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Multinomial theorem |
2001-11-28 |
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From Murray:
Could you please state and explain the multinomial theorem (I already know the binomial theorem etc, to give you an idea of where i am)
Answered by Harley Weston. |
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Slope intercept form |
2001-11-27 |
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From A student:
what is slope intercept form?
Answered by Penny Nom. |
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Numerical problems |
2001-11-27 |
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From Yossi:
I am preparing a 45 minutes class for K-12 students. The problem is to show that algebraic equivalent expressions are not always numerically equivalent. In particular I would like to show one of these dangers: cancellation that occurs during the subtraction of nearly equal quantities. Do you have a good reference I could use to prepare my class. In particular to be able to show some examples and how one can avoid this type of error. I also would like to show examples with practical use. I tried to look up in the web but did not find anyhting appropriate.
Answered by Chris Fisher. |
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Original value |
2001-11-27 |
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From Lisa:
We are trying to find the original value of a product marked up by 10%. What is the formula to determine the original value?
Answered by Penny Nom. |
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Dual spaces |
2001-11-26 |
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From Hoda:
In the book "Linear Functional Analysis" from Epstein there is a proof (page 116) of the following theorem: The dual space of Lp is equal to Lq. Later, it is stated as a theorem without proof that for 1 <= p < +infinite, The dual space of lp is equal to lq.
Answered by Doug Farenick. |
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Ratios and proportions |
2001-11-26 |
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From Adam:
I am doing a project where I come to this website and ask a math expert about a certain topic. My topic is ratios and proportions. Can you please tell me what your job is and how you use ratio's and proportions in your job. Can you also please explain what ratios and proportions are.
Answered by Harley Weston. |
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A health club |
2001-11-25 |
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From Maria:
A health club with a membership of 650 people operates a running track and an indoor swimming pool. A survey of the membership indicates that 68% use the running track, 44% use the swimming pool, and 8% use neither. If a member is chosen at random, what is the prbability that the member uses: a) Both the track and the pool? b) Only the track?
Answered by Penny Nom. |
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L'Hopital's Rule |
2001-11-25 |
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From Mike:
I'm a high school senior. I'm in ap calculus and was wondering if you know the proof of L'Hopital's Rule? Our teacher said he has never been able to find it in a math book and was unable to derive it himself.
Answered by Claude Tardif. |
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Undetermined coefficients |
2001-11-22 |
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From Hoda:
The equation is: y" - 2y' + y = t et + 4 We need to use The method of Undetermined coefficients. I have tried assuming that the solution is Atet+Bet+C, but all I get is C=4 and I tried (At2+Bt+C)et+D, but again I get 0=0 when I calculate the first and second derivatives, so i get no information on the constants. Any suggestions?
Answered by Harley Weston. |
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Ratios |
2001-11-21 |
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From Mike:
Simplify these ratios. 7 1/4 inches to 2 feet. $0.02 per $1.75
Answered by Peny Nom. |
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Matrix |
2001-11-21 |
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From Hoda:
I have a question about matrix multiplication; well, actually, matrix division. I am assuming that matrices are divided the same as they are multiplied; that is, row by column. But what happens if you have to divide by zero? How does this affect the resulting matrix?
Answered by Patrick Maidorn and Penny Nom. |
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A tangent line |
2001-11-21 |
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From A student:
write an equation of the line tangent to the graph of
ey + ln(xy) = 1 + e at (e,1)
Answered by Harley Weston. |
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A hypercube |
2001-11-20 |
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From Ace:
Can I get a picture of a hypercube
Answered by Patrick Maidorn. |
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Rewriting and evaluating formulas |
2001-11-19 |
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From A conserned mother:
Due to the wide range of temperatures experienced in Canada, engineers who construct roads must allow for expansion and contraction of the road surface. The following formula is used to calculate the amount of expansion E to allow for: E= kL(T-t), where k is the constant of expansion for the road surface. L is the length of the section of highway in metres. T is the temperature of the air in degrees Celsius. t is the temperature, in degress Celsius, at which the section of the highway was constructed.
Answered by Walter Whiteley. |
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Cardinality of sets |
2001-11-19 |
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From Tania:
- Show that the cardinality of P(X) (the power set of X) is equal to the cardinality of the set of all functions from X into {0,1}.
- Show that (the cardinality of the natural numbers set) |N| = |NxNxN|.
- Show that the cardinality of the set of prime numbers is the same as the cardinality of N+
Answered by Walter Whiteley. |
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