Find A ∩ B given A = {the Integers} and B = {the Rational numbers}.
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The time it will take the tank to be empty is;
<em><u>t = 1.26 minutes</u></em>
The image of the initial tank is missing and so i have attached it.
Let's call the area of the hole be A_h
- From conservation of energy, velocity at which water leaves the tank is; v = √2gh
Thus, volumetric rate; = A_h(√2gh)
- If we consider possible friction and contraction, we differentiate to get;
dV/dt = -cA_h(√2gh)
Now, volume of tank is;
V = ¹/₃πr²h
V' = dv/dt = (¹/₃πr²h)dh/dt
Thus; -cA_h(√2gh) = (¹/₃πr²h)dh/dt
- Integrating to get t gives us;
t = (2(√H - √h))/(3c√2g × (r'/r)²)
where;
r' is radius of circular hole = 4 inches = 0.333 ft
h = 0 since the tank has a hole
c = 0.6
g = 32 ft/s²
H = 8 ft
- Since the vertex has an angle of 60°, then a line of symmetry across it divides the angle into two which will be 30° each. We can use trigonometry to find the current radius r.
Thus; r/H = tan 30°
r = 8 tan 30°
r = 4.6188 ft
Thus;
t = (2(√8 - √0))/(3 × 0.6(√2 × 32) × (0.333/4.6188)²)
t = 75.5757 seconds
Converting to minutes gives; t = 1.26 minutes
Read more at; brainly.com/question/24319549
