 |
|
|
|
|
|
|
|
|
Two Problems |
2004-07-12 |
|
From Justina:
i cant figure out the range of this equation in interval form because the highest point seems to be a decimal. please help f(x) = x + sqrt(4-x2)
.............................................................................
Building Design A circular air duct of diameter D is fit firmly into the right-angle corner where a basement wall meets the floor (see figure). Find the diameter of the largest water pipe that can be run in the right-angle corner behind the air duct.
Answered by Claude Tardif and Penny Nom. |
|
|
|
|
|
|
The tangent of theta |
2004-07-10 |
|
From Jacob:
P is a point on a unit circle with coordinates(0.6,0.8). Find tan of theta. My book shows me how to do it,"tan of theta=opp./adj.=0.8/0.6=4/3,"and leaves it as that's the answer(4/3).When do we know from a problem to find the angle measure (in this case, the angle measure of theta) and how do we know when to give something like 4/3 without converting it to the angle measure?
Answered by Penny Nom. |
|
|
|
|
|
|
Four digits |
2004-07-10 |
|
From Rob:
I am always interested to know how the for digit works. I mean, you have correctly put it that the total numbers obtain from 0000 thru 9999 are 10,000. My question is, is there any simple formula to turn this simple 4 figures of say: 1234.
Answered by Penny Nom. |
|
|
|
|
|
|
The circle through three points |
2004-07-06 |
|
From Jim:
I am a student trying to solve math problem. I'd like to calculate the radius of the circle that exactly fits any three points. If the points are (X1,Y1), (X2,Y2), and (X3,Y3), what is the radius of the circle that contains those three points?
Answered by Penny Nom. |
|
|
|
|
|
|
Vectors |
2004-07-06 |
|
From Annie:
a=3i-j+2k and b=i+3j-2k, determine the magnitude and direction cosines of the product vector and show that it is perpendicular to a vector c=9i+2j+2k.
Answered by Chris Fisher. |
|
|
|
|
|
|
An ineqlality with absolute values |
2004-07-05 |
|
From Uneeza:
abs(x2 - 4x) > 3
Answered by Claude Tardif. |
|
|
|
|
|
|
Factoring integers |
2004-07-02 |
|
From A student:
After looking at all the info I could get about NFS, I still have some questions that are unsolved:
First of all: If someone found an algorithm that has a worst case running time of N*Log(N) to factor an integer n into his divisors, would it be quicker or slower then the number field sieve algorithm?
secondly, what exactly is the time complexity of the Number Field Sieve algorithm, if I would factor an integer n?
Answered by Claude Tardif. |
|
|
|
|
|
|
Choosing 5 numbers from 1,...,36 |
2004-06-30 |
|
From A lottery player?:
how many combinations are there for the numbers 1thru 36 when only using each number once in groups of five
Answered by Penny Nom. |
|
|
|
|
|
|
Simplify |
2004-06-27 |
|
From Tiff:
Simplify:
-3x (x2 + 2)
(x + 2) (x + 3)
Answered by Penny Nom. |
|
|
|
|
|
|
Aunt Lucy's letter |
2004-06-27 |
|
From Olivia:
"Dear bob,
now that i am getting on (70 today). i want to give you some of my money, i shall give you a sum each year, starting now. you can choose which of the following schemes you would like me to use.
a) £100 now, £90 next year,£80 the yaer after and so on.
b) £10 now, £20 next year, £ 30 the next year and so on.
c) £10 now, 1.5 times as much next year, 1.5 times as much the year after that and so on.
d)£1 now, £2 next year, £ 4 the year after, £8 the year after and so on.
of course these schemes will only operate while i am alive. i look forward to hearing which scheme you choose and why!
Best wishes,
Aunt Lucy."
Answered by Penny Nom and Claude Tardif. |
|
|
|
|
|
|
Undercapatalized small businesses |
2004-06-26 |
|
From Greg:
Suppose that 30% of all small businesses are undercapitalized. 40% of all
undercapitalized small businesses fail and 20% of all small businesses that
are not undercapitalized fail. A small business is chosen at random. The
probability that the small business succeeds if it is undercapitalized is? Greg
Answered by Penny Nom. |
|
|
|
|
|
|
Pick a number greater than 1 |
2004-06-25 |
|
From A student:
I understand that when you pick a number greater than 1 and less than 10; multiply it by 7 and add 23, then add the digits of that number until you get a one digit number. Then multiply that number by 9, add the digits of that number until you get a one digit number, subtract 3 from that number and divide the difference by 3; that this process will always give you the result of 2. Does this have a name or theory for it as to why the answer will always be 2?
Answered by Penny Nom. |
|
|
|
|
|
|
(a+b) + 5i = 9 + ai |
2004-06-25 |
|
From Josh:
The question which someone gave you (a+b) + 5i = 9 + ai question) gave me trouble.
Answered by Penny Nom. |
|
|
|
|
|
|
(ln(50/x)) / (ln(40/x)) = a |
2004-06-21 |
|
From Un eleve:
(ln(50/x)) / (ln(40/x)) = a = constante
comment extraire la variable x ???
Answered by Claude Tardif. |
|
|
|
|
|
|
How much loam to fill a hole? |
2004-06-19 |
|
From Harry:
Can you tell me how much loam I would need to fill a hole 15 feet in dia. x 6 inches deep.
Answered by Penny Nom. |
|
|
