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2 answers:
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Answer:
Hence, option: B is correct (11.02 seconds)
Step-by-step explanation:
Spencer hits a tennis ball past his opponent. The height of the tennis ball, in feet, is modeled by the equation h(t) = –0.075t2 + 0.6t + 2.5, where t is the time since the tennis ball was hit, measured in seconds.
Now we are asked:
How long does it take for the ball to reach the ground?
i.e. we have to find the value of t such that height is zero i.e. h(t)=0.
or
i.e. we need to find the roots of the above quadratic equation.
on solving the equation we get two roots as:
t≈ -3.02377 and t≈11.0238
As time can't be negative; hence we will consider the value of t as t≈11.0238.
Hence it takes 11.02 seconds for the ball to reach the ground.
Hence option B is correct (11.02 seconds).
I assume there are some plus signs that aren't rendering for some reason, so that the plane should be 
.
You're minimizing
subject to the constraint 
. Note that 
and 
attain their extrema at the same values of 
, so we'll be working with the squared distance to avoid working out some slightly more complicated partial derivatives later.
The Lagrangian is
Take your partial derivatives and set them equal to 0:
Adding the first three equations together yields
and plugging this into the first three equations, you find a critical point at
.
The squared distance is then
, which means the shortest distance must be 
.
You're minimizing
The Lagrangian is
Take your partial derivatives and set them equal to 0:
Adding the first three equations together yields
and plugging this into the first three equations, you find a critical point at
The squared distance is then