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3 years ago

What is the of A in a partial fraction decomposition below?

Mathematics

1 answer:

denis-greek [22]3 years ago

8 0

Answer:

Step-by-step explanation:

(8x + 28) / ((x − 1) (x + 2) (x + 3)) = A / (x − 1) + B / (x + 2) + C / (x + 3)

Multiply both sides by (x − 1) (x + 2) (x + 3).

8x + 28 = A (x + 2) (x + 3) + B (x − 1) (x + 3) + C (x − 1) (x + 2)

If x = 1:

8 + 28 = A (3) (4)

36 = 12A

A = 3

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-5(t + 6) + 7t = 100

Mila [183]

Use distribution
-5t - 30 + 7t = 100
Combine like terms
2t - 30 = 100
Add 30 to both sides
2t = 130, t = 65
Solution: t = 65

3 0

3 years ago

Need to know b and c : picture available ; worth 10 points

bulgar [2K]

B;

$6.00 lb + 15% = 6.00 x 1.15 = $6.90

$6.90 x 2.6lbs = $17.94

C;

New price is $.90 more.

3.5 x .90 = $3.15 more

6 0

3 years ago

Help anyone please i need it

zheka24 [161]

Answer:

The sum is equal to $-905,200$

Step-by-step explanation:

we know that

The formula to calculate the sum is equal to

$Sn=n\frac{(a1+an)}{2}$

In this problem

$n=775$ -----> number of terms

a1 is the first term

$a1=(-3(1)-4)=-7$

an is the last term

$an=(-3(775)-4)=-2,329$

substitute

$Sn=775\frac{(-7-2,329)}{2}=-905,200$

4 0

3 years ago

4x - 6 = 22<br> Answer ?

Alex777 [14]

4x-6= 22

Move -6 to the other side.

Sign changes from -6 to +6.

4x-6+6= 22+6

4x= 22+6

4x= 28

Divide by 4 for both sides

4x/4= 28/4

x= 7

Answer : x= 7

6 0

3 years ago

Read 2 more answers

Problem 1: Use the Laplace Transforms to solve:

Leokris [45]

Transforming the ODE yields

$L\left\{y'' - y'\right\} = L\left\{e^{-3t}\right\}$

$(s^2 Y(s) - sy(0) - y'(0)) - (s Y(s) - y(0)) = \dfrac1{s+3}$

$(s^2 - s) Y(s) = \dfrac1{s+3}$

$Y(s) = \dfrac1{(s^2 - s)(s+3)} = \dfrac1{s(s-1)(s+3)}$

Partial fractions:

$Y(s) = \dfrac as + \dfrac b{s-1} + \dfrac c{s+3}$

$\implies 1 = a(s-1)(s+3) + b s(s+3) + c s(s - 1)$

$\implies 1 = -3 a + (2 a + 3 b - c) s + (a + b + c) s^2$

$\implies \begin{cases}-3a=1 \\ 2a+3b-c=0 \\ a+b+c=0\end{cases} \implies a=-\dfrac13, b=\dfrac14, c=\dfrac1{12}$

$\implies Y(s) = -\dfrac13 \times \dfrac1s + \dfrac14 \times \dfrac1{s-1} + \dfrac1{12} \times \dfrac1{s+3}$

Take the inverse transform:

$\boxed{y(t) = -\dfrac13 + \dfrac{e^t}4 + \dfrac{e^{-3t}}{12}}$

3 0

2 years ago