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A matrix problem |
2005-04-04 |
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From Alan:
| Let A = |
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1 | -1 | 0 |
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| a | b | c |
where a, b, c are constant real numbers. For what values of a, b, c is A invertible? [Hint: Your answer should be an equation in a, b, c which satisfied if and only if A is invertible.]
Answered by Judi McDonald. |
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Ax + By = C |
2005-04-03 |
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From Farzana:
I was wondering if you could please explain to me how I would write the equation of line through the given points [(-3,7), (0,5)] in Ax+By=C form.
Answered by Penny Nom. |
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Some liquid in a cone |
2005-04-03 |
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From Vasuki:
There are 2 right cones, height is X. one of them is filled from the bottom up (round side) = x/2, when you invert the cone and add the same amount of liquid inside the second cone, what is the HEIGHT of the liquid?
Answered by Penny Nom. |
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Bayes Theorem |
2005-04-03 |
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From wei:
In the January 11,1988,issue of the Oil&Gas Journal, R.A.Baker
describes how the Bayesian approach can be used to revise probabilities
that a prospect field will produce oil. In one case he describes,
geological assessment indicates a 25% chance the field will produce
oil. Further,there is an 80% chance that a particular well will strike
oil given that oil is present on the prospect field.
- Suppose that one well is drilled on the field and
it comes up dry. What is the probability the prospect field will
produce oil?
- If two wells come up dry, what is the probability
the field will produce oil?
- The oil company would like to keep looking as long
as the chances of finding oil are greater than 1%. How many dry wells
must be drilled before the field will be abandoned
- If the first well produces oil,what is the chance
the field will produce oil?
Answered by Andrei Volodin and Penny Nom. |
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Gallons in a tank |
2005-04-02 |
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From Jim:
Would you be so kind as to help me with a problem? My memory has failed me in remembering how to calculate how much liquid in gallons a tank will hold. The tank is 8 feet long and 44 inches in diameter.
Answered by Penny Nom. |
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An asphalt driveway |
2005-04-02 |
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From Bob:
I'm trying to convert square
feet to cubic yard.
I have an asphalt drive way I'd like to replace with concrete. Concrete
is sold by the cubic yard and I keep telling myself that their must be an easy
conversion table out there somewhere.
My driveway is 18 feet wide and 47 feet long with a proposed depth of 4
inches.
Answered by Penny Nom. |
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An inequality |
2005-03-31 |
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From Ambross:
demostrate the following inequality:
2.Sqrt(K+1)-2.Sqrt(k)<1/Sqrst(K)<2.Sqrt(K)-2.Sqrt(k-1)
Answered by Penny Nom. |
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The integral of tan^4x |
2005-03-31 |
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From Nicole:
college student. need help with tough integral.
the integral of 2tan4xdx
Answered by Penny Nom. |
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tan55.tan65.tan75=tan85 |
2005-03-30 |
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From Jesus:
My name is Jesus and I´m a secondary student. I´m trying to verify a trigonometric identity but I don´t know how to do it.please help me!!!!!!!!!.
The identity is : tan55º.tan65º.tan75º=tan85º (the sign (.) indicates multiplication)
Answered by Chris Fisher and Penny Nom. |
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Two matrix problems |
2005-03-30 |
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From Sue:
Question 1
Suppose all matrices in the equation below are square and invertible. Solve for x .
BA-1XB-1 + 2BA + In = 0 (the symbol "0" here denotes the matrix of all 0's in it)
Also, A-1 or B-1 is indicating inverse and "In" = for example, A-1 times A
I hope you understand the above. I have to show all the steps.
Question 2
Suppose we consider the set of all 2x2 matrices along with the operations of matrix addition and multiplication. Do they form a field? Why or why not?
I think the answer is no because under multiplication it is not commutative and not all square matrices are invertible. I not positive so I'd like some help.
Answered by Penny Nom. |
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The shortest distance from a point to a line |
2005-03-30 |
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From carly:
Find the shortest distance from the point (-15, 2.5) to the line 5x+6y=30.
Answered by Penny Nom. |
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A wishing well |
2005-03-28 |
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From Don:
I am building a wishing-well
out of pieces of 2-by-4. I have included a picture of a miniature version
of what I want. There are to be ten 2-by-4 pieces around the well and
I want the circle around the outside of the structure to have a diameter
of approximately 3 feet. How long to I cut the 2-by-4's to build the
wishing-well.
Thanks,
Don
Answered by Harley Weston. |
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Explain why 3(x+2) = 3x+2 is incorrect |
2005-03-28 |
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From Cynthia:
An algebra student incorrectly used the distributive property and wrote 3(x+2) = 3x+2. How would you explain to him the correct result, without the use of the distributive law?
Explain why the square of the sum of two numbers is different from the sum of the squares of two numbers.
Answered by Penny Nom. |
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A product equals a sum |
2005-03-27 |
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From Tor:
Can you please help me with a general formula for the following system:
2+2=2*2
3+3/2=3*3/2
4+4/3=4*4/3
and how will you prove the formula?
Answered by Penny Nom. |
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A torus and a sphere |
2005-03-27 |
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From Tony:
Is it possible to shrink a torus into a sphere?
Answered by Andrei Volodin and Penny Nom. |
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