Question about Bagatrix Algebra Solved! 2005 (105101) for PC

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1.01^1000000 is greater or 10000 ?

This has to be solved using binomial theorem

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Try this... here we represent 1.01 as 1+.01
and so we have nCr and stuff... it can be noted that a number lesser than .01 when raised to power will result in a number lesser than it and hence the first term which is 1^1000000 will be greatest among the terms... so it can never be greater than 10000

Posted on Jan 31, 2008

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  • Bagatrix Master
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I am sorry to come in like that (5 years after the question was asked) and spoil your fun.
If you try to enter it on a regular calculator you will get an overflow error, memory error or some such thing. On the Windows calculator here is what I get.
2.3647358888701483369966440045217x10^(4321)

Posted on Mar 01, 2013

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2.gif
FOIL stands for:
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TI-89 Titanium: I want to solve a Binomial Theorem problem (x+y)^6 how would i go about solving this in the calculator?


Using elementary algebria in the binomial theorem, I expanded the power (x + y)^n into a sum involving terms in the form a x^b y^c. The coefficient of each term is a positive integer, and the sum of the exponents of x and y in each term is n. This is known as binomial coefficients and are none other than combinatorial numbers.

Combinatorial interpretation:

Using binomial coefficient (n over k) allowed me to choose k elements from an n-element set. This you will see in my calculations on my Ti 89. This also allowed me to use (x+y)^n to rewrite as a product. Then I was able to combine like terms to solve for the solution as shown below.
(x+y)^6= (x+y)(x+y)(x+y)(x+y)(x+y)(x+y) = x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4+6xy^5+y^6

This also follows Newton's generalized binomial theorem:


oneplusgh_15.jpg
Now to solve using the Ti 89.


Using sigma notation, and factorials for the combinatorial numbers, here is the binomial theorem:

oneplusgh.gif

The summation sign is the general term. Each term in the sum will look like that as you will see on my calculator display. Tthe first term having k = 0; then k = 1, k = 2, and so on, up to k = n.
Notice that the sum of the exponents (n ? k) + k, always equals n.



oneplusgh_26.jpg


The summation being preformed on the Ti 89. The actual summation was preformed earlier. I just wanted to show the symbolic value of (n) in both calculations. All I need to do is drop the summation sign to the actual calculation and, fill in the term value (k), for each binomial coefficient.



oneplusgh_18.jpg

This is the zero th term. x^6, when k=0. Notice how easy the calculations will be. All I'm doing is adding 1 to the value of k.


oneplusgh_19.jpg

This is the first term or, first coefficient 6*x^5*y, when k=1.
Solution so far = x^6+6*x^5*y



oneplusgh_20.jpg


This is the 2nd term or, 2nd coefficient 15*x^4*y^2, when k=2.
Solution so far = x^6+6*x^5*y+15*x^4*y^2



oneplusgh_27.jpg



This is the 3rd term or, 3rd coefficient 20*x^3*y^3, when k=3.
Solution so far = x^6+6*x^5*y+15*x^4*y^2+20*x^3*y^3



oneplusgh_28.jpg



This is the 4th term or, 4th coefficient 15*x^2*y^4, when k=4.
Solution so far = x^6+6*x^5*y+15*x^4*y^2+20*x^3*y^3+15*x^2*y^4



oneplusgh_21.jpg


This is the 5th term or, 5th coefficient 6*x*y^5, when k=5.
Solution so far = x^6+6*x^5*y+15*x^4*y^2+20*x^3*y^3+15*x^2*y^4+6*x*y^5



oneplusgh_22.jpg

This is the 6th term or, 6th coefficient y^6, when k=6.
Solution so far = x^6+6*x^5*y+15*x^4*y^2+20*x^3*y^3+15*x^2*y^4+6*x*y^5+y^6



oneplusgh_23.jpg

Putting the coefficients together was equal or, the same as for when I used the expand command on the Ti 89.

binomial coefficient (n over k) for (x+y)^6
x^6+6*x^5*y+15*x^4*y^2+20*x^3*y^3+15*x^2*y^4+6*x*y^5+y^6












Jan 04, 2011 | Texas Instruments TI-89 Calculator

1 Answer

{Use the binomial theorem to find the eight term of (3x-2y)^13}


This may help:
http://en.wikipedia.org/wiki/Binomial_theorem
Rate me, thanks.

Jun 19, 2009 | Texas Instruments TI-89 Calculator

1 Answer

Applying "IF"


=IF(K>50,(IF(K>66,A*300,A*200),10000))

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Your friend John asks you for advice concerning life insurance. John is 32 years old and graduated from law school last year. he currently earns $48,000 per year as a first year attorney. John is married and has two children, Billy, age 10, and Sarah, age 4. John's wife, Mary, is a professor who currently earns $58,000 per year. Mary is 34 years old. John and Mary pay $1,700 per month for their home mortgage, which will be paid off in 20 years. The interest rate on their mortgage is 4.5%. (Their current equity in the home is $75,000.) The couple owns two cars, both 8 years old, and personal property (such as clothes, electronics, furniture, etc.) values at $45,000. Their investments have been used up paying for John's law school education, so they currently have only $1,000 in savings and checking accounts, and $2,000 in a mutual fund. John has no life insurance. Mary has $100,000 of life insurance provided by her employer. mary's pension plus social security are expected to total $45,000 per year, beginning when she is 67 years old. If John should die, Mary would receive approximately $10,000 per year from social security until Sarah reaches age 18. John and Mary spend most of their current income, although they do try to save about $50 per month. Their investments earn approximately 5% per year. In addition to their home mortgage, John has a student loan of $15,000 that he must start making payments on in 6 months. he plans to pau back the loan in 5 years and the loan's interst rate is 6% per year. Given that Mary enjoys a flexible work schedule, and because Mary's mother lives close by and watches the kids two days per week, the currently are not paying any child care expenses.

Nov 22, 2013 | Bagatrix Algebra Solved! 2005 (105101) for...

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Your friend John asks you for advice concerning life insurance. John is 32 years old and graduated from law school last year. he currently earns $48,000 per year as a first year attorney. John is married and has two children, Billy, age 10, and Sarah, age 4. John's wife, Mary, is a professor who currently earns $58,000 per year. Mary is 34 years old. John and Mary pay $1,700 per month for their home mortgage, which will be paid off in 20 years. The interest rate on their mortgage is 4.5%. (Their current equity in the home is $75,000.) The couple owns two cars, both 8 years old, and personal property (such as clothes, electronics, furniture, etc.) values at $45,000. Their investments have been used up paying for John's law school education, so they currently have only $1,000 in savings and checking accounts, and $2,000 in a mutual fund. John has no life insurance. Mary has $100,000 of life insurance provided by her employer. mary's pension plus social security are expected to total $45,000 per year, beginning when she is 67 years old. If John should die, Mary would receive approximately $10,000 per year from social security until Sarah reaches age 18. John and Mary spend most of their current income, although they do try to save about $50 per month. Their investments earn approximately 5% per year. In addition to their home mortgage, John has a student loan of $15,000 that he must start making payments on in 6 months. he plans to pau back the loan in 5 years and the loan's interst rate is 6% per year. Given that Mary enjoys a flexible work schedule, and because Mary's mother lives close by and watches the kids two days per week, the currently are not paying any child care expenses.

Nov 22, 2013 | Bagatrix Algebra Solved! 2005 (105101) for...

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