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Have the sons ride each others horses. That way they're motivated to win with the horse they're on so the horse they own doesn't. Or tie up the sons and strap them to the horses. I like that answer too.
didn't read all the way to the bottom i guess...
Hi all, stuck on a related rate problem that i could use some help with. Basically I need to find a formula for the change of height of the water level in a sphere that's being filled at a constant volume. Starting with an empty sphere (r = 1.25in) water is flowing into the sphere at a constant rate (dV/dt = 1.3635 in^3/sec) and I need to find the rate of change of the height of the water level (dh/dt) as it related to time. Struggling because when I differentiate the formula for a spherical cap, V = ((pi*h^2)/3)(3r-h), it becomes something that isn't very easy to work with. Unlike a cylinder, where the volume of liquid is also a cylinder, or a cube, where the fluid volume is also a prism, obviously a partially filled sphere is not a sphere. I think this is the source of my issues. Help would be appreciated! Thanks.
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