How much sand is begin removed: use the formula R(t)=2+5sin(4piet/25)
nInt(2+5sin(4piet/25)),t,0,6) = 31.815931 cubic yards of sand [exactly how you input it into a TI-89 calc.]
(b) Write an expression for Y(t), the total number of cubic yards of sand on the beach at time t.
At time t=0, the beach contains 2500 cubic yards of sand.
Create a new formula with the formulas given.
Y(t)=(15t/(1+3t))-2+5sin(4piet/25) dt +2500 (add the 2500)
(c) Find the rate at which the total amount of sand on the beach is changing at time t=4.
find the derv. of y(t)
Y'(t)=(15t/(1+3t))-2+5sin(4piet/25)
plug in 4 for t
Y'(4)=(15(4)/(1+3(4)))-2+5sin(4pie(4)/25)
4.6153846- 6.5241353
= -1.908yard^3 per hour
Y'(t)=(15t/(1+3t))-2+5sin(4piet/25)
plug in 4 for t
Y'(4)=(15(4)/(1+3(4)))-2+5sin(4pie(4)/25)
4.6153846- 6.5241353
= -1.908yard^3 per hour
(d) For 
, at what time t is the amount of sand on the beach a minimum? What is the minimum value? Justify your answers.
need to find where t is a minimum...
equal Y'(t)= 0 to find critical points.
nDeriv or Y(t)
in the interval of 0 to 6...t= 5.117
min value at 2492
im not sure if that's right though...
, at what time t is the amount of sand on the beach a minimum? What is the minimum value? Justify your answers.need to find where t is a minimum...
equal Y'(t)= 0 to find critical points.
nDeriv or Y(t)
in the interval of 0 to 6...t= 5.117
min value at 2492
im not sure if that's right though...
hmmm. for a and b i got the same answers as you. but for c and d.. its kinda different. this is what i did for c:
ReplyDeletey'(t) = nDeriv((15t/(1+3t)) - (2+5sin(4π t/25) + 2500)
y'(4)= 1.159 cubic yard/hour/hour
i think your mistake is forgetting to use ( ) around (2+5sin(4π t/25) so the negative in the front will also apply to the 5sin...
and because of that, it might have been the reason that leads to how you got the answer for D.
but I might be wrong :)
hi tefani! i got all the same answers as you...!
ReplyDeleteHOwever u should explain more how you got the critical point t=5.117 and rember the endpoints 0 and 6 are critical points also :)
I got the same answers as you too steph!! But dont forget to explain why you know it is a minimum! c(: And dont forget that they are approximations! (:
ReplyDeleteGood job !
ReplyDeleteThis just needs a little more explanation, make sure you show that you know why you're doing what you're doing ! :]