Answer:
Step-by-step explanation:
A) The equation for the volume of a sphere is 
As the diameter of each ball is 3 inches, that would mean that the radius of each is 1.5 inches.
Now we can plug our value into the equation
This would simplify to
V = 14.12716694 
B) The equation for the volume of a cylinder is 
As there are 3 balls in a container and the diameter of each is 3, that would mean that the height is 9 inches
Now we can plug in our values into the equation
This would mean that this equation would simplify to
27\pi 
C) To find the empty space, we must take the total volume, the volume of the cylinder, and subtract the volume of the tennis balls
This would mean that the equation would look like this
This would simplify to
42.41150082 of empty space.
Let the speed of river be x km/hr down stream.
Time = Distance / speed
Since river flows downstream, speed of boat down stream = Speed of boat + speed of river = (15 + x).
Since river flows downstream, speed of boat upstream = Speed of boat - speed of river = (15 - x).
Time Upstream - Time Downstream = 75 minutes
Time Upstream = 45 / (15 - x)
Time Downstream = 45 / (15 + x)
75 minutes = 75/60 = 5/4 hours
Time Upstream - Time Downstream = 75 minutes = 5/4 hours
45 / (15 - x) - 45 / (15 + x) = 5/4 Divide both sides by 45
1 / (15 - x) - 1 / (15 + x) = (5/4)*(1/45)
1 / (15 - x) - 1 / (15 + x) = 1/36
((15 + x) - (15 -x)) / (15-x)(15+x) = 1/36
(15 +x - 15 +x) / (15-x)(15+x) = 1/36
2x / (15-x)(15+x) = 1/36
(15-x)(15+x) = 2x*36
(15-x)(15+x) = 72x
225 - x² = 72x
0 = x² + 72x -225
x² + 72x -225 = 0 This is a
quadratic function, use a calculator that can solve the function, by
inputting the function.
x = 3, or -75. Since we are solving for speed, we can not have negative values.
x = 3 is the only valid solution.
Speed of the river = 3 km/hr downstream.
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