Mth 158
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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I was looking over the comments to the Chapter 1 test that you posted in Blackboard. I can see now (I believe) what you mean. I solved them on paper and wanted to submit it to you to see if that was the correct way to solve.
I do have a question on the first one.
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sqrt(3q-2) = 2 square both sides
(sqrt(3q-2))^2 = 2^2
3q-2 = 4 (Here, why does sqrt of 3q-2 squared end up with just 3q-2?) It seems like it would still be written as sqrt of 3q-2. Is it because the square root * square root = 3q-2? NEVER MIND I THINK I JUST ANSWERED MY OWN QUESTION!
you did; very good
So
3q -2 = 4 add 2 to both sides, then divide both sides by 3
3q = 6
q = 2
Then solve sqrt(3 * 2 - 2) = 2
sqrt(6-2) = 2
2 = 2
The next problem was |r + 7|= 9
I believe on the test I stopped at just saying r + 7 = 9 or -9 and I didn't solve for r. (These are the kinds of things that I just forget to do) so,
r = 9 - 7
r = 2
r = -9 -7
r = -16
then solve for r
|2 + 7| = 9 and |-16 + 7| = -9
Right. SOlving was no problem for you.
The last problem was the 40lb bag differing in weight by as much as .75lbs. I can see where you would say
the absolute value of weight-40lbs is less than .75 lbs.
because by using the absolute value, you would be including the + and -
is that right?? Would the final answer to that one be
|wt-40lbs| < .75lbs
or do you have to solve further than that step?
The solution to this would be
-.75 lbs < wt - 40 lbs < .75 lbs
and it would be fine to include this, but the problem asked for an absolute value inequality, so the answer
|wt-40lbs| < .75lbs
is both required and sufficient by itself.
Mth 158
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Here is a step by step answer of what I do not understand about the problem from my last submission.
I have copied the entire problem with the question, then my solution (with the detailed description of what I do not understand), the given solution, and your response.
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Question: * 1.7.36 \ 32 (was 1.2.42). Explain how you set up and solved an equation for the problem. Include your equation and the reasoning you used to develop the equation. Problem (note that this statement is for instructor reference; the full statement was in your text) pool enclosed by deck 3 ft wide; fence around deck 100 ft. Pond dimensions if pond square, if rectangular 3/1 ratio l/w, circular; which pond has most area?
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Your solution:
A pond is enclosed by a deck 3ft wide. the fence surrounding the deck is 100 ft long.
a) if it is square, what are the dimensions (I don't understand what dimensions it is looking for. Is it asking for the pond dimensions? or the deck dimensions? And either one, I would not even begin to know how to solve. I have drawn a pond on my paper and put a 3 ft diameter around it with a fence that is 100 ft long. Is it 100ft all the way around? or is it 100ft on one side? I just don't understand word problems.)
Be sure you are going by the problem as it is stated in your book, rather than the abbreviated version given here.
The fence around the deck is 100 ft long.
If the pond is square, then the 3-ft-wide deck around it is also square, and so therefore is the fence.
What are the dimensions of a square with a perimeter of 100 ft?
What would be the dimensions of the pond?
b) if it is rectangular, and the length of the pond is to be three times its width, what are its dimensions (Same thing here, I don't even know what it is asking to even set up the problem to solve it)
Sketch a picture of a rectangle which is 3 times as long as wide, labeling the width w and the length 3w.
Sketch a 3 ft wide deck around the rectangle.
In terms of w, what are the length and width of this rectangle?
In terms of w, what is the perimeter of this rectangle?
Set your expression for the perimeter equal to 100 ft and solve for w.
What therefore are the length, width and area of the pond?
c) if pond is circular, what is its diameter (I know to find the diameter of a circle, it is 2 times the radius, but I don't know what the radius of this pond is or how to find it.)
You should know that the circumference of a circle is 2 pi * radius or pi * diameter.
Whichever you prefer to use, set it equal to 100 ft and solve for either radius or diameter, as appropriate.
Having found the radius or diameter of the fence, what is the radius or diameter of the pond, taking into consideration the 3 ft deck?
What therefore is the area of the pond?
d) which pond has the most area (again, I don't how to answer this because I couldn't answer the previous questions to find out)
I have tried for about an hour to search the book to help me understand how to solve these problems, but I have so much trouble understand them. I don’t know how to answer these. I will see my tutor this week, but it will be after I take the test. In the meantime, I will try to learn how to solve these types of problems on my own.
confidence rating: 0
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Given Solution:
* * If the deck is circular then its circumference is C = 2 pi R and its radius is r = C / (2 pi). C is the 100 ft length of the fence so we have
R = 100 ft / ( 2 pi ) = 50 ft / pi.
The radius of the circle is 3 ft less, due to the width of the deck. So the pool radius is
r = 50 ft / pi - 3 ft.
This gives us pool area
A = pi r^2 = pi ( 50 / pi - 3)^2 = pi ( 2500 / pi^2 - 300 / pi + 9) = 524, approx..
If the pool is square then the dimensions around the deck are 25 x 25. The dimensions of the pool will be 6 ft less on each edge, since each edge spans two widths of the deck. So the area would be
A = 19 * 19 = 361.
The perimeter of the rectangular pool spans four deck widths, or 12 ft. The perimeter of a rectangular pool is therefore 12 ft less than that of the fence, or 100 ft - 12 ft = 88 ft.
If the pool is rectangular with length 3 times width then we first have for the
2 l + 2 w = 88 or
2 (3 w) + 2 w = 88 or
8 w = 88, giving us
w = 11.
The width of the pool will be 11 and the length 3 times this, or 33.
The area of the pool is therefore 11 * 33 = 363.
The circular pool has the greatest area, the rectangular pool the least. **
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Self-critique (if necessary):
Even after reading the given solution, I don’t think I could solve the problem. I will continue to work on this for this week.
A detailed self-critique of your thinking on each line the given solution might be helpful. Feel free to submit one.
See my notes. Try to answer the questions I pose without looking at the given solution. Then look at the given solution to see if it makes more sense.
I'll be glad to answer additional questions.
Mth 158
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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I am full of questions today.
I was working on some of the word problems in Chapter 1 and I came across this example. When I tried to set it up to solve, I couldn't do it. I just sat there looking at it and then thought about it. I came up with the correct answer, but I still don't know how to do it as a mathmatical equation. I will post the question and my answer in the next box.
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A total of $20,000 is to be invested, some in bonds and some in certificates of deposit (CD's). If the amount invested in bonds is to exceed that in CDs by $3,000, how much will be invested in each type of investment?
I thought about it and took the 20,000 and divided it by 2 giving me $10,000 each. I subtracted 3,000 from 10,000 and that gave me 7,000 for one and 10,000 for the other, but that's not enough, so the remaining $3,000 I divided by 2 and added 1,500 to each amount. I came up with $8,500 for one and $11,500 for the other. I know this is the right answer, but how do you set it up in a formula?
If you know how much is invested in bonds, then what arithmetic operation do you perform to get the amount invested in CDs?
Let x stand for the amount invested in bonds. Then, using the arithmetic operation of your answer to the first question, how much is invested in CDs?
You should now have two expressions, both involving x, one representing the amount invested in CDs and the other the amount invested in bonds.
If you are given two numbers, then what calculation do you do to see if the second is $3000 greater than the first?
If the amounts of the investments are represented by your two expressions (in terms of x), then what expression represents this calculation?