Your answer is the 3rd option.
You must divide by π on both sides, therefore d=c/π
This is a freefall problem with an acceleration of -10m/s (a poor approximation of g :P)
a=g
v=gt+v0
h=gt^2/2+v0t+h0 where v0 is initial velocity and h0 is initial height.
You have:
h=-5t^2+10t+3
Since h0=3, the springboard is 3 meters above the water.
...
The diver hits the water when h=0.
5t^2-10t-3=0
Using the quadratic equation for simplicity:
t=(10±√160)/10
t=(10±4√10)/10 seconds, since t>0
t≈2.26 seconds (to nearest hundredth of a second)
So the diver hits the water about 2.26 seconds after (s)he leaves the springboard.
<span>Generate a function for the height of the cyliner as a function of radius. Use this function to generate a function of r for the material used. Take the derivative of that function, set it to zero, and solve for r.
</span><span>V=πr2h</span>h=d h=d=2r h=2r <span>V=πr22r
</span><span>V(r,h)=180.5=πr2h⟹h=<span>180.5/<span>πr2</span></span></span><span>⟹A(r)=r(r+h)=r2+<span>180.5/<span>πr
</span></span></span><span>A(r)=2r(2r+h)=4r2+<span>361/<span>πr
</span></span></span>
<span>A′(r)=8r−<span>361/<span>π<span>r2</span></span></span></span>