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frez [133]
2 years ago
13

Find the volume of the rectangular prism

Mathematics
1 answer:
krek1111 [17]2 years ago
3 0

Answer:

\Large\boxed{\sf{8 m}}

Step-by-step explanation:

You can find the volume of the rectangular prism using the formula for rectangular prisms.

<u>Given:</u>

<u></u>

<u>Note: </u>

\Longrightarrow: \sf{V=L*W*H}

L: (length) = 4m

W: (width) = 2m

H: (height) = 1m

Multiply.

4*2*1

Use the order of operations.

PEMDAS stands for:

  • Parentheses
  • Exponents
  • Multiply
  • Divide
  • Add
  • Subtract

Do multiply.

4*2*1

4*2=8

8*1=8

  • <u>Therefore, the volume is 8m, which is our answer.</u>

I hope this helps, let me know if you have any questions.

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Answer:  The required answer is

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We will be using the following formulas of inverse Laplace transform :

(i)~L^{-1}\{\dfrac{1}{s-a}\}=e^{ax},\\\\\\(ii)~L^{-1}\{\dfrac{s}{s^2+a^2}\}=\cos ax,\\\\\\(iii)~L^{-1}\{\dfrac{1}{s^2+a^2}\}=\dfrac{1}{a}\sin ax.

By partial fractions, we have

\dfrac{s^2}{(s-1)(s^2+1)}=\dfrac{A}{s-1}+\dfrac{Bs+C}{s^2+1},

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Multiplying both sides of the above equation by the denominator of the left hand side, we get

2s^2=A(s^2+1)+(Bs+C)(s-1).

If s = 1, we get

2\times 1=A(1+1)\\\\\Rightarrow A=1.

Also,

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Comparing the coefficients of x² and 1, we get

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Taking inverse Laplace transform on both sides of the above, we get

L^{-1}\{\dfrac{2s^2}{(s-1)(s^2+1)}\}=L^{-1}\{\dfrac{1}{s-1}\}+L^{-1}\{\dfrac{s}{s^2+1}+\dfrac{1}{s^2+1}\}\\\\\\\Rightarrow f(x)=e^{1\times x}+\cos (1\times x)+\dfrac{1}{1}\sin(1\times x)\\\\\\\Rightarrow f(x)=e^x+\cos x+\sin x.

Thus, the required answer is

f(x)=e^x+\cos x+\sin x.

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4 years ago
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7 0
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