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djverab [1.8K]
3 years ago
11

Use the Laplace transform to solve the given initial value problem. y' + 6y = e^4t ; y(0)=2 ...?

Mathematics
1 answer:
TiliK225 [7]3 years ago
4 0
Performing laplace transform of the equation.

sY(s) - y(0) + 6Y(s) = 1/(s-4)
(s+6)Y(s) - 2 = 1/(s-4)
Y(s) = 2/(s+6) + 1/(s-4)(s+6), by partial fraction decomposition
Y(s) = 2/(s+6) + 1/10 * (1/(s-4) + 1/(s+6))
Y(s) = 0.1/(s-4) + 2.1/(s+6)

Performing inverse laplace transform,
y(t) = 0.1e^4t + 2.1e^(-6t)


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
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Solve x2+6x=7 by completing the square.Which is the solution set of the equation?
NARA [144]

Answer:

x = - 7, x = 1

Step-by-step explanation:

Given

x² + 6x = 7

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(3)x + 9 = 7 + 9

(x + 3)² = 16 ( take the square root of both sides )

x + 3 = ± \sqrt{16} = ± 4 ( subtract 3 from both sides )

x = - 3 ± 4

x = - 3 - 4 = - 7

x = - 3 + 4 = 1

Solution set = { - 7, 1 }

4 0
3 years ago
You decide to put $150 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate
zheka24 [161]
The formula is
A=p (1+r/k)^kt
A future value 3000
P present value 150
R interest rate 0.025
T time?
3000=150 (1+0.025/12)^12t
Solve for t
3000/150=(1+0.025/12)^12t
Take the log
Log (3000/150)=log (1+0.025/12)×12t
12t=Log (3000/150)÷log (1+0.025/12)
T=(log(3,000÷150)÷log(1+0.025÷12))÷12
T=119.95 years
8 0
3 years ago
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3<br> 5<br> y = mx + c<br> Find the value of y when m= -2, r = -7 and c= -3.
mario62 [17]

Answer:

<u>This assume the equation is 35y = mx + c, and that r is meant to be x.</u>

Step-by-step explanation:

35y = mx + c

35y = -2(-7) - 3

35y = 14 - 3

35y = 11

y = (11/35)

Please check the formatting of your question.

6 0
2 years ago
prem gave 1/3 of his property for charity of the rest he gave 2/3 to his wife and rest divided equally between his son and daugh
Anna11 [10]

Given parameters:

Fraction given to charity = \frac{1}{3}

Fraction given to wife = \frac{2}{3}

Unknown:

Fraction given to son and daughter =?

Solution:

Let the total property  = x

    Fraction given to charity  = \frac{1}{3} x

    Fraction given to wife  = \frac{2}{3} x

The remaining was given to son and daughter = F

    So;

     Total property  = fraction given to charity + fraction given to wife + fraction given to son and daughter

         x  = \frac{1}{3} x + \frac{2}{3} x + F

            F = x - (\frac{1}{3} x + \frac{2}{3} x)

            F = 0

The son and daughter will not inherit anything

8 0
3 years ago
Which could be the area of one face of the triangular prism? Select three options.
katovenus [111]

Answer:

(A)24 square units

(C)72 square units

(D)96 square units

Step-by-step explanation:

<u>Triangular face</u>

Height of the Triangle=6 Units

Base of the Triangle=8 Units

Area of the Triangular Face

=\frac{1}{2}bh\\ =\frac{1}{2}*8*6\\=24 $ square units

<u>Rectangular Faces</u>

Area of Rectangular face with dimension 12 by 10=12 x 10=120 Square Units

Area of Rectangular face with dimension  12 by 8= 12 X 8=96 Square Units

Area of Rectangular face with dimension 12 X 6=12 x 6=72 Square Units

From the options, the areas are:

  • 24 square units
  • 72 square units
  • 96 square units

4 0
3 years ago
Read 2 more answers
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