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3 years ago

Simplify the complex fraction-2/7÷1 1/3

Mathematics

1 answer:

Ilia_Sergeevich [38]3 years ago

4 0

Answer:

-2/231 or -0.008658

Step-by-step explanation:

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Find a particular solution to y" - y + y = 2 sin(3x)

leonid [27]

Answer with explanation:

The given differential equation is

y" -y'+y=2 sin 3x------(1)

Let, y'=z

y"=z'

$\frac{dy}{dx}=z\\\\d y=zdx\\\\y=z x$

Substituting the value of , y, y' and y" in equation (1)

z'-z+zx=2 sin 3 x

z'+z(x-1)=2 sin 3 x-----------(1)

This is a type of linear differential equation.

Integrating factor

$=e^{\int (x-1) dx}\\\\=e^{\frac{x^2}{2}-x}$

Multiplying both sides of equation (1) by integrating factor and integrating we get

$\rightarrow z\times e^{\frac{x^2}{2}-x}=\int 2 sin 3 x \times e^{\frac{x^2}{2}-x} dx=I$

$I=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{3}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{3} dx -\int \frac{2\cos 3x e^{\fra{x^2}{2}-x}}{3} dx\\\\I=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{3}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{3} dx-\frac{2I}{3}\\\\\frac{5I}{3}=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{3}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{3} dx\\\\I=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{5}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{5} dx$

8 0

3 years ago

10. Do these figures have the same or the opposite orientation?

Jet001 [13]

Answer:

Opposite

Step-by-step explanation:

3 0

2 years ago

In how many ways can 10 people be seated in 10badjacenr seats in a theater

kupik [55]

3,628,800 is the correct answer

5 0

3 years ago

What is x in this equation 2-3/4x=11

vladimir2022 [97]

Answer:

x=-12

Step-by-step explanation:

2-3/4x=11

3/4x=2-11

3/4x=-9

x=-9/(3/4)

x=(-9/1)(4/3)

x=-36/3

x=-12

3 0

3 years ago

What is the total depreciation (at 10% rate) on a blower purchased 3 years ago for $499?

GrogVix [38]

$\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &499\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=\textit{elapsed time}\dotfill &3\\ \end{cases} \\\\\\ A=499(1-0.10)^3\implies A=499(0.9)^3\implies A=363.771 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{total depreciation 499 - 363.771}}{135.229}~\hfill$

6 0

3 years ago