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WINSTONCH [101]
3 years ago
11

what is a linear function and a nonlinear fuction and how can you tell if the ordered pairs go to them

Mathematics
1 answer:
vfiekz [6]3 years ago
4 0

9514 1404 393

Answer:

  • linear: slope between any two points is the same
  • non-linear: slope between two points may differ

Step-by-step explanation:

A function is a linear function if the slope between any two ordered pairs is the same as it is between any other two. That is, the ordered pairs of a linear function will all fall on the same line when they are graphed.

__

A nonlinear function is one that is not linear. That is, its points do not all fall on the same line when graphed. Slopes between different pairs of points may differ.

_____

<em>Detailed Example</em>

If you are given two tables to compare, it is easiest if the x-values (inputs) are separated by a constant amount. For example, x = -2, 0, 2, 4. These all differ by 2. Then the y-values (outputs) of a linear function will all differ by the same quantity. For example, outputs 10, 15, 20, 25 for the above inputs would correspond to a linear function. This one is y = 2.5x +15.

If the output values for that same set of inputs do not have constant differences, then the function is nonlinear. For example, outputs 10, 15, 21, 27 have differences of 5, 6, 7, so correspond to a nonlinear function. This one happens to be y = (x^2 +22x +120)/8.

__

If the input values are not uniformly spaced, then you can check to see if the slope between one pair of points is the same as the slope for the next pair, and so on. The slope formula is ...

  m = (y2 -y1)/(x2 -x1)

For our first table, the first pair of points (-2, 10) and (0, 15) are on a line with slope ...

  m = (15 -10)/(0 -(-2)) = 5/2

Of course, when the calculations are repetitive, it is convenient to use a spreadsheet or calculator to do them. See the attachment for the calculations for this example.

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Step-by-step explanation:

All you have to do is find out 85% of 1560 which is 1326 students!

4 0
3 years ago
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Nesterboy [21]

Answer:

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Step-by-step explanation:

3x² - 17a + 10

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3 years ago
The value of good wine increases with age. Thus, if you are a wine dealer, you have the problem of deciding whether to sell your
Katyanochek1 [597]

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Step-by-step explanation:

Let assume the dealer sold the bottle now for $P, then invested that money at 5% interest. The return would be:

R1 = P(1.05)^t,

This means that after t years, the dealer would have the total amount of:

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If the dealer prefer to wait for t years from now to sell the bottle of wine, then he will get the return of:

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The value of t which will make both returns equal, will be;

R1 = R2.

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P will cancel out

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Log both sides

Log1.05^t = Log21

tLog1.05 = Log21

t = Log21/Log1.05

t = 64 years

The best time to sell the wine is therefore 64years from now.

7 0
3 years ago
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