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3 years ago

9

(x5 + y5) ÷ (x + y) please answer ASAP

1 answer:

Shkiper50 [21]3 years ago

3 0

Answer:

$\frac{x^5+y^5}{x+y}=x^4-x^3y+x^2y^2-xy^3+y^4$

Step-by-step explanation:

Given the expression

$\left(x^5+y^5\right)\div \left(x+y\right)$

$\mathrm{Apply\:factoring\:rule:\:}x^n+y^n=\left(x+y\right)\left(x^{n-1}-x^{n-2}y+\:\dots \:-\:xy^{n-2}\:+\:y^{n-1}\right)\:\quad \quad \mathrm{n\:is\:odd}$

$x^5+y^5=\left(x+y\right)\left(x^4-x^3y+x^2y^2-xy^3+y^4\right)$

$=\frac{\left(x+y\right)\left(x^4-x^3y+x^2y^2-xy^3+y^4\right)}{x+y}$

Cancel the common factor: x+y

$=x^4-x^3y+x^2y^2-xy^3+y^4$

Thus,

$\frac{x^5+y^5}{x+y}=x^4-x^3y+x^2y^2-xy^3+y^4$

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What is 1/4 divided by 9/10 rewritten with an important fraction?

lutik1710 [3]

Step-by-step explanation:

${:}\hookrightarrow\sf \dfrac {1}{4}\div \dfrac {9}{10}$

${:}\hookrightarrow\sf \dfrac {1}{4}\times \dfrac {10}{9}$

${:}\hookrightarrow\sf \dfrac {10}{36}$

${:}\hookrightarrow\sf \dfrac {5}{18}$

8 0

3 years ago

“encontrar la integral indefinida y verificar el resultado mediante derivación”

Oliga [24]

$I=\displaystyle\int\frac x{(1-x^2)^3}\,\mathrm dx$

Haz la sustitución:

$y=1-x^2\implies\mathrm dy=-2x\,\mathrm dx$

$\implies I=\displaystyle-\frac12\int\frac{\mathrm dy}{y^3}=\frac1{4y^2}+C=\frac1{4(1-x^2)^2}+C$

Para confirmar el resultado:

$\dfrac{\mathrm dI}{\mathrm dx}=\dfrac14\left(-\dfrac{2(-2x)}{(1-x^2)^3}\right)=\dfrac x{(1-x^2)^3}$

$I=\displaystyle\int\frac{x^2}{(1+x^3)^2}\,\mathrm dx$

Sustituye:

$y=1+x^3\implies\mathrm dy=3x^2\,\mathrm dx$

$\implies I=\displaystyle\frac13\int\frac{\mathrm dy}{y^2}=-\frac1{3y}+C=-\frac1{3(1+x^3)}+C$

(Te dejaré confirmar por ti mismo.)

$I=\displaystyle\int\frac x{\sqrt{1-x^2}}\,\mathrm dx$

Sustituye:

$y=1-x^2\implies\mathrm dy=-2x\,\mathrm dx$

$\implies I=\displaystyle-\frac12\int\frac{\mathrm dy}{\sqrt y}=-\frac12(2\sqrt y)+C=-\sqrt{1-x^2}+C$

$I=\displaystyle\int\left(1+\frac1t\right)^3\frac{\mathrm dt}{t^2}$

Sustituye:

$u=1+\dfrac1t\implies\mathrm du=-\dfrac{\mathrm dt}{t^2}$

$\implies I=-\displaystyle\int u^3\,\mathrm du=-\frac{u^4}4+C=-\frac{\left(1+\frac1t\right)^4}4+C$

Podemos hacer que esto se vea un poco mejor:

$\left(1+\dfrac1t\right)^4=\left(\dfrac{t+1}t\right)^4=\dfrac{(t+1)^4}{t^4}$

$\implies I=-\dfrac{(t+1)^4}{4t^4}+C$

4 0

4 years ago

A ski rental store rents a pair of skis for $44 a day and a snowboard for $58 a day. Yesterday, the store made $2,232 on ski and

Katen [24]

First, let the number of skis rented by x and the number of snowboards rented by y. We can then assemble the first equation from the amount of money made from the rentals.

44x + 58y = 2232

The second equation can come from the fact that 9 more skis were rented than snowboards.

y = x - 9

Therefore our system is:

44x + 58y = 2232

y = x - 9

3 0

4 years ago

Dr. Tu must administer emergency medicine to his patient, Mrs. Jones. The

galben [10]

Answer:

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Step-by-step explanation: You would do 140/100 = 1.4 then multiply 120 by 1.4 which is 168.

3 0

3 years ago

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Bingel [31]

I don’t think f would have any value in this equation and f would represent 1 zero??

4 0

3 years ago