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balandron [24]
3 years ago
12

Solve the given integral equation for LaTeX: y(t)y ( t ). LaTeX: y(t)+9\displaystyle{\int_{0}^{t}e^{9(t-v)}y(v)\, dv}=\sin(3t)y

( t ) + 9 ∫ 0 t e 9 ( t − v ) y ( v ) d v = sin ⁡ ( 3 t ) Group of answer choices LaTeX: y(t)=3\cos(3t)+9\sin(3t)-9 y ( t ) = 3 cos ⁡ ( 3 t ) + 9 sin ⁡ ( 3 t ) − 9 LaTeX: y(t)=3\cos(3t)+\sin(3t)-3 y ( t ) = 3 cos ⁡ ( 3 t ) + sin ⁡ ( 3 t ) − 3 LaTeX: y(t)=3\cos(3t)+\sin(3t) y ( t ) = 3 cos ⁡ ( 3 t ) + sin ⁡ ( 3 t ) LaTeX: y(t)=3\cos(3t)+9\sin(3t) y ( t ) = 3 cos ⁡ ( 3 t ) + 9 sin ⁡ ( 3 t ) LaTeX: y(t)=\cos(3t)+3\sin(3t)-3
Mathematics
1 answer:
choli [55]3 years ago
6 0

Looks like the equation is

y(t)+9\displaystyle\int_0^te^{9(t-v)}y(v)\,\mathrm dv=\sin(3t)

Differentiating both sides yields the linear ODE,

y'(t)+9e^{9(t-t)}y(t)=3\cos(3t)

or

y'(t)+9y(t)=3\cos(3t)

Multiply both sides by the integrating factor e^{9t}:

e^{9t}y'(t)+9e^{9t}y(t)=3e^{9t}\cos(3t)

\left(e^{9t}y(t)\right)'=3e^{9t}\cos(3t)

Integrate both sides, then solve for y(t):

e^{9t}y(t)=\dfrac1{10}e^{9t}(\sin(3t)+3\cos(3t))+C

y(t)=\dfrac{\sin(3t)+3\cos(3t)}{10}+Ce^{-9t}

The given answer choices all seem to be missing <em>C</em>, so I suspect you left out an initial condition. But we can find one; let t=0, then the integral vanishes and we're left with y(0)=0. So

0=\dfrac{0+3}{10}+C\implies C=-\dfrac3{10}

So the particular solution is

y(t)=\dfrac{\sin(3t)+3\cos(3t)-3e^{-9t}}{10}

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Answer:

The unknown value is being subtracted from 226 is 160

Step-by-step explanation:

Long division setup showing an incomplete calculation

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so,

The dividend = 3426

 The divisor = 16

2 hundreds means 200 and 1 tens means 10

∵ The quotient = 200 + 10 + x

∵ Dividend = divisor × quotient

∴ (16 × 200) + (16 × 10) + (16 × x) +remainder  = 3426  

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∴ 226- 160 = 66

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∵ 16 × x = 16x  

∵ 66 - 16x = 0

∴ 66 = 16x

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∴ x = 4  and remainder = 2

∴ 3426 ÷ 16 = 200 + 10 + 4

∴ 3426 ÷ 16 = 214  

∴ From the steps above the missing number subtracted from

  226 is 160

The unknown value is being subtracted from 226 is 160

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