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zzz [600]
3 years ago
6

Need help please...answer correctly ​

Mathematics
2 answers:
charle [14.2K]3 years ago
8 0

<u>Answer with step-by-step explanation:</u>

a) Assuming x to be the speed of the boat and y to be the speed of the water, we can write an expression for:

- the distance traveled downstream: 3(x+y)

- the distance traveled upstream: 3.6(x-y)

b) setting expressions in part a equal to each other:

3(x+y) = 3.6(x-y)

3x +3y = 3.6x - 3.6y

3y + 3.6y = 3.6x - 3x

6.6y = 0.6x

y = 0.6/6.6x

y = 1/11x

c) 1/11 * 100 = 9.1%

Lelechka [254]3 years ago
3 0

Answer:

9.09

Step-by-step explanation:

x=speed of boat

y=speed of water current

Downstream relative speed = x+y

Upstream relative speed = x-y

Distance remains the same for both upstream and downstream.

a) Distance travelled downstream = speed x time = 3(x+y)

Distance travelled upstream = speed x time = 3.6(x-y)

b) Since both distances are equal, we can write

3(x+y)= 3.6(x-y)

3x+3y = 3.6x-3.6y

6.6y = 0,6x

x=11y: y=x/11

c) Water current has speed as 1/11 times of that of boat

In percent this equals 100/11 = 9.09%

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KatRina [158]
The next step is to solve the recurrence, but let's back up a bit. You should have found that the ODE in terms of the power series expansion for y

\displaystyle\sum_{n\ge2}\bigg((n-3)(n-2)a_n+(n+3)(n+2)a_{n+3}\bigg)x^{n+1}+2a_2+(6a_0-6a_3)x+(6a_1-12a_4)x^2=0

which indeed gives the recurrence you found,

a_{n+3}=-\dfrac{n-3}{n+3}a_n

but in order to get anywhere with this, you need at least three initial conditions. The constant term tells you that a_2=0, and substituting this into the recurrence, you find that a_2=a_5=a_8=\cdots=a_{3k-1}=0 for all k\ge1.

Next, the linear term tells you that 6a_0+6a_3=0, or a_3=a_0.

Now, if a_0 is the first term in the sequence, then by the recurrence you have

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Finally, the quadratic term gives 6a_1-12a_4=0, or a_4=\dfrac12a_1. Then by the recurrence,

a_4=\dfrac12a_1
a_7=-\dfrac{4-3}{4+3}a_4=\dfrac{(-1)^1}2\dfrac17a_1
a_{10}=-\dfrac{7-3}{7+3}a_7=\dfrac{(-1)^2}2\dfrac4{10\times7}a_1
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Now, the solution was proposed to be

y=\displaystyle\sum_{n\ge0}a_nx^n

so the general solution would be

y=a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5+a_6x^6+\cdots
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