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3 years ago

7

Eric and Carly each made a bowl of punch. Carly used 5 times as much lemonade as Eric did. If Eric used 1/4 of a

1 answer:

Viktor [21]3 years ago

8 0

Answer:

carly used 1 1/4 cups of lemonade

Step-by-step explanation:

I think that is simplified

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A family of two adults and four children is going to and amusement park admission is $21.75 for adults and $15.25 for children w

mote1985 [20]

The Answer Is 104.50 Because You Have To Multiply The Two Adults By The Admission ( 21.75×2 ) And Also Multiply The Four Kids By The Admission ( 15.25×4 ) And Add Both Of Those Answers Together ( 43.50+61.00=104.50)

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Equation for circumference is c = 2(pi)r

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Click and drag like terms onto each other to simplify fully.<br> 2-5+7y-5x+7x-2y

nikdorinn [45]

Answer: 5y + 2x - 3

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3 years ago

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Earn 100 points for this question and a brainiest

padilas [110]

Answer:

the answer is C

Step-by-step explanation:

$\frac{7}{7} - \frac{4}{7} + \frac{2}{7}$

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3 years ago

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Consider the differential equation:

Wewaii [24]

(a) Take the Laplace transform of both sides:

$2y''(t)+ty'(t)-2y(t)=14$

$\implies 2(s^2Y(s)-sy(0)-y'(0))-(Y(s)+sY'(s))-2Y(s)=\dfrac{14}s$

where the transform of $ty'(t)$ comes from

$L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)$

This yields the linear ODE,

$-sY'(s)+(2s^2-3)Y(s)=\dfrac{14}s$

Divides both sides by $-s$ :

$Y'(s)+\dfrac{3-2s^2}sY(s)=-\dfrac{14}{s^2}$

Find the integrating factor:

$\displaystyle\int\frac{3-2s^2}s\,\mathrm ds=3\ln|s|-s^2+C$

Multiply both sides of the ODE by $e^{3\ln|s|-s^2}=s^3e^{-s^2}$ :

$s^3e^{-s^2}Y'(s)+(3s^2-2s^4)e^{-s^2}Y(s)=-14se^{-s^2}$

The left side condenses into the derivative of a product:

$\left(s^3e^{-s^2}Y(s)\right)'=-14se^{-s^2}$

Integrate both sides and solve for $Y(s)$ :

$s^3e^{-s^2}Y(s)=7e^{-s^2}+C$

$Y(s)=\dfrac{7+Ce^{s^2}}{s^3}$

(b) Taking the inverse transform of both sides gives

$y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right]$

I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that $\frac{7t^2}2$ is one solution to the original ODE.

$y(t)=\dfrac{7t^2}2\implies y'(t)=7t\implies y''(t)=7$

Substitute these into the ODE to see everything checks out:

$2\cdot7+t\cdot7t-2\cdot\dfrac{7t^2}2=14$

5 0

3 years ago