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Mth163
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
c=Pi(D) vs. C = 2 pi r
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We use the formula C = 2 pi r. The formula for the area involves r^2, which will give us squared units of the radius. Circumference is not measured in squared units.
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which do you prefer me to use c=Pi(D) or C = 2 pi r and i don't really understand what the difference is.
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D = 2 * r, i.e., diameter is double the radius.
pi is by definition the ratio of circumference to diameter, so C = pi * D follows directly from the definition.
However this says exactly the same thing as
C = 2 pi r.
You should be able to use both relationships interchangeably.
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#$&*
Mth163
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
simultaneous linear equations6
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The system consists of the three equations obtained in the last problem:
a + b + c = -2
9 a + 3 b + c = 5
49 a + 7 b + c = 8.
This system is solved in the same manner as in the preceding exercise. However in this case the solutions don't come out to be whole numbers.
The solution of this system, in decimal form, is approximately
a = - 0.45833,
b = 5.33333 and
c = - 6.875.
If you obtained a different solution, you should show your solution. Start by indicating the system of two equations you obtained when you eliminated c, then indicate what multiple of each equation you put together to eliminate either a or b.
ADDITIONAL DETAILS ON SOLUTION OF SYSTEM
You should have enough practice by now to be able to solve the system; however signs can trip us all up, and I've decided to append the following:
The second equation minus the first gives us 8a + 2 b = 7.
To avoid a common error in subtracting these questions, note that the right-hand sides of these equations are 5 and -2, and that 5 - (-2) = 5 + 2 = 7. It is very common for students (and the rest of us as well) to get a little careless and calculate the right-hand side as 5 - 2 = 3.
The third equation minus the first gives us 48 a + 6 b = 10 (again the right-hand side can trip us up; 8 - (-2) = 10. I often see the incorrect calculation 8 - 2 = 6).
Now we solve these two equations, 8 a + 2 b = 7 and 48 a + 6 b = 10:
If you subtract 3 times the first from the second you will get 24 a = -11, so that a = -.45833.
Substituting this into 8 a + 2 b = 7 and solving for b you get b = 5.33333.
Substituting these values of a and b into any of the three original equations you get c = -6.875.
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What exactly are these problems called, is there something more specific than simultaneous linear equations?
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If you subtract 3 times the first from the second you will get 24 a = -11, so that a = -.45833.??? can you explain this a little more
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The second of the equations is
48 a + 6 b = 10
and 3 times the first is
24 a + 6 b = 21
Subtracting 24 a from 48 a leaves 24 a.
Subtracting 6 b from 6 b gives you 0.
Subtracting 21 from 10 gives you -11.
So the result of subtracting the equations is
24 a + 0 = -11
or just
24 a = -11.
Dividing both sides by 24 you end up with a = 0.45833.
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