Question about SoftMath Algebrator - Algebra Homework Solver (689076614429)
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Posted on Jan 02, 2017
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Using sigma notation, and factorials for the combinatorial numbers, here is the binomial theorem:
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.
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.
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.
This is the first term or, first coefficient 6*x^5*y, when k=1.
Solution so far = x^6+6*x^5*y
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
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
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
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
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
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
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Wattage is a term used to express magnitude of power. A common use is to define the electrical power consumption of your home appliances (check the labels). For example, look at the back label of your kitchen toaster. It might read 120 volts, 60 Hz, and 1200 Watts. The 1200 Watts is the power drawn by your toaster when you turn it on. You can get that (Watts) information for any appliance or device that runs on electricity in your house. That's important because that is the unit of measure the electric company uses to charge you in your electricity bill. The electric company bills your electric consumption in kilowatt-hour (KWH). All they are doing is calculating the watts by the thousands (that's the meaning of "kilo") for every hour you have your appliance turned on. The amount 22 cents per kilowatt-hour is close to how much the electricity is costing today. Back to your toaster, 1200 watts is equal to 1.2kilowatts. If you are using your toaster every day for an hour your monthly consumption is 1.2KWH times 30 days equals to 36KWH. That means at 22 cents per kilowatt-hour your toaster is costing you (36KWH times 22cents/KWH) $7.92 on that month. That's the toaster alone, now you can repeat this exercise for every appliance or device using electricity in your home. Start by just doing an inventory of each, do a log with four columns: (1)Name of the appliance, (2)Location, (3)Watts, and (4)Watts/1000 (to get the number in KW). Make a fifth (5) column and call it Hours. Make a sixth (6) column and call it KWH. Then sit down to estimate (think) for how many hours per month each device is turned on. Now multiply each value of column 4 by its corresponding hour number in column 5. Write the results in column 6. Add the results of column 6 and voila! You just have a pretty good estimate of the total KWH consumed in your home in 30 days. Multiply that by $0.22 (or get the actual cost per KWH from your electric service company) and see how close you are to the actual billing. Hope there is no surprises.
There are the science and engineering definitions of the term watt you can research to come to the same conclusion hereto, I just laid a practical perspective.
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