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zavuch27 [327]
3 years ago
12

Ralph and Jody go to the store to buy chips and candy bars. Ralph buys 3 bags of potato chips and 4 candy bars for 375 cents. Jo

dy buys 6 bags of potato chips and 4 candy bars for 600 cents. Later, Maria meets up with Ralph and Jody. She wants to buy one bag of potato chips and one candy bar from them. Ralph and Jody need to figure out what the charge her for the items.
Write a system of equations that will help Ralph and Jody figure out the price of each item. Explain.
Mathematics
1 answer:
s2008m [1.1K]3 years ago
3 0
3x+4y = 375
6x+ 4y= 600
-------------------
6x-3x  = 600 - 375

3x=225
x=225:3
x=75 cents

3*x+4y= 375
3*75+4y=375
225 +4y = 375
4y=375-225
4y=150
y=150:4
y=37,5 cents

the price is 75+37,5=112,5 cents for one bag of potato chips and one candy bar

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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}

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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

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Answer:

  • A. (x^{2/7})(y^{-3/5})

Step-by-step explanation:

<u>The numerator is:</u>

  • \sqrt[7]{x^2}  = (x^2)^{1/7} = x^{2/7}\\

<u>The denominator is:</u>

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<u>The fraction is equivalent to:</u>

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Correct choice is A

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