Assignment 9 Query

course Mth 163

On number one I got a different answer. I was going to check and see where I went wrong.

assignment #009009. `query 9

Precalculus I

10-01-2008

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15:30:08

`questionNumber 90000

Symbolic calculation of slope, preliminary exercise

What was the function, between which two points were you to calculate the average slope and how did you get this slope?

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RESPONSE -->

y=.1x^2-3

between x=-2 and x=7

then work out equation

y=.1(-2)^2-3=-2.6

(-2,-2.6)

y=.1(7)^2-3=1.9

(7,1.9)

4.5/9=.5

confidence assessment: 2

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15:31:16

`questionNumber 90000

** For the function y = .1 x^2 - 3 between x = -2 and x = 7 we get:

slope = (y2 - y1) / (x2 - x1).

For x1 = 2 and x2 = 7 we have y2 = .1 * 7^2 - 3 = 1.9 and y1 = .1 * 2^2 - 3 = -2.6, so

slope = (1.9 - (-2.6) ) / ( 7 - 2) = 4.5 / 5 = .9. **

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RESPONSE -->

My answer was .5 b/c the first x va

You were correct.

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15:32:46

`questionNumber 90000

problem 2 symbolic expression for slope, fn depth(t).

What is the expression for the slope between the two specified t values?

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RESPONSE -->

depth(t)

T=10 and t=30

Rise=depth(30)-depth(10)

Run=30-10=20

slope=depth(30)-depth(10)/20

confidence assessment: 2

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15:32:53

`questionNumber 90000

** The function is given a name: depth(t).

t values are 10 and 30.

So rise = depth(30) - depth(10) and run = 30 - 10 = 20.

Thus slope = [ depth(30) - depth(10) ] / 20 . **

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RESPONSE -->

self critique assessment: 3

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15:33:28

`questionNumber 90000

What is the rise between the two specified t values?

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RESPONSE -->

As I already stated

rise=depth(30)-depth(10)

confidence assessment: 3

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15:33:36

`questionNumber 90000

** The rise is the change in depth. The two depths are depth(10) and depth(30).

The change in depth is final depth - initial depth, which gives us the expression

depth(30)-depth(10) **

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RESPONSE -->

got it

self critique assessment: 3

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15:33:58

`questionNumber 90000

What is the run between the two specified t values?

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RESPONSE -->

As specified before

run=30-10=20

confidence assessment: 3

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15:34:05

`questionNumber 90000

** run = 30 - 10 = 20 **

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RESPONSE -->

self critique assessment: 3

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15:35:41

`questionNumber 90000

What therefore is the slope and what does it mean?

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RESPONSE -->

slope=rise/run

rise=depth(30)-depth(10) (signifies change in depth)/

run=20 (signifies change in time)

confidence assessment: 3

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15:35:55

`questionNumber 90000

** rise = depth(30)-(depth(10) indicates change in depth.

run = 30 - 10 = 20 = change in clock time.

Slope = rise / run = (depth(30) - depth(10) ) / 20, which is the average rate at which depth changes with respect to clock time between t = 10 and t = 30. **

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RESPONSE -->

I understand

self critique assessment: 3

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15:36:45

`questionNumber 90000

problem 5 graph points corresponding to load1 and load2

What are the coordinates of the requested graph points?

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RESPONSE -->

Coordinates are (load1,springlength(load1)) and

(load 2, springlength(load2))

confidence assessment: 2

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15:36:59

`questionNumber 90000

** The horizontal axis is the 'load' asix, the vertical axis is the springLength axis.

The load axis coordinates are load1 and load2.

The corresponding spring lengths are springLength(load1) and springLength(load2).

The springLength axis coordinates are springLength(load1) and springLength(load2).

The graph points are thereofore (load1, springLength(load1) ) and (load2, springLength(load2) ). **

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RESPONSE -->

i understand

self critique assessment: 3

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15:37:57

`questionNumber 90000

What is your expression for the average slope of the graph between load1 and load2?

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RESPONSE -->

Expression for average slope=

springlength (load 2)- spring length (load1)/ load2-load1

confidence assessment: 2

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15:38:05

`questionNumber 90000

** rise = springLength(load2) - springLength(load1)

run = load2 - load1 so

slope = [ springLength(load2) - springLength(load1)] / (load2 - load1). **

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RESPONSE -->

i got it

self critique assessment: 3

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15:40:00

`questionNumber 90000

problem 6 symbolic expression for slope of depth function

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RESPONSE -->

depth(t)

t=t1 and t=t2

depth(t1) and depth(t2)

Rise=depth(t2)-depth(t1)/) =slope

Run=t2-t1 )

confidence assessment: 2

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15:40:08

`questionNumber 90000

** the name of the function is depth(t).

We need the slope between t = t1 and t = t2.

The depths are depth(t1) and depth(t2).

Thus rise is depth(t2) - depth(t1) and run is t2 - t1.

Slope is [ depth(t2) - depth(t1) ] / (t2 - t1). **

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RESPONSE -->

i understand

self critique assessment: 3

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15:43:04

`questionNumber 90000

problem 8 average rate from formula f(t) = 40 (2^(-.3 t) ) + 25 intervals of partition (10,20,30,40)

What average rate do you get from the formula? Show your steps.

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RESPONSE -->

average rate= change in depth/ change in time

f(20)-f(10)/(20-10)=(25.625-30)/(20-10)=.4375

f(30)-f(20)/(30-20)=(25.0781-25.625)/(30-20)=-.05469

f(40)-f(30)/ (40-30)=(25.0097-25.0781)/(40-30)=-.00684

confidence assessment: 2

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15:43:21

`questionNumber 90000

** ave rate = change in depth / change in t. For the three intervals we get

(f(20)-f(10))/(20-10) = (25.625 - 30 )/(20 - 10) = -4.375 / 10 = -.4375

(f(30)-f(20))/(30-20) = (25.07813 - 25.625)/(30 - 20) = -.5469 / 10 = -.05469.

(f(40)-f(30))/(40-30) = (25.00977 - 25.07813)/(40 - 30) = -.0684 / 10 = -.00684. **

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RESPONSE -->

I totally understand this.

self critique assessment: 3

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15:43:28

`questionNumber 90000

Add comments on any surprises or insights you experienced as a result of this assignment.

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RESPONSE -->

self critique assessment:

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15:43:32

`questionNumber 90000

STUDENT RESPONSE:

Ummm I know the slope formula is (y2-y1)/(x2-x1), but I always just put the number into the expression in the order I see them, but that is ok because I keep the order and get the correct answere because the y2,y1,x2,x1 or all relative. I am correct in doing this?

INSTRUCTOR COMMENT:

In other words you use (y1 - y2) / (x1 - x2) instead of (y2 - y1) / (x2 - x1).

It's more conventional to regard, say, 10 as x1 and 20 as x2, so f(20) is y2 and f(10) is y1. If you start from the lower x number and change to the higher the difference is higher - lower, and this is the way we usually think about changes. According to this convention we calculate change in y as y2 - y1 and change in x as x2 - x1.

You are doing (y1 - y2) / (x1 - x2) and you get a negative change in x, a negative denominator, and if you are thinking about change from the first quantity to the second this is backwards.

However as you say both numerator and denominator follow the same order so you still get the right answer, since (y1-y2)/(x1-x2)= (y2-y1) / (x2-x1). **

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RESPONSE -->

self critique assessment:

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&#Your work looks very good. Let me know if you have any questions. &#