neurosis

Members

4

1. "Work" problem

I believe you guys are correct; the bag has to be assumed negligable. There really isn't any other way of solving for the bag. I just was worried maybe I missed something! But I do see now that I was most likely making it more complicated than it is.
2. Pre-Calculus before I take it.

Yea, it's basically a review of algebra and geometry, so you'll probably do very well. Here's some specifics that I remember: *Composition functions and how to compute them. Example of a composition function is cos x^2, since cos x is a function and x^2 is also one. *learning how to graph functions by hand, and how to shift them up, down, left, right given an equation. Example: y = x^2 + 5 ... you take the basic parabola x^2, which has it's vertex at the origin, and you shift it up 5 units so that its vertex is at (0, 5) * The conic sections (parabola, circle, ellipse, hyperbola) and how to graph them and what their equations are. * Logranithms and exponential functions *lograithmic expansion and contraction (ex: log 5 + log 7 = log 35, because 7*5 is 35 and they have the same base) * basic series That's mostly what comes to my mind. You won't get into any actual calculus in pre-calc...it's all just algebra and geometry that you will need to understand when you do get to calculus. If you want to learn a few things about actual calculus itself, I can give you a few starting points. I can't think of any websites off the top of my head, but I'm sure you could do a google search and find some.
3. "Work" problem

Here's a problem I recently came across in a very old calculus book. Unfortunately, it was an even-number, and I can't quite figure out for sure how to solve it. A bag of sand originally weighing 144 lbs is lifted at a constant rate of 3ft/min. The sand leaks out uniformly at such a rate that half the sand is lost when the bag has been lifted 18 ft. FInd the work done lifting the bag this distance. The thing about it is this would be easy to solve, except that we don't know the weight of the bag *alone* and can not just assume that it's negligable. I know that the work is force times distances, and that you use infinite sums to find the work over that particular distance (since it's changing) so we have an integral from 0 to 18 of the f(X)...but what is the function of x? THe sand is all gone by 36 ft (in 12 minutes) but we don't know the weight of the bag, so therefore we don't know the weight of the sand that was lost. This is frustrating! Does anyone have any idea? (I originally thought Integral from 0-18 of 144-4x, but I don't feel right about that)
4. A plane wreck in a desert

Here's a tricky optimization problem. I'm having a hard time figuring it out and it's driving me CrAzY!! I know that I have to set the first derivative equal to zero to find the minimum; my problem is figuring out the equations involved. Anyone have any ideas? I'm getting really frustrated with it. The wreck of a plane in a desert is 18 miles from the nearest point "A" on a straight road. A truck starts for the wreck at a point on the road that is 40 miles distant from A. If the truck can travel at 70mph on the road and at 35mph on a straight path in the desert, how far from point "A" should the truck leave the road to reach the wreck in minimum time?
×
×
• Create New...