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The Work required to pump water out of the spout would be equal to 464,062.5 π
<h3>How can we calculate the work done?</h3>Given data :
3 ft, 4 ft, 5 ft A right triangular prism tank with a spout is given.
weight of water = 62.5 Ib/ft³
inner radius ( r ) = 3 x 2 =6 ft
Outer radius ( R ) = 3 x 4 = 12 ft
Height ( h ) = 3 x 5 = 15 ft
To determine the work required to pump water out of the spout
y = Vertical distance
dv = cross-section volume
dw = weight
The radius of the tank
Radius = ( r - R ) y/h + R
Radius = ( 6 - 12 ) y/15 + 12
So, Radius = 12 - 0.4y
dv ( cross section volume )
Weight of cross-section ( dw ) = 62.5 ( 12.5 - 0.4y )² π dy
The work done to pump water out of the spout will be
Work done = ∫¹⁵₀ 62.5 ( 12.5 - 0.4y )² π dy
∴ Work done ( W ) = 464,062.5
Hence we can conclude that the Work required to pump water out of the spout would be 464,062.5 π
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Answer:
Both candles will have the same height after 4 hours.
Step-by-step explanation:
The equation for the amount of candle remaining can be given by the following equations:
In which Q(t) is the amount after t hours, Q(0) is the initial amount and a is how much it decreases, in inches, per hour.
Red candle:
8 inches tall and burns at a rate of 7 divided by 10 inch per hour. This means that . So
Blue candle:
6 inches tall and burns at a rate of 1 divided by 5 inch per hour. This means that . So
After how many hours will both candles be the same height ?
This is t when
Multiplying by (-1)
Both candles will have the same height after 4 hours.