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Maclaurin series again |
2000-09-23 |
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From Jason Rasmussen:
I suppose my confusion comes into play when I am trying to figure out where the xn term comes from. I know that the Power Series notation is directly related to the Geometric Series of the form sigma [ brn ] where the limit is b/(1-r) for convergence at | r | <1. Therefore, the function f(x) needs to somehow take the form of b/(1-(x-a)), which may take some manipulation, and by setting r = (x-a) and b = Cn, we get the Geometric Series converted to the Power Series. Taking the nth order derivative of the Power Series gives Cn = fn(a)/n!. There must be a gap in my knowledge somewhere because I cannot seem to make f(x) = ex take the form of f(x) = b/(1-(x-a)). Maybe I should have labelled my question as "middle" because it may be more of a personal problem with algebra and logarithms. Or, am I to assume that all functions can be represented by sigma [fn(a) * (x-a)n / n!]?
Answered by Harley Weston. |
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BEDMAS |
2000-09-22 |
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From Monica Zimmer:
In the Math rule BEDMAS does it matter if you do the division or the multiplication first?
Answered by Penny Nom. |
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Mode |
2000-09-22 |
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From James Barton:
I have always been told that a mode is the "one" number that appears most in the set of numbers: ex.{1,3,4,6,3,2} the mode is 3. What if you have {1,1,3,4,5,5}is there a mode. I was taught long ago that there is no mode, Not i am having to teach there is two modes. 1 and 5. If this is the case if we have {1,1,2,2,3,3,4,4,5,5} that every number is the mode. True or false. This is being ambigiuous if we say all are the mode. Because no one number is used more than the others.
Answered by Claue Tardif and Harley Weston. |
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Permutations and Multiplication Principle |
2000-09-22 |
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From Candice:
A forester selects 4 pink and 4 white dogwoods. The trees are to be planted in row. If a tree is distinguished by color only, in how many ways can the eight dogwoods be planted? How many of these arrangements have at least two trees of the same color side by side?
Answered by Denis Hanson and Claude Tardif. |
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Dividing a region in half |
2000-09-21 |
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From Kerry:
There is a line through the origin that divides the region bounded by the parabola y=x-x2 and the x-axis into two regions with equal area. What is the slope of the line?
Answered by Penny Nom. |
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A Maclaurin series |
2000-09-21 |
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From Jason Rasmussen:
I have a question regarding power series notation for certain functions within the interval of convergence.
Answered by Harley Weston. |
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Leap Year |
2000-09-20 |
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From Jennifer:
The earth revolves around the sun in 365.24 days. How does our calendar deals with the extra 0.24 day?
Answered by Penny Nom. |
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A cycloid in Cartesian form |
2000-09-20 |
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From Billy:
The parametric equation of cycloid is given:
x=r(t-sint)
y=r(1-cost) How to eliminate t?
Answered by Harley Weston. |
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Arithmetic in base 5 |
2000-09-20 |
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From Lesley Emerson:
my daughter is 9 and has been aske to solve the following in base 5 3+2
4+10
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Answered by Penny Nom. |
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A proof that 1=2 |
2000-09-19 |
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From sporky:
Why does the proof for 1=2 not work? x = 1
x2 = 1
x = x2
1 = 2x (derivitive)
1 = 2(1)
1 = 2 ???
please tell me where the false logic is.
Answered by Walter Whiteley. |
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Order of operations |
2000-09-19 |
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From Nicole:
the problem is, 4x8-18 divided by 6= do you solve this by doing 4x8=32 then by dividing 18by 6= 3, then subtracting 3 from 32 = 29? If not what is the order of operation?
Answered by Penny Nom. |
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Circular Permutations |
2000-09-18 |
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From J. Stuart:
I am able to understand the simple theory behind circular permutations (that is, there are (n-1)! ways to arrange n people in a circle. One question, however, is giving me some difficulty. It reads: In how many ways can four married couples be arranged around a circular table if each man must sit beside his wife? Any suggestions you have would be greatly appreaciated.
Answered by Penny Nom. |
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Buying art supplies |
2000-09-18 |
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From Travis:
An art teacher buys exactly 100 items at this sale, and the total cost before tax is $100. She buys at least one of each item. How many of each item does she buy? Markers $0.50
Sketch Pads $3.00
Paint Sets $10.00
Answered by Denis Hanson. |
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Probability of a square |
2000-09-18 |
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From Nick:
What is the probability that four different points chosen at random from the fifteen equally-spaced points shown are the vertices of a square? I need to have my answer expressed as a common fraction. Help! I don't know how to write it.
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Answered by Penny Nom. |
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Review problems |
2000-09-18 |
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From Dee:
A card is selected from an ordinary deck of cards. What is the probability of. . . selecting 2 aces in a row? If you toss two dice, what would be your probability of the following?
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Answered by Penny Nom. |
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