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3 years ago

Can anyone help me on this one? Thank you in advance!

Mathematics

1 answer:

vampirchik [111]3 years ago

7 0

$\bf \cfrac{4}{2(x-3)}=\cfrac{5}{3(14-x)}\implies \stackrel{\textit{distributing in the denominators}}{\cfrac{4}{2x-6}=\cfrac{5}{42-3x}} \\\\\\ 4(42-3x)=5(2x-6)\implies \stackrel{\textit{distributing again}}{168-12x=10x-30}\implies 198=22x \\\\\\ \cfrac{198}{22}=x\implies \boxed{9=x}$

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The value is $W= 2640 \ ft \cdot lb$

Step-by-step explanation:

From the question we are told that

The weight of the bucket is $F = 5 lb$

The depth of the well is $x_1 = 60 \ ft$

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The rate at which the bucket with water is pulled is $v = 1.5 \ ft/s$

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Generally the workdone is mathematically represented as

$W = \int\limits^{x_1}_{x_o} {G(x)} \, dx$ ]

Here G(x) is a function defining the weight of the system (water and bucket ) and it is mathematically represented as

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Here I is the rate of water loss in lb/ft mathematically represented as

$I = \frac{r}{v}$

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=> $G(x) = 47- 0.1x)$

$W = \int\limits^{60}_{0} {47- 0.1x} \, dx$ ]

=> $W = [47x - \frac{0.1x^2}{2} ]|\left 60} \atop {0}} \right.$

=> $W= [47(60) - 0.05(60)^2]$

=> $W= 2640 \ ft \cdot lb$

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