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earnstyle [38]
2 years ago
11

It took boat to travel from pier A to pier B 5 hours going upstream. It made the return trip downstream in 3 hours and 30 minute

s. What is the distance between two piers, if the speed of the current is 3 mph?
Mathematics
2 answers:
aleksley [76]2 years ago
8 0
Distance =  speed * time
Upstream
d = 5 * (x - 3)
Downstream
d = 3.5(x + 3)        where d = distance beween piers  and x =  speed of the boat
    Equating:-
5x - 15 = 3.5x + 10.5
1.5x = 25.5
so x =   17 mph 

so d = 5(17) - 15 = 85-15  = 70 miles Answer
Assoli18 [71]2 years ago
4 0
9.5 miles, I think. (If not, I'm sorry!)
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Investigate the following harvesting model both qualitatively and analytically. If a constant number h of fish are harvested fro
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Step-by-step explanation:

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dP/dt = P(a-bP)-h, P(0) = P_0

If we rearrange and replace the constants we have:

\frac{dP}{P(7-P)-49/4} =dt\\\\-4 (\frac{dP}{4(P-7)P+49}) =dt\\\\-4 \frac{dP}{(2P-7)^2} =dt\\\\-4 \int\frac{dP}{(2P-7)^2} =\int dt\\\\-4(-\frac{1}{2(2P-7)})=t+C\\\\\frac{2}{2P-7}=t+C\\\\ t=0 \,\,\, P(0)=P_0\\\\\frac{2}{2P_0-7}=0+C\\\\C=\frac{2}{2P_0-7}

Now we can calculate if the population become 0 in any finite time

\frac{2}{2P-7}=t+\frac{2}{2P_0-7}\\\\\frac{2}{2*0-7}=t+\frac{2}{2P_0-7}\\\\-\frac{2}{7}=t+\frac{2}{2P_0-7}\\\\

To be a finite time, t>0

t=-\frac{2}{7}-\frac{2}{2P_0-7}=0\\\\-\frac{2}{2P_0-7}=\frac{2}{7}\\\\7-2P_0=7\\\\P_0=0

We can conclude that the only finite time in which P=0 is when the initial population is 0.

Because P0 is a positive constant, we can say that the population does not become extint in finite time.

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