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-Dominant- [34]
3 years ago
11

Three sailors were marooned on a deserted island that was also inhabited by a band of monkeys. The sailors worked all day to col

lect coconuts but were too tired that night to count them, They agreed to divide them equally the next morning. During the night, one sailor woke up and decided to take his share. He found that he could make three equal piles, with one coconut left over, which he threw to the monkeys. Thereupon, he put his own share in a pile down the beach, and left the remainder in a single pile near where they all slept. Later that night, the second sailor awoke and, likewise, decided to take his share of coconuts. He also was able to make three equal piles, with one coconut left over, which he threw to the monkeys. Somewhat later, the third sailor awoke and did exactly the same thing with the remaining coconuts. In the morning, all three sailors noticed that the pile was considerably smaller, but each thought that he knew why and said nothing. When they then divided what was left of the original pile of coconuts equally, each sailor received seven and one was left over, which they threw to the monkeys. How many coconuts were in the original pile
Mathematics
1 answer:
noname [10]3 years ago
7 0

Step-by-step explanation:

x-the initial number of coconuts

x=3y+1

2y=3z+1

2z=3×7+1=>z=11=>y=17=>x=52

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Find thd <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D" id="TexFormula1" title="\frac{dy}{dx}" alt="\frac{dy}{dx}" a
NARA [144]

x^3y^2+\sin(x\ln y)+e^{xy}=0

Differentiate both sides, treating y as a function of x. Let's take it one term at a time.

Power, product and chain rules:

\dfrac{\mathrm d(x^3y^2)}{\mathrm dx}=\dfrac{\mathrm d(x^3)}{\mathrm dx}y^2+x^3\dfrac{\mathrm d(y^2)}{\mathrm dx}

=3x^2y^2+x^3(2y)\dfrac{\mathrm dy}{\mathrm dx}

=3x^2y^2+6x^3y\dfrac{\mathrm dy}{\mathrm dx}

Product and chain rules:

\dfrac{\mathrm d(\sin(x\ln y)}{\mathrm dx}=\cos(x\ln y)\dfrac{\mathrm d(x\ln y)}{\mathrm dx}

=\cos(x\ln y)\left(\dfrac{\mathrm d(x)}{\mathrm dx}\ln y+x\dfrac{\mathrm d(\ln y)}{\mathrm dx}\right)

=\cos(x\ln y)\left(\ln y+\dfrac1y\dfrac{\mathrm dy}{\mathrm dx}\right)

=\cos(x\ln y)\ln y+\dfrac{\cos(x\ln y)}y\dfrac{\mathrm dy}{\mathrm dx}

Product and chain rules:

\dfrac{\mathrm d(e^{xy})}{\mathrm dx}=e^{xy}\dfrac{\mathrm d(xy)}{\mathrm dx}

=e^{xy}\left(\dfrac{\mathrm d(x)}{\mathrm dx}y+x\dfrac{\mathrm d(y)}{\mathrm dx}\right)

=e^{xy}\left(y+x\dfrac{\mathrm dy}{\mathrm dx}\right)

=ye^{xy}+xe^{xy}\dfrac{\mathrm dy}{\mathrm dx}

The derivative of 0 is, of course, 0. So we have, upon differentiating everything,

3x^2y^2+6x^3y\dfrac{\mathrm dy}{\mathrm dx}+\cos(x\ln y)\ln y+\dfrac{\cos(x\ln y)}y\dfrac{\mathrm dy}{\mathrm dx}+ye^{xy}+xe^{xy}\dfrac{\mathrm dy}{\mathrm dx}=0

Isolate the derivative, and solve for it:

\left(6x^3y+\dfrac{\cos(x\ln y)}y+xe^{xy}\right)\dfrac{\mathrm dy}{\mathrm dx}=-\left(3x^2y^2+\cos(x\ln y)\ln y-ye^{xy}\right)

\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x^2y^2+\cos(x\ln y)\ln y-ye^{xy}}{6x^3y+\frac{\cos(x\ln y)}y+xe^{xy}}

(See comment below; all the 6s should be 2s)

We can simplify this a bit by multiplying the numerator and denominator by y to get rid of that fraction in the denominator.

\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x^2y^3+y\cos(x\ln y)\ln y-y^2e^{xy}}{6x^3y^2+\cos(x\ln y)+xye^{xy}}

3 0
3 years ago
I need help plz giving brainlist
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Answer:

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Step-by-step explanation:

it is essentially 5*5*5*5

6 0
2 years ago
Form a sequence that has two arithmetic means between -1 and 59.
9966 [12]

Answer:

Correct choice is B

Step-by-step explanation:

For the numbers -1 and 59, find the difference 59-(-1):

since 59-(-1)=60 and \dfrac{60}{3}=20 (two arithmetic means tells you there will be three intervals), two arithmetic means will be

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The only correct sequence is -1, 19, 39, 59.

7 0
3 years ago
Read 2 more answers
A storage container consists of a box of length 90cm, width 42 cm and height 34 cm, and a lid
Ivanshal [37]

Answer:

20079.05 cm^2,

Step-by-step explanation:

Surface area of the box without the lid

=  90*42 + 2(90*34) + 2(42*34) = 12756.

Now find Surface area of the half cylinder:

The diameter of the 2 half circles = 42 so the radius = 21.

The area of the lid  

= 2 + 1/2 π (21)^2 + π r * 90

= 7323,052

Total = 20079.052

 

7 0
2 years ago
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liubo4ka [24]
You have 50 ways because if there are 10 different types of prizes with 5 prizes you can just multiply that to get your different ways to select the prizes.
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3 years ago
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