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borishaifa [10]
3 years ago
11

Question 6

Mathematics
1 answer:
Firdavs [7]3 years ago
7 0
So hmmmmm, notice... the boat went up in 3hrs, came back to the starting point in 2hrs, it went up 108km, it came back, well, from 108km to distance 0, so the distance on the way back is just the same 108km

now... let's say the stream has a speed rate of "r", and the boat has a still water speed rate of "b"

bear in mind that, when the boat is going UP, is not really going "b" fast, because the stream's "r" rate is going against it, and thus subtracting "r" from "b", so is really going " b - r " fast

when the boat is going down, is not going "b" fast either, because, again the stream's rate "r" is adding to it, because is going with the current, so is really going " b + r " fast

now, recall your d =rt, distance = rate * time

\bf \begin{array}{lccclll}
&distance&rate&time\\
&-----&-----&-----\\
upstream&108&b-r&3\\
downstream&108&b+r&2
\end{array}\\\\
-------------------------------\\\\
\begin{cases}
108=3(b-r)\implies \frac{108}{3}=b-r\\
\qquad 36=b-r\implies 36+r=\boxed{b}\\\\
108=2(b+r)\implies 54=b+r\\
\qquad 54=\boxed{36+r}+r
\end{cases}

solve for "r"

what's b?  well, 36+ r = b
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(10 points) Consider the initial value problem y′+3y=9t,y(0)=7. Take the Laplace transform of both sides of the given differenti
Rashid [163]

Answer:

The solution

Y (s) = 9( -1 +3 t + e^{-3 t} ) + 7 e ^{-3 t}

Step-by-step explanation:

<u><em>Explanation</em></u>:-

Consider the initial value problem y′+3 y=9 t,y(0)=7

<em>Step(i)</em>:-

Given differential problem

                           y′+3 y=9 t

<em>Take the Laplace transform of both sides of the differential equation</em>

                L( y′+3 y) = L(9 t)

 <em>Using Formula Transform of derivatives</em>

<em>                 L(y¹(t)) = s y⁻(s)-y(0)</em>

  <em>  By using Laplace transform formula</em>

<em>               </em>L(t) = \frac{1}{S^{2} }<em> </em>

<em>Step(ii):-</em>

Given

             L( y′(t)) + 3 L (y(t)) = 9 L( t)

            s y^{-} (s) - y(0) +  3y^{-}(s) = \frac{9}{s^{2} }

            s y^{-} (s) - 7 +  3y^{-}(s) = \frac{9}{s^{2} }

Taking common y⁻(s) and simplification, we get

             ( s +  3)y^{-}(s) = \frac{9}{s^{2} }+7

             y^{-}(s) = \frac{9}{s^{2} (s+3}+\frac{7}{s+3}

<em>Step(iii</em>):-

<em>By using partial fractions , we get</em>

\frac{9}{s^{2} (s+3} = \frac{A}{s} + \frac{B}{s^{2} } + \frac{C}{s+3}

  \frac{9}{s^{2} (s+3} =  \frac{As(s+3)+B(s+3)+Cs^{2} }{s^{2} (s+3)}

 On simplification we get

  9 = A s(s+3) +B(s+3) +C(s²) ...(i)

 Put s =0 in equation(i)

   9 = B(0+3)

 <em>  B = 9/3 = 3</em>

  Put s = -3 in equation(i)

  9 = C(-3)²

  <em>C = 1</em>

 Given Equation  9 = A s(s+3) +B(s+3) +C(s²) ...(i)

Comparing 'S²' coefficient on both sides, we get

  9 = A s²+3 A s +B(s)+3 B +C(s²)

 <em> 0 = A + C</em>

<em>put C=1 , becomes A = -1</em>

\frac{9}{s^{2} (s+3} = \frac{-1}{s} + \frac{3}{s^{2} } + \frac{1}{s+3}

<u><em>Step(iv):-</em></u>

y^{-}(s) = \frac{9}{s^{2} (s+3}+\frac{7}{s+3}

y^{-}(s)  =9( \frac{-1}{s} + \frac{3}{s^{2} } + \frac{1}{s+3}) + \frac{7}{s+3}

Applying inverse Laplace transform on both sides

L^{-1} (y^{-}(s) ) =L^{-1} (9( \frac{-1}{s}) + L^{-1} (\frac{3}{s^{2} }) + L^{-1} (\frac{1}{s+3}) )+ L^{-1} (\frac{7}{s+3})

<em>By using inverse Laplace transform</em>

<em></em>L^{-1} (\frac{1}{s} ) =1<em></em>

L^{-1} (\frac{1}{s^{2} } ) = \frac{t}{1!}

L^{-1} (\frac{1}{s+a} ) =e^{-at}

<u><em>Final answer</em></u>:-

<em>Now the solution , we get</em>

Y (s) = 9( -1 +3 t + e^{-3 t} ) + 7 e ^{-3t}

           

           

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Hello! What is 8 x 3 + 4 according to PEMDAS? :)
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F(-3)=(-2)*(-3)-4=6-4=2

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What the sum of -1 2/3÷(2 1/5)
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-20/21

Step-by-step explanation:

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How do you solve (X-2)^1/4=5
yanalaym [24]

Answer:

x=22

Step-by-step explanation:

(x-2)^1 =5                  Anything to the 1st power is 1 Multiply both sides by 4                                                            

x-2=20                      Move the constant (20) to the right and change its

x=20+2                      sign

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