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Arte-miy333 [17]
3 years ago
6

In a taste test people were asked which of 4 soft drinks they liked best. of those surveyed 1/3 chose orange crush 2/5 chose kil

la kola and 1/6 chose lime sublime. what fraction chose the fourth drink pls show all work and answer
Mathematics
1 answer:
motikmotik3 years ago
7 0
1/3 = 10/30
2/5 = 12/30
1/6 = 5/30
sum of all of them = 27/30
the fraction that chose the lime sublime is 1/10
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Step-by-step explanation:

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Solve y" + y = tet, y(0) = 0, y'(0) = 0 using Laplace transforms.
irina1246 [14]

Answer:

The solution of the diferential equation is:

y(t)=\frac{1}{2}cos(t)- \frac{1}{2}e^{t}+\frac{t}{2} e^{t}

Step-by-step explanation:

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ℒ[y" + y]=ℒ[te^{t}]

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By using the Table of Laplace Transform we get:

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Y(s)=\frac{1}{(s^{2}+1)(s-1)^{2}}

To be able to separate in terms, we use the partial fraction method:

\frac{1}{(s^{2}+1)(s-1)^{2}}=\frac{As+B}{s^{2}+1} +\frac{C}{s-1}+\frac{D}{(s-1)^2}

1=(As+B)(s-1)² + C(s-1)(s²+1)+ D(s²+1)

The equation is reduced to:

1=s³(A+C)+s²(B-2A-C+D)+s(A-2B+C)+(B+D-C)

With the previous equation we can make an equation system of 4 variables.

The system is given by:

A+C=0

B-2A-C+D=0

A-2B+C=0

B+D-C=1

The solution of the system is:

A=1/2 ; B=0 ; C=-1/2 ; D=1/2

Therefore, Y(s) is equal to:

Y(s)=\frac{s}{2(s^{2} +1)} -\frac{1}{2(s-1)} +\frac{1}{2(s-1)^{2}}

By using the inverse of the Laplace transform:

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y(t)=\frac{1}{2}cos(t)- \frac{1}{2}e^{t}+\frac{t}{2} e^{t}

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3 years ago
I need help for all those
Alekssandra [29.7K]

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