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In one hour, the distance, 
d(s), in kilometers that a ferry can travel up and down a river flowing with a constant speed, 
s, in meters per second is:

d(s)=10.7-1.2s^(2)
where 
s and 
d(s) are positive. Which of the following equivalent expressions for 
d(s) contains the speed of the river in meters per second, as a constant or coefficient, for which the ferry can travel a distance of 8 kilometers in one hour?
Choose 1 answer:
(A) 
8-1.2(s-1.5)(s+1.5
(B) 
8+1.2(2.25-s^(2))
(c) 
8(1-0.15s^(2))+2.7
(D) 
11.9-1.2(s-1)^(2)-2.4

In one hour, the distance, d(s) d(s) , in kilometers that a ferry can travel up and down a river flowing with a constant speed, s s , in meters per second is:\newlined(s)=10.71.2s2 d(s)=10.7-1.2 s^{2} \newlinewhere s s and d(s) d(s) are positive. Which of the following equivalent expressions for d(s) d(s) contains the speed of the river in meters per second, as a constant or coefficient, for which the ferry can travel a distance of 88 kilometers in one hour?\newlineChoose 11 answer:\newline(A) 81.2(s1.5)(s+1.5 8-1.2(s-1.5)(s+1.5 \newline(B) 8+1.2(2.25s2) 8+1.2\left(2.25-s^{2}\right) \newline(C) 8(10.15s2)+2.7 8\left(1-0.15 s^{2}\right)+2.7 \newline(D) 11.91.2(s1)22.4 11.9-1.2(s-1)^{2}-2.4

Full solution

Q. In one hour, the distance, d(s) d(s) , in kilometers that a ferry can travel up and down a river flowing with a constant speed, s s , in meters per second is:\newlined(s)=10.71.2s2 d(s)=10.7-1.2 s^{2} \newlinewhere s s and d(s) d(s) are positive. Which of the following equivalent expressions for d(s) d(s) contains the speed of the river in meters per second, as a constant or coefficient, for which the ferry can travel a distance of 88 kilometers in one hour?\newlineChoose 11 answer:\newline(A) 81.2(s1.5)(s+1.5 8-1.2(s-1.5)(s+1.5 \newline(B) 8+1.2(2.25s2) 8+1.2\left(2.25-s^{2}\right) \newline(C) 8(10.15s2)+2.7 8\left(1-0.15 s^{2}\right)+2.7 \newline(D) 11.91.2(s1)22.4 11.9-1.2(s-1)^{2}-2.4
  1. Given Equation: We are given the original equation for the distance d(s)d(s) that the ferry can travel in one hour: d(s)=10.71.2s2d(s) = 10.7 - 1.2s^2 We need to find an equivalent expression that results in d(s)d(s) being equal to 88 kilometers.
  2. Set Equal to 88 Kilometers: First, let's set the given equation equal to 88 kilometers to find the expression that will give us the speed of the river:\newline8=10.71.2s28 = 10.7 - 1.2s^2
  3. Solve for s2s^2: Now, we need to solve for s2s^2 in the equation:\newline1.2s2=10.781.2s^2 = 10.7 - 8\newlines2=10.781.2s^2 = \frac{10.7 - 8}{1.2}\newlines2=2.71.2s^2 = \frac{2.7}{1.2}\newlines2=2.25s^2 = 2.25

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