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saw5 [17]
3 years ago
10

Pls help this stuff is so hard to understand

Mathematics
1 answer:
ZanzabumX [31]3 years ago
3 0

Answer:

y = 0.5 (2)^x

Step-by-step explanation:

3rd option

you can plug in a coordinate point like (2, 2) to check this.

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In a parking lot, the ratio of the number of trucks to the number of cars is 2:5.
olchik [2.2K]

Answer:

100 trucks

Step-by-step explanation:

2:5 t:c

x:150+x

2(150+x)=5x

300=2x=5x

300=3x

x=100

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3 years ago
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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
PLEASE HELP I AM BEHIND!!!!
romanna [79]

Answer:

The answer is c definitely

6 0
3 years ago
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A polygon has 29 sides.<br><br> Work out the sum of its interior angles.
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Answer:

29

Step-by-step explanation:

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