Assignment 8 Query

course Mth 271

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17:09:00

What functions f(z) and g(t) express the function 2^(3t-5) as a composite f(g(t))?

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RESPONSE -->

f(a)=2^a

g(t)=3t-5

f(g(t)) = 2^g(t) = 2^(3t-5)

confidence assessment: 3

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17:09:04

CORRECT STUDENT RESPONSE: f(z)=2^z and g(t)=3t-5, so that f(g(t)) = 2^g(t) = 2^(3t-5).

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RESPONSE -->

self critique assessment: 3

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17:09:13

1.3.81 (was 1.3.66 temperature conversion. What linear equation relates Celsius to Fahrenheit?

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RESPONSE -->

F = 1.8 C + 32

confidence assessment: 3

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17:09:15

CORRECT STUDENT RESPONSE: degrees Fahrenheit=1.8(degrees Celsius)+32, or F = 1.8 C + 32.

INSTRUCTOR COMMENT:

Since each Fahrenheit degree is 1.8 Celsius degrees a graph of F vs. C will have slope 1.8. Since F = 32 when C = 0 the graph will have vertical intercept at (0, 32) so the y = m x + b form will be F = 1.8 C + 32.

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RESPONSE -->

self critique assessment: 3

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17:09:26

How did you use the boiling and freezing point temperatures to get your relationship?

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RESPONSE -->

F = 1.8 (0) + 32 = 32F

F = 1.8 (100) + 32 = 212F

To find the slope (212-32)/(100-0) = 1.8

y = 1.8x + b

212 = 1.8(100) + b

b = 32

F = 1.8x + 32

confidence assessment: 3

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17:09:28

A graph of Fahrenheit vs. Celsius temperatures gives us the two (x,y) points (o,32) and (100,212).

We use these two points to find the slope m=(y2-y1)/(x2-x1) = (212 - 32) / 100 = 1.8.

Now we insert the coordinates of the point (0,32) and into the point-slope form y = 1.8 x + b of a line to get 32 = 1.8 * 0 + b. We easily solve to get b = 32.

{So the equation is y = 1.8 x + 32, or F = 1.8 C + 32. **

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RESPONSE -->

self critique assessment: 3

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Very good.

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