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denis-greek [22]
9 months ago
15

a motorboat travels 456 km in 8 hours going upstream and 783 km in 9 hours going downstream. what is the rate of the boat in sti

ll water and what is the rate of current?
Mathematics
1 answer:
Galina-37 [17]9 months ago
4 0
\begin{gathered} \text{Let;s assume the sp}e\text{d of boat in still water is x.} \\ And\text{ the spe}ed\text{ of stream is y.} \\ For\text{ upstream,} \\ (x-y)\times8=456 \\ x-y=57\ldots(1)_{} \\ (x+y)\times9=783 \\ x+y=87 \\ x=87-y\ldots(2) \\ \text{Now, substitute the value of x in the equation (1).} \\ 87-y-y=57 \\ -2y=57-87 \\ 2y=30 \\ y=15\text{ km/hours (rate of current)} \\ \text{Substitute the value of y in the equation (2).} \\ x=87-15 \\ x=72\text{ km/hours (boat in still water)} \end{gathered}

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Answer:

θ = 2 π n_1 + π/2 for n_1 element Z  or θ = 2 π n_2 for n_2 element Z

Step-by-step explanation:

Solve for θ:

cos(θ) + sin(θ) = 1

cos(θ) + sin(θ) = sqrt(2) (cos(θ)/sqrt(2) + sin(θ)/sqrt(2)) = sqrt(2) (sin(π/4) cos(θ) + cos(π/4) sin(θ)) = sqrt(2) sin(θ + π/4):

sqrt(2) sin(θ + π/4) = 1

Divide both sides by sqrt(2):

sin(θ + π/4) = 1/sqrt(2)

Take the inverse sine of both sides:

θ + π/4 = 2 π n_1 + (3 π)/4 for n_1 element Z

or θ + π/4 = 2 π n_2 + π/4 for n_2 element Z

Subtract π/4 from both sides:

θ = 2 π n_1 + π/2 for n_1 element Z

or θ + π/4 = 2 π n_2 + π/4 for n_2 element Z

Subtract π/4 from both sides:

Answer: θ = 2 π n_1 + π/2 for n_1 element Z

or θ = 2 π n_2 for n_2 element Z

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Step-by-step explanation:

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