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A triangle and a circle |
2003-03-21 |
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From Jynks:
We need a formula that we can use to figure this out for work. We aren't math wiz's or students. Basically we know 3 points in space of a triangle, we know the length of each side and the length of the line from apex to base line. Each point of the base line ends upon the circumference of a circle. IS three a way to work out the radius of that circle.
Answered by Penny Nom. |
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Scientific notation |
2003-03-20 |
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From A student:
what is one millionth times one thousand in scientific notation.
Answered by Penny Nom. |
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Gallons in a tank |
2003-03-20 |
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From Leslie:
I am trying to figure the liquid gallons in a water tank that is 19" wide by 29.25" long and is 12.25" high. Could you tell me the formula to figure this out.
Answered by Penny Nom. |
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Harmonic numbers |
2003-03-19 |
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From Becky:
Harmonic numbers are Hn = 1 + ? + 1/3 + . . . + 1/n
Use induction to prove the following theorem:
For all natural numbers n, H1 + H2 + . . . + Hn = (1+n)Hn - n
Answered by Penny Nom. |
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A recurrence relation |
2003-03-19 |
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From Becky:
Solve this recurrence relation, with the initial conditions.
A1 = 10
A2 = 100
An = 10a n-1 + 29a n-2
Answered by Penny Nom. |
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The origin of integers |
2003-03-19 |
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From Travis:
What are the real life usages of integers? Also what is the origin of integers?
Answered by Harley Weston. |
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1 followed by a million zeros |
2003-03-19 |
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From David:
What do you call the number represented by the numeral '1' followed by one million zeros?
Answered by Penny Nom. |
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Two algebra problems |
2003-03-18 |
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From Kayla:
1st question- If a+b divided by a equals 6 and b+c divided by c equals 9, compute the numerical value of a divided by c. ( Your answer will be mumbers only, no variables.)
2nd question- Three adjacent faces of a box (a rectangular prism) have areas of 7, 14, and 18 square inches. Find the volume of the box. (Hint: Choose variables to represent the three sides of the box and then figure out the problem.)
Answered by Peny Nom. |
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Three proffs of a trig identity |
2003-03-18 |
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From Nadene:
Prove the identity. cos [x + (y-pi/2)] = sin (x+y)
A hint was also provided which is: "Apply cos (alpha + beta) first then within that apply cose (alpha-beta)"
Answered by Penny Nom. |
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An equilateral triangle |
2003-03-17 |
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From Shirley:
An equilateral triangle is one in which all three sides are of equal length. If two vertices of an equilateral triangle are (0,4) and (0,0), find the third vertex. How many of these triangles are possible?
Answered by Penny Nom. |
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A sequence that converges to e |
2003-03-16 |
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From Dane:
Something I noticed fooling around with a calculator about 30 years ago.
Considering e = 2.718281828459045....
Using Window's Calculator you will find
1.111 = 2.8531167...
1.01101 = 2.731861...
1.0011001 = 2.71964085...
1.000110001 = 2.71841774...
1.00001100001 = 2.7182954...
1.00000110000011 = 2.178231875...
1.000000110000001 = 2.178219643...
There apears to be a pattern. My conjecture is:
1.'infinite number of zeros'11'infinite number of zeros'1 = e.
Answered by Penny Nom. |
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Runs |
2003-03-16 |
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From Diana:
How many arrangements are there with n 0's and m 1's, with k runs of 0's? (A run is a consecutive set [1 or more] of the same digit; eg. 000 111 0 11 00 has three runs.)
Answered by Penny Nom. |
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Distributing r identical balls into n distinct boxes |
2003-03-16 |
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From Diana:
How many ways to distribute r identical balls into n distinct boxes with exactly m boxes empty?
Answered by Penny Nom. |
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Working backwards |
2003-03-14 |
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From Melody:
Triva went to the ardcade at the state fair to win some goldfish. She already had some goldfish at home, but wanted more. She won enough goldfish to double her stock. Her mom made her give four away. She put her new ones in the tank with the others, by the morning half of the goldfish had died. Triva's friend gave her six more. The next morning two-thirds of her goldfish died. She was left with two goldfish after giving one to a friend. How many goldfish did she start with?
Answered by Penny Nom. |
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1575 |
2003-03-13 |
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From Sharyn:
find 6 integers that when multiplied with each other equal +1575 and when the same integers are added together equal zero. there are more positives than negatives and one of the numbers is a double digit between 10 and 20
Answered by Penny Nom. |
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