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Elodia [21]
3 years ago
12

a paddle boat can move at a speed of 6km/h in still water. the boat is paddeled 16km downstream in a river in the same time it t

akes to go 8km upstream what is the speed of the river?
Mathematics
1 answer:
kaheart [24]3 years ago
5 0
v-the\ speed\ of\ the\ river\\\\16:(6+v)=8:(6-v)\\\\\frac{16}{6+v}=\frac{8}{6-v}\\-------------\\multiply\ on\ the\ cross\\-------------\\8(6+v)=16(6-v)\\\\48+8v=96-16v\\\\8v+16v=96-48\\\\24v=48\ \ \ /:24\\\\v=2\ (km/h)\leftarrow Answer
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mariarad [96]
To solve the given equation, w need to review some rules:
(1) \ ln \ e = 1 \\ 
(2) \ ln \  b^{a} = a*ln \ b \\
(3) \ ln \ a + ln \ b = ln \ (ab) \\
(4) \ ln \ a - ln \ b = ln \  \frac{a}{b}  \\

The given equation is :
ln \  e^{ln \ x} + ln \  e^{ln \  x^{2}} = 2 \ ln \ 8
ln \ x * ln \ e + ln \  x^{2} * ln \ e = 2 \ ln \ 8  ⇒⇒⇒⇒ rule (2)
ln \ x + ln \  x^{2} = ln \  8^{2}  ⇒⇒⇒⇒ rule (1) and rule (2)

ln \ ( x*  x^{2} ) = ln \ 64          ⇒⇒⇒⇒ rule (3)
removing the nature logarithm from both sides

x^{3} = 64 =  4^{3}
∴ x = 4


So, the correct answer is option (2) ⇒⇒⇒⇒ x = 4


5 0
3 years ago
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lorasvet [3.4K]
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If our equation is in the form y = ax^2 + bx + c, you can find the minimum by using the equation min = c - b²/4a.

The first step is to determine whether your equation gives a maximum or minimum. This can be done by looking at the x² term.

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