R1 6-17-11

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course MTH 158

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course Phy 201

If the velocity of the object changes from 4 cm / sec to 16 cm / sec in 8 seconds, then at what average rate is the velocity changing?1.5m/sec^2

A ball rolling from rest down a constant incline requires 8.2 seconds to roll the 97 centimeter length of the incline.

• What is its average velocity?

.055m/sec

& .97m / 8.2sec = .118m/sec. don't know how i got .055 &

@& I know how you got this result but I can't tell what you were thinking. There are two possible routes to this incorrect result.

This is why you need to show the steps of your solution. You mixed up something, but it could have been a mixup in numbers or a mixup in procedure.*@

An object which accelerates uniformly from rest will attain a final velocity which is double its average velocity.

• What therefore is the final velocity of this ball?

.11m/sec

& .236m/sec is the correct answer &

• What average rate is the velocity of the ball therefore changing?

.01m/sec^2

& (.236m/sec - 0m/sec) / 8.2sec = .029m/sec^2 &

@& I suspect your reasoning was correct in this step, even though you used an incorrect result from the preceding. However you haven't showed how you got the result. The result has only 1 significant figure (so I can't reverse-engineer your solution).*@

An automobile accelerates uniformly down a constant incline, starting from rest. It requires 10 seconds to cover a distance of 132 meters. At what average rate is the velocity of the automobile therefore changing?

1.32m/sec^2 

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Self-critique (if necessary):

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Self-critique rating:

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@& It looks like you divided the average velocity by the time interval; if so you're on the right track. However yYou need to divide the change in velocity by the time interval. *@

@&

&#Please see my notes and, unless my notes indicate that revision is optional, submit a copy of this document with revisions and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).

Be sure to include the entire document, including my notes.

If my notes indicate that revision is optional, use your own judgement as to whether a revision will benefit you.

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*@"

&#Very good work. Let me know if you have questions. &#

R1 6-17-11

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course MTH 158

6/17 2:21 pm

If your solution to stated problem does not match the given solution, you should self-critique per instructions at http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

Your solution, attempt at solution:

If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

001. `* 1

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Question: * R.1.26 \ was R.1.14 (was R.1.6) Of the numbers in the set {-sqrt(2), pi + sqrt(2), 1 / 2 + 10.3} which are counting numbers, which are rational numbers, which are irrational numbers and which are real numbers?

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Your solution:

Counting numbers - none

Rational numbers 1/2+10.3

Irrational numbers -sqrt(2), pi+sqrt(2)

Real numbers everything

confidence rating #$&*: 3

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Given Solution:

* * ** Counting numbers are the numbers 1, 2, 3, .... . None of the given numbers are counting numbers

Rational numbers are numbers which can be expressed as the ratio of two integers. 1/2+10.3 are rational numbers.

Irrational numbers are numbers which can be expressed as the ratio of two integers. {-sqrt(2)}, pi+sqrt(2) are irrational numbers.. **

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Self-critique (if necessary): ok

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Self-critique Rating: 3

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Question: * R.1.44 \ 32 (was R.1.24) Write in symbols: The product of 2 and x is the product of 4 and 6

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Your solution:

2x=4*6

confidence rating #$&*: 3

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Given Solution:

* * ** The product of 2 and x is 2 * x and the product of 4 and 6 is 4 * 6. To say that these are identical is to say that 2*x=4*6. **

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Self-critique (if necessary): I didn’t use multiplication symbol for product of 2 and x

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Self-critique Rating: 3

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Question:

* R.1.62 \ 50 (was R.1.42) Explain how you evaluate the expression 2 - 5 * 4 - [ 6 * ( 3 - 4) ]

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Your solution:

PEMDAS

Evaluate the inner parenthesis first (3-4)

Then the outer parenthesis [6*-1]= -6

Multiply 5*4 =20

Then work left to write 2-20+6= -12

confidence rating #$&*: 3

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Given Solution:

* * **Starting with

2-5*4-[6*(3-4)]. First you evaluate the innermost group to get

2-5*4-[6*-1] . Then multiply inside brackets to get

2-5*4+6. Then do the multiplication to get

2-20+6. Then add and subtract in order, obtaining

-12. **

* R.1.98 \ 80 (was R.1.72) Explain how you use the distributive property to remove the parentheses from the express (x-2)(x-4).

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Your solution:

By FOIL method

confidence rating #$&*: 3

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Given Solution:

* * ** COMMON ERROR: Using FOIL. FOIL is not the Distributive Law. FOIL works for binomial expressions. FOIL follows from the distributive law but is of extremely limited usefulness and the instructor does not recommend relying on FOIL.

Starting with

(x-2)(x-4) ; one application of the Distributive Property gives you

x(x-4) - 2(x-4) . Applying the property to both of the other terms we get

x^2 - 4x - (2x -8). Simplifying:

x^2 - 4x - 2x + 8 or

x^2 - 6x + 8. *

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Self-critique (if necessary): I guess I am common, will learn to use distributive property

Since foil works why isn’t it recommended?

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Self-critique Rating: 3

@& It only works for binomials. Students often learn FOIL but bypass the distributive law.

The distributive law is why FOIL works in the first place.*@

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Question:

* R.1.102 \ 86 (was R.1.78) Explain why (4+3) / (2+5) is not equal to 4/2 + 3/5.

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Your solution:

Because the expressions in the parenthesis must be evaluated first

(4+3)/(2+5)

7/7 = 1

confidence rating #$&*:

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Given Solution:

* * ** Good answer but at an even more fundamental level it comes down to order of operations:

(4+3)/(2+5) means

7/7 which is equal to

1.

By order of operations, in which multiplications and divisions precede additions and subtractions,

4/2+3/5 means

(4/2) + (3/5), which gives us

2+3/5 = 2 3/5

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

That last one got me, but now I am knowledgeable enough to hopefully not error like that again

"

Self-critique (if necessary):

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Self-critique rating:

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Question:

* R.1.102 \ 86 (was R.1.78) Explain why (4+3) / (2+5) is not equal to 4/2 + 3/5.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

Because the expressions in the parenthesis must be evaluated first

(4+3)/(2+5)

7/7 = 1

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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Given Solution:

* * ** Good answer but at an even more fundamental level it comes down to order of operations:

(4+3)/(2+5) means

7/7 which is equal to

1.

By order of operations, in which multiplications and divisions precede additions and subtractions,

4/2+3/5 means

(4/2) + (3/5), which gives us

2+3/5 = 2 3/5

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

That last one got me, but now I am knowledgeable enough to hopefully not error like that again

"

Self-critique (if necessary):

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Self-critique rating:

#*&!

&#Good responses. See my notes and let me know if you have questions. &#