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course Mth163
I am going to try and go through to put the questions through the other form so please excuse my questions in this one, promise the rest one won't have them!(on the Submit Work form)
003. PC1 questions
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Question: `q001 A straight line connects the points (3, 5) and (7, 17), while another straight line continues on from (7, 17) to the point (10, 29). Which line is steeper and on what basis to you claim your result?
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Your solution:
When you find the slope of (3,5)and (7,17) your rise over run is 12/4=3, while from (7, 17) to the point (10, 29) your rise over run is 12/3=4. The 1st line has the steeper slope because when you have less ramp to get to a higher elevation it makes the ramp steeper, but in the 2nd one you have more ramp to reach the desired elevation therefore your ramp is less step than the first.
confidence rating #$&*: 3
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Self-critique Rating:OK
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Question: `q002. The expression (x-2) * (2x+5) is zero when x = 2 and when x = -2.5. Without using a calculator verify this, and explain why these two values of x, and only these two values of x, can make the expression zero.
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Your solution:
When plugging in x=2, you get (2-2)=0, you really don’t even need to do the other half of the problem because we all know what times 0 equals 0. When plug in x=-2.5 lets start on the other side of the *, (2(-2.5))=-5,(-5+5)=0, and anything times zero equals zero.
confidence rating #$&*: 3
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Self-critique Rating: OK
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Question: `q003. For what x values will the expression (3x - 6) * (x + 4) * (x^2 - 4) be zero?
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Your solution:
My algebra 2 teacher did not see it as necessary to solve a four unknown variable equation in class so I did the last half of the work on the calculator, but I did try to do as much of it by hand as possible. To make the equation as small as possible I first combined (3x-6)*(x+4) to get 3x^2+12-6x-24, then I multiplied x^2(3x^2+12-6x-24)-4(3x^2+12-6x-24)=3x^4-6x^3-12x^2+12+48, then I took the 3 out 3(x^4-2x^3-4x^2+4x+16) This Is the point I stared doing a bunch of weird stuff to find the answer that failed so I went back and typed this into my calculator under cSlove(((3x - 6) * (x + 4) * (x^2 - 4))=0,x). My answers are x=-4,x=-2,x=2.
confidence rating #$&*: by hand 1.5, calculator 3
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Self-critique (if necessary): so the idea here is to set one of the groups equal to zero, so when they all multiply just in end equals the whole equation to zero. Simpler the better, I always tend to over complicate things. This makes much more sense.
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Self-critique Rating:2
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Question: `q004. One straight line segment connects the points (3,5) and (7,9) while another connects the points (10,2) and (50,4). From each of the four points a line segment is drawn directly down to the x axis, forming two trapezoids. Which trapezoid has the greater area? Try to justify your answer with something more precise than, for example, 'from a sketch I can see that this one is much bigger so it must have the greater area'.
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Your solution:
Using ((base one+ base two)*height)/2 . After graphing my points I counted the units needed (I cannot remember of I am supposed to use the spaces or lines to count???),( (5+5)*3.5)/2=35/2=17.5 units^2 .I did the same to the larger trapezoid ((2+4)*40)=240/2=120 units^2. Therefore our trapezoid the greatest area is (10,2) and (50,4).
confidence rating #$&*: 1
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Question: I got confused with the orientation of the trapezoid see how it was so stretched out, so have any tips for keeping things strait???
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Question: `q005. Sketch graphs of y = x^2, y = 1/x and y = `sqrt(x) [note: `sqrt(x) means 'the square root of x'] for x > 0. We say that a graph increases if it gets higher as we move toward the right, and if a graph is increasing it has a positive slope. Explain which of the following descriptions is correct for each graph:
As we move from left to right the graph increases as its slope increases.
As we move from left to right the graph decreases as its slope increases.
As we move from left to right the graph increases as its slope decreases.
As we move from left to right the graph decreases as its slope decreases.
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Your solution:
Y=x^2,my coordinates were (1,1)(2,4)(2,9)(4,16) with slopes of 1,2,3,4, As we move from left to right the graph increases as its slope increases. y = 1/x, my coordinates were (1,1)(2,.5)(3,.333)(4,.25), with slopes of 1,.25,.111,.06, As we move from left to right the graph decreases as its slope decreases. y = `sqrt(x) , my coordiantes are (1,1)(2,1.414)(3,1.732)(4,2) with slopes of 1,.707,.577,.5, As we move from left to right the graph increases as its slope decreases.
confidence rating #$&*: 3
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Self-critique Rating:OK
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Question: `q006. If the population of the frogs in your frog pond increased by 10% each month, starting with an initial population of 20 frogs, then how many frogs would you have at the end of each of the first three months (you can count fractional frogs, even if it doesn't appear to you to make sense)? Can you think of a strategy that would allow you to calculate the number of frogs after 300 months (according to this model, which probably wouldn't be valid for that long) without having to do at least 300 calculations?
