Gonzalez Manufacturing 30,000. Part of the money was borrowed at 6%, part at 8%, and part at 10%. The annual interest was $2440,
and the total amount borrowed at 6% and 8% was twice the amount borrowed at 10%. Use Gaussian elimination or Gauss-Jordan elimination to find the amount borrowed at each rate.
How much money was borrowed at 6%?
How much money was borrowed at 8%?
How much money was borrowed at 10%?
How much money was borrowed at 6%?
How much money was borrowed at 8%?
How much money was borrowed at 10%?
1 answer:
Answer:
8,000 at 6%; 12,000 at 8%; 10,000 at 10%
Step-by-step explanation:
Let a, b, c represent the amounts borrowed at 6%, 8%, 10%, respectively. Then the problem statement gives rise to three equations:
... a + b + c = 30,000 . . . . . the total borrowed
... a + b - 2c = 0 . . . . . . . . . . the relationship between the quantities
... .06a +.08b + .10c = 2440 . . . . the total interest charge
_____
Subtracting the second equation from the first, it becomes
... 3c = 30,000
... c = 10,000 . . . . . divide by 3 . . . [equation 4]
Subtracting 0.06 times the first equation from the third, we have
... .02b +.04c = 640
Multiplying [equation 4] by 0.04 and subtracting from this, we get
... .02b = 240
... b = 12,000 . . . . divide by 0.02 .
Substituting for b and c into the first equation, we find ...
... a + 22000 = 30000
... a = 8000
Then the amounts are ...
- 8000 was borrowed at 6%
- 12000 was borrowed at 8%
- 10000 was borrowed at 10%
_____
Most graphing calculators are capable of solving matrix problems such as this one. The attachment shows a TI-84 solution.
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Answer:
is not a function
Step-by-step explanation:
Given
Required
Which is not a function
A function is of the form
Assume a function is:
In simple terms:
For an ordered pair to be regarded as a function, no x value must be repeated
Analyzing the options:
1.
This is a function because none of the x values (-3, 8, 0 and -9) appeared more than once
2.
This is a function because none of the x values (5, -3, 0 and -9) appeared more than once
3.
This is a function because none of the x values (9, -5, 5 and 6) appeared more than once
4.
This is not a function because one of the x values (2) appeared more than once.
i.e.
and