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viva [34]
3 years ago
11

At noon, ship A is 170 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 20 km/h. How fast is

the distance between the ships changing at 4:00 PM?

Mathematics
1 answer:
garik1379 [7]3 years ago
8 0
Check the picture below.

now, keep in mind that ship B is going at 20kph, thus from noon to 4pm, is 4 hours, so it has travelled by then 20 * 4 or 80 kilometers, thus b = 80.

whilst the ship B is moving north, the distance "a" is not really changing, and thus is a constant, that matters because the derivative of a constant is 0.

\bf c^2=a^2+b^2\implies \stackrel{chain~rule}{2c\cfrac{dc}{dt}}=0+2b\cfrac{db}{dt}\implies \cfrac{dc}{dt}=\cfrac{b\frac{db}{dt}}{c}
\\\\\\
\begin{cases}
\frac{db}{dt}=20\\
c=10\sqrt{353}\\
b=80
\end{cases}\implies \cfrac{dc}{dt}=\cfrac{80\cdot 20}{10\sqrt{353}}\implies \cfrac{dc}{dt}=\cfrac{160}{\sqrt{353}}
\\\\\\
\textit{and rationalizing the denominator}\implies \cfrac{160\sqrt{353}}{353}

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Step-by-step explanation:

Given the geometric sequence

7, 14, 28, ...

We know that a geometric sequence has a constant ratio 'r' and is defined by

a_n=a_1\cdot r^{n-1}

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Computing the ratios of all the adjacent terms

\frac{14}{7}=2,\:\quad \frac{28}{14}=2

The ratio of all the adjacent terms is the same and equal to

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now substituting r = 2 and a₁ = 7 in the nth term

a_n=a_1\cdot r^{n-1}

a_n=7\cdot \:2^{n-1}

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a_n=7\cdot \:2^{n-1}

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Step-by-step explanation:

|3x + 15| > 21, |3x + 15| < -21

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------------------   -------------------

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÷3  ÷3               ÷3     ÷3

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