Oh damn... I need paper
And calculator...
Okay, (a) How much sand will the tide remove from the beach during this 6-hour period? Indicate units of measure.[I'm not writing the functions, it's early and I'm lazy, ha.]
fnInt(R(t),x,0,6)≈ 31.816 cubic yards
(b) Write an expression for Y(t), the total number of cubic yards of sand on the beach at time t.
Y(t)=S(t)-R(t)+2500
(c) Find the rate at which the total amount of sand on the beach is changing at time t=4.
What is this? rate of change... instantaneous? I think I forgot how to do this.
Wait a minute. Change of y over change of t at 4
So... Y(4)/4≈2498.091/4=624.52275 cubic yards per hour
(d) For 0≤t≤6, at what time t is the amount of sand on the beach a minimum? What is the minimum value? Justify your answers.
Find critical points S'(t)-R'(t)=0 at t=3.007 and t=.505
t=3.007, S(t)-R(t)=-2.49
t=.505, S(t)-R(t)=-.253
endpoint values
t=0, S(t)-R(t)=-2
t=6, S(t)-R(t)=2.11
So absolute minimum at t=3.007
I think I got most of them wrong... If they are, someone explain please?
Well now, off to do the rest of the calculus homework... woohoo... homework...
