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3 years ago

1/3 ÷ 3/8 = ?????????????????

2 answers:

7 0

Flip the fraction in the denominator 3/8 and multiply by the numerator.
1/3 *8/3. Multiply straight across.
1*'8=8
3*3=9
=8/9

Dvinal [7]3 years ago

5 0

0.0138 hope that helps

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There are 4 circles and 8 squares. What is the simplest ratio of circles to squares?

fgiga [73]

4:8 the equivalent of 4 circles and 8 squares and you obviously want the most simplest answer so you would divide each number by the first number which make 2:4 (2 circle : 4 squares).

Again, this ain’t the simplest answer so you divide it again but this time you divide it by 2 which makes 1:2 or (1 circle : 2 squares).

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3 years ago

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Step-by-step explanation:

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3 years ago

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3 years ago

Find the inverse Laplace transforms, as a function of x, of the following functions:

inn [45]

Answer: The required answer is

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

Step-by-step explanation: We are given to find the inverse Laplace transform of the following function as a function of x :

$F(s)=\dfrac{2s^2}{(s-1)(s^2+1)}.$

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

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

where A, B and C are constants.

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,

$2s^2=A(s^2+1)+(Bs^2-Bs+Cs-C)\\\\\Rightarrow 2s^2=(A+B)s^2+(-B+C)s+(A-C).$

Comparing the coefficients of x² and 1, we get

$A+B=2\\\\\Rightarrow B=2-1=1,\\\\\\A-C=0\\\\\Rightarrow C=A=1.$

So, we can write

$\dfrac{2s^2}{(s-1)(s^2+1)}=\dfrac{1}{s-1}+\dfrac{s+1}{s^2+1}\\\\\\\Rightarrow \dfrac{2s^2}{(s-1)(s^2+1)}=\dfrac{1}{s-1}+\dfrac{s}{s^2+1}+\dfrac{1}{s^2+1}.$

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

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

4 0

4 years ago