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Maths!!! Help Needed
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| Louk |
I have a maths problem that is really bugging me and I do not know how to do it - can someone explain - it is in two parts.
A can of orange juice is in the form of a right-circular cylinder and holds a volume of 1000 cm^3 of fluid. What dimensions of the can will give the smallest surface area?
Part 2
A body moves in a straight line with acceleration of magnitude m/s^2, given by a = t + 3 at time [i] t seconds. If Initially the speed of the body is 2 m/s, find it's speed after 2 seconds and the distance it travels in the next 2 seconds.
This problem has me stumped any help at all??
Louk |
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| Noctone |
| quote: | Originally posted by Louk
I have a maths problem that is really bugging me and I do not know how to do it - can someone explain - it is in two parts.
A can of orange juice is in the form of a right-circular cylinder and holds a volume of 1000 cm^3 of fluid. What dimensions of the can will give the smallest surface area?
Part 2
A body moves in a straight line with acceleration of magnitude m/s^2, given by a = t + 3 at time [i] t seconds. If Initially the speed of the body is 2 m/s, find it's speed after 2 seconds and the distance it travels in the next 2 seconds.
This problem has me stumped any help at all??
Louk |
I take it this is a calculus class? These seem like classic calc. problems to me.
Part 1)
Surface area total = SA bottom + SA top + SA cylinder wall
= pi*r^2 + pi*r^2 + 2*pi*r*h
Volume = pi*r^2*h = 1000 is our constraint equation.
h = 1000/(pi*r^2)
Thus SA(r) = 2*pi*r^2 + 2000/r
I figure you should at least do part of the problem, so I'll leave the rest to you (hint: use derivatives to find the minimum).
Part 2)
a(t) = v'(t), thus v(t) = integral(a(t))
a(t) = t + 3, thus v(t) = (t^2)/2 + 3t + C
taking C = v(0), v(t) = (t^2)/2 + 3t + v(0) = (t^2)/2 + 3t + 2
You should be able to do the rest. |
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