500+0+12+44+55+500+0+12+44+55+ 500+0+12+44+55+500+0+12+44+55 = 500 + 12 + 44 + 55 + 500 + 12 + 44 + 55 + 500 + 12 + 44 + 55 + 500 + 12 + 44 + 55 = 4(500 + 12 + 44 + 55) = 4(512 + 99) = 4(611) = 2,444.

Hope this helps!

4 0

3 years ago

Read 2 more answers

Please help!!! I don’t understand

Allushta [10]

Answer:

first you would add 5 on both sides

then you should have 15y = 28

then you will divide 15 by 15

then do the same to 28

Step-by-step explanation:

4 0

3 years ago

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:

Given $y" + y = te^{t}$ ; y(0) = 0 ; y'(0) = 0

We need to use the Laplace transform to solve it.

ℒ[y" + y]=ℒ[ $te^{t}$ ]

ℒ[y"]+ℒ[y]=ℒ[ $te^{t}$ ]

By using the Table of Laplace Transform we get:

ℒ[y"]=s²·ℒ[y]+s·y(0)-y'(0)=s²·Y(s)

ℒ[y]=Y(s)

ℒ[ $te^{t}$ ]= $\frac{1}{(s-1)^{2}}$

So, the transformation is equal to:

s²·Y(s)+Y(s)= $\frac{1}{(s-1)^{2}}$

(s²+1)·Y(s)= $\frac{1}{(s-1)^{2}}$

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:

ℒ⁻¹[Y(s)]=ℒ⁻¹[ $\frac{s}{2(s^{2} +1)}$ ]-ℒ⁻¹[ $\frac{1}{2(s-1)}$ ]+ℒ⁻¹[ $\frac{1}{2(s-1)^{2}}$ ]

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

8 0

3 years ago