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2 years ago

Find the missing angles of the triangle (number 5)

Mathematics

1 answer:

meriva2 years ago

4 0

M1=62°
m2=50°
m3=49°
m4=50°
m5=89°
m6=1°

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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

Which of the following is a polynomial?

Rom4ik [11]

Answer:

A. 3x^2+6x is a polynomial

8 0

3 years ago

4(-9x + 1) =<br> Answer?

faltersainse [42]

Answer:

−36+4

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

How do you solve 3.36/1.4

Leto [7]

Answer:

2.4

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Cole paid $24 for two calculators and one pack of pens. Kai paid $45 for three calculators and two packs of pens. Cole and Kai b

FrozenT [24]

$2.00 more.

gathered info from question:

Kai paid $45

Cole paid $24

It is $6 for each pack of pens

So I did 24- 6 (pack of pens) = 18 (what he used for calculators) and then did 18/2 because he bought two calculators. He paid 9 dollars for each calculator

Kai bought two packs of pens = 12 dollars. 45-12=33, how much he used for the calculators. He bought three calculators so I did 33/3=11. He used 11 dollars for each calculator.

11-9=2.

Kai paid $2.00 more than Cole.

Please mark be brainliest :)

8 0

3 years ago