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dem82 [27]
3 years ago
8

Evaluate csc (3pi/14) and cot (5pi/12) using a calculator.

Mathematics
1 answer:
ELEN [110]3 years ago
5 0
The drop down answers are
csc= 1.604
cot= .268
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An oil tank is leaking into a lake at a rate of 0.1 m3/day. The oil slick forms a semicircular disk whose center is at the leak
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Answer:

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Step-by-step explanation:

Volume of the slick =  0.5 x π r² h--------------------------------- (1)

Where r = radius of slick

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If 0.5m³ of oil leaked, then the radius of the semicircular slick can be calculated from equation (1)

V  =  0.5 x π r² h

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r²   =  10⁶/ π

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dV/dt =   πrh dr/dt  + 0.5π r² dh/dt----------------------------------- (2)

Asumming the film thickness is constant , equation (2) becomes

dV/dt =   πrh dr/dt-------------------------------- (3)

dV/dt = 0.1m³/day

r=  10³/√π

dr/dt= rate of expansion of the slick

Substituting  into (3);

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dr/dt = 0.1  x 10⁶/ ( π x 10³/√π)

       =  17.9479 m/s

       ≅  17.9  m/s

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