrt{1-(x^2)^2}}\,dx=-\,\frac{1}{2}\,arccos(x^2)+C_2}$ ✔

which is fine, because those two functions have the same derivative, as the difference between them is a constant:

$\mathsf{\dfrac{1}{2}\,arcsin(x^2)-\left(-\dfrac{1}{2}\,arccos(x^2)\right)}\\\\\\
=\mathsf{\dfrac{1}{2}\,arcsin(x^2)+\dfrac{1}{2}\,arccos(x^2)}\\\\\\
=\mathsf{\dfrac{1}{2}\cdot \left[\,arcsin(x^2)+arccos(x^2)\right]}\\\\\\
=\mathsf{\dfrac{1}{2}\cdot \dfrac{\pi}{2}}$

$\mathsf{=\dfrac{\pi}{4}}$ ✔

and that constant does not interfer in the differentiation process, because the derivative of a constant is zero.

I hope this helps. =)

6 0

3 years ago

What is the distance between the two points (-2 ,1 )and (4, 3)

kirill [66]

Solution:

Distance between two points = √(3−4)^2+(−2−3)^2

= √(−1)^2+(−5)^2

= √1+25

= √26

= 5.099

Distance between points (4, 3) and (3, -2) is 5.099.

3 0

3 years ago

About 12% of individuals write with their left hands. If a class of 130 students meets in a classroom with 130 individual desks,

Lynna [10]

Answer:

0.1019

Step-by-step explanation:

Probability, p=12%=0.12

Sample size, n=130 students

Those writing with left=14 students

Using the formula for binomial distribution

P(X≤x)= $\left[\begin{array}{}n\\x\end{array}\right]p^{x}(1-p)^{n-x}$

Substituting 0.12 for p, 130 for n, 14 for x we obtain

P(X≤x)= $\left[\begin{array}{}130\\14\end{array}\right]0.12^{14}(1-0.12)^{130-14}$

P(X≤x)= $130C14*0.12^{14}(0.88)^{116}$

P(X≤x)=0.1019

3 0

3 years ago