a) R(t) is the rate at which sand is being removed by cubic yards/hour, so if you take the integral, it would give you the amount of sands by cubic yards (which the question is asking for )
eq: fnInt (2+5sin((4 pi t)/25), x, 0, 6) = about 31.816, so at t = 6, 31.816 cubic yards of sand has been removed
b) asking for amount of sand, so integral is needed,
fnInt(S(t)), x , 0, 6) - fnInt (R(t)), x, 0, 6) + 2500
c) asking for the rate, so no need to integrate, just plug in t=4
so... S(4) - R(4) = -1.909,
so at t = 4, the amount of sand is decreasing by 1.909 cubic yards/hour
d) Asking for amount of sand, so the graph of S(t) - R(t) would give you the slope, when the slope changes from - to +, you'll have a min,
at t= 5.1179 you have a minimum, that is where slope changes from - to + on the graph of S(t) - R(t) (slope graph)
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i like how accurate you are with you numbers :)
ReplyDeletewow. hey.. you're the third blog that i've read.. and so far, we've been getting the same answers for parts a, b but for part c,d.. i think i am a little lost. because my answer is different from all your...
ReplyDelete:( i got x=3.007 for d....
hey... i checked my word.. now i got the same answer as you did :)
ReplyDeletealot of people got different answers for the d part. but i think you got it right.
ReplyDeletethats really good
for part d, i did it a different way
ReplyDeleteinstead of graphing S(t) - R(t), i graphed them seperately
i dont know if i did right though.. ;)