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Your solution:
After 3 months your increase of frogs would be 26.26, Month 1,.1*20=2 then 20+2=22, M2, .1*22=2.2 then 22+2.2=24.2, M3 .1*24.2=2.42, 2.42+24.2=26.62. while trying to find a common difference between the populations of the first 3 months I found that it is increasing by .2 from the last increase, so in-between 22 and 24.2 it increases by 2.2 and between 24.2 and 26.62 the increase is 2.4 to confirm that the increases were increasing by .2 each time I found the 3rd month I added 2.6+26.62=29.22, I also did it the first way (to make sure) .1*26.62=2.662 then 26.62+2.662=29.282 ( it was a pretty close match but not perfect, still best I had so far.) With a common difference of my differences I apply it to a z score z=(x-mean)/standard deviation z=(300-2.2)/.1=2978 Knowing this may be terribly wrong I do not like to give up on things without trying.
confidence rating #$&*: 1
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Question: can you explain this part a little more as how you got 1.1 exactly???”The key to extending the strategy is to notice that multiplying a number by .1 and adding it to the number is really the same as simply multiplying the number by 1.1.”
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Question: `q007. Calculate 1/x for x = 1, .1, .01 and .001. Describe the pattern you obtain. Why do we say that the values of x are approaching zero? What numbers might we use for x to continue approaching zero? What happens to the values of 1/x as we continue to approach zero? What do you think the graph of y = 1/x vs. x looks for x values between 0 and 1?
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Your solution:
Describe the pattern you obtain: multiplying by 10. The values of x are approaching zero because it is getting closer to the x axis. .0001,.00001,ect. The numbers keep getting bigger. I think the graph would look incredibly smaller than if you used the first x values x = 1, .1, .01 and .001
confidence rating #$&*: 2
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Self-critique (if necessary): 1/x , 1= were counting all the ones it takes to get to one 1/.01 counting all the .numbers it takes to get to 1. The reason I could not find 1/0 is because no matter how many zeros you have it will never amount to anything. Zero is nothing. our x is approaching zero ( but not actually toughing it) and our y values keep increasing , as the graph becomes steeper and steeper (because of y values high increasing numbers) you approach our asymptote.
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Self-critique Rating:2
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Question: `q008. At clock time t the velocity of a certain automobile is v = 3 t + 9. At velocity v its energy of motion is E = 800 v^2. What is the energy of the automobile at clock time t = 5?
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Your solution:
3(5)+9=v=24,E=800(24^2)=800(576)=460800E at clock time 5
confidence rating #$&*: 3
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Question: `q009. Continuing the preceding problem, can you give an expression for E in terms of t?
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Your solution:
An equation for E that finds t. E=800((3t+9)^2) We know E=460800 so 460800=800((3t+9)^2) when I tried to work this out I was wrong but here is what I did 800(9t^2+9)=7200t^2+64800=460800-6480=7200t^2 so 39600=7200t^2, took the square root of each 60*`sqrt(110)/7200=t I got `sqrt(110)/120= t that was definitely not right so I went back I and did it without squaring the t and I got 55, not right either so then I tried 460800=800(3t+9) 800(3t+9)=93
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Self-critique (if necessary): alright now I get it I was not doing (3t+9)(3t+9) instead I was doing something quite dumb I was trying to square the numbers within the Parentheses individually!!!
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Question: For what x values is the value of the expression (2^x - 1) ( x^2 - 25 ) ( 2x + 6) zero?
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Your solution:
X=-3, (2(-3)+6)=0
confidence rating #$&*: 3
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Question: One straight line segment connects the points (3,5) and (7,9) while another connects the points (3, 10) and (7, 6). From each of the four
points a line segment is drawn directly down to the x axis, forming two trapezoids. Which trapezoid has the greater area?
Any solution is good, but a solution that follows from a good argument that doesn't actually calculate the areas of the two trapezoids is better.
Your solution:
points (3, 10) and (7, 6) have larger y values which means it will take more units to get to the x axis than it would points (3,5) and (7,9) because they have slightly smaller y values
confidence rating #$&*: 3
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Question:
Suppose you invest $1000 and, at the end of any given year, 10% is added to the amount. How much would you have after 1, 2
and 3 years?
What is an expression for the amount you would have after 40 years (give an expression that could easily be evaluated using a calculator, but don't bother to actually evaluate it)?
What is an expression for the amount you would have after t years?
Your solution:
After 3 years 1.1*1000=1,100(year 1) 1.1*1100=1,210(year2) 1.1*1210=1,331(year 3). 1.1*40 I am not sure what you are referring to when you say t years???
confidence rating #$&*:2
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Self-critique Rating:2
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Self-critique (if necessary):
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Self-critique rating:
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I can't comment on your solutions without the given solutions. As I believe I indicated in another response to be posted today, I need to see the details of the wording of the given solutions in order to compare your results with the information you have to evaluate them. Among other things, this helps me avoid giving you redundant information. It's also important that you have the given solutions for reference in your portfolio.
Please take a couple of minutes and insert your solutions into a copy of the complete document and resubmit it.
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