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2 years ago

5

Simplify the polynomial. Then find its value for the given value of the variable.

1 answer:

vekshin12 years ago

3 0

Answer:

Step-by-step explanation:

Simplified expression:

$3x^3 -x^3 +5x^3-9x^3$

$2x^3 +5x^3-9x^3$

$7x^3 -9x^3$

$-2x^3$

If x = -1, the value of the expression is:

$-2x^3$

$-2(-1^3)$

$-2(-1)$

$2$

Hope this helps!

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4> Solve by using Laplace transform: y'+5y'+4y=0; y(0)=3 y'(o)=o

harina [27]

Answer:

$y=3e^{-4t}$

Step-by-step explanation:

$y''+5y'+4y=0$

Applying the Laplace transform:

$\mathcal{L}[y'']+5\mathcal{L}[y']+4\mathcal{L}[y']=0$

With the formulas:

$\mathcal{L}[y'']=s^2\mathcal{L}[y]-y(0)s-y'(0)$

$\mathcal{L}[y']=s\mathcal{L}[y]-y(0)$

$\mathcal{L}[x]=L$

$s^2L-3s+5sL-3+4L=0$

Solving for $L$

$L(s^2+5s+4)=3s+3$

$L=\frac{3s+3}{s^2+5s+4}$

$L=\frac{3(s+1)}{(s+1)(s+4)}$

$L=\frac3{s+4}$

Apply the inverse Laplace transform with this formula:

$\mathcal{L}^{-1}[\frac1{s-a}]=e^{at}$

$y=3\mathcal{L}^{-1}[\frac1{s+4}]=3e^{-4t}$

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The answer would be

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I hope this was helpful :D

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