If I read the problem correctly, you end up giving all 24 cans to the students.
Why not just count the ways this can be done?
first you must hand two cans to each, as they must receive at least two cans.
Then figure out how to distribute the remaining 18 among three students.
label them 1, 2...
In your first equation, where did you get the 48 from? Maybe it should be 52. Then at t=4weeks, you would have t=4/52 years. I think your answer is in terms of years, not weeks.
Same for the second equation. You converted 18 months into 1.5 years. The solution you have is in terms of grams...
so, by the constraint you have two numbers which add up to twenty. Call one x, and the other 20-x. square both, and add.
what do you know about a quadratic that gives a maximum or minimum?
what kind of class is this problem from? A little context might help know where to go. I might be able to help you with showing a midpoint convex function is convex if it is continuous..
My first observation: You do not know the speed of the plane. If you assign a vector <1,1> here, you may be saying that the plane is traveling at sqrt(2) ground speed.
adding the big vector, you can see you are actually reversing the direction of the plane.
I think a good assumption would be...
The wind from the west is moving east.
I think that is the problem here.. the east wind is contributing to the horizontal component you posted. In other words, I think you may want to try adding instead of subtracting.
what vectors did you add? You have to separate the original vector into horizontal and vertical components. then add the individual horizontal and vertical components.
the wind form the west, does not add or subtract from the vertical component.
A reasonable answer as to ground speed would...
It is a lot easier to show the limit does not exist. All you have to do is find one path towards (0,0) that produces a limit that is not zero. Maybe you could try a quadratic, or a cubic..
Or you could use the hint. You have an equation of a line. Find the coordinates for two points. If you have two coordinates, can you find the vector?
Matrices transform vectors to vectors by multiplication.
excuse lack of latex code here.
from my general statistics book:
1. Yes, the mean of x(bar) is the population mean.
2. The standard deviation of the sample is sigma/sqrt(n).
You need to calculate the z score of 610. Then use this with standard tables, or calculator to find P(.67<Z<Infinity).
A few mathematicians tried to reduce math and reality itself to logic. Bertrand Russel comes to mind..
Now they call it naive set theory.
If the barber of Seville is the only one to cut the beards of unshaven men of Seville who do not shave themselves. The barber is clean cut..
I'm looking for old lecture notes from Calculus classes in the 1920's and prior. Or lesson plans. Or anything to establish the identity of those enrolling in the courses then, or why they were taking the course.
as far a "lucky" is concerned.. gawd almighty.. with the economy the way it is, an an older normally non-employable individual being offered this kind of opportunity..
well, what can I say..
I just hope I can "deliver"..
I think I can..
As far as teaching is concerned.. I have no problem helping those with algebra concepts as "rise over run" and such.. it was as hard for me then, as complex analaysis was last semester.
I don't think I'll be dealing with epsilon-delta concepts with students, for at least a couple of years...
Thanks for the "advice".. I think..
:biggrin:
now for the important item, or items..
living on a stipend. "It's (almost) a living.."
so what kind of scams am I to expect from fellow program participants? Will I find them pitching pennies on the local corner or something like that...
I have been accepted into a graduate program at local university, along with being offered a teaching assistantship. Now comes the choice of what courses to choose.
The master's program requires thirty credits of course work, along which includes introduction to real analysis, intro to...
I think almost anything you can find would help. I personally like something written in front of me. Almost anything published in the last fifty years won't exactly steer you in the wrong direction..
anything that deals with differential and integral calculus would probably help..
MIT...
The book name is worn off the cover.. on the title page it's just "Calculus".
Looks like it really was published in U.S.
New York
John Wiley and Sons Inc
Stewart's was really good though.
This old book didn't go into a lot of explanation about the algebra involved. Forced me to go to other...
I first studied Calculus on my own from an old book from the book sale here.. it was published in something like 1927 or so.
H.B. Phillips, PHD
Published in London, wonder how it made it's way to the states..
1927.
The only difference between this and the class I later took.. they showed me...
I love the local friend of the library book sale. I have a library full of stuff from these sales from geometry to number theory, tensor analysis, advanced calculus, all kinds of stuff..
the advanced calculus book by Solkonikoff and the other by Apostel really helped prepare me for real...