The first step in solving this problem would be to draw a diagram:
-treat the height given of the waterfall as the value of your y-axis -treat the distance away of the fish from the waterfall as your x-axis -things are always easier with visuals
Then you would need to find the value of 4p:
-Standard form of a vertical parabola: (x-h)2 = 4p(y-k) -looking at the graph you could see we are given values of x and y -substitute values into the variables -also looking at graph, the vertex is at (0,25) -all that is needed is to substitute the values in and solve for 4p -the 4p is negative, from looking at graph it opens down
Equation of the parabola:
-now that we have the value for 4p our equation is done -we know from above that V = (0,25) -so our equation will be x2 = -784(y-25)
To find if the bird or fish meet you’d have to:
-find the point where the line touches the x axis -make y =0 to find value of x -you then plug the coordinates of that point into the equation of the parabola -if this point is indeed on the parabola then both sides of the equation should equal -if it doesn’t, it isn’t on any points of the parabola
Reading the question, many details are given like how many mice were born, a time length, a period that shows when the mouse reproduces. Being given a time length and period shows that we must be using the formula:
A = Ao (model)t/p
Step 1: Plug in numbers into variables
Step 2: Isolate the model -refer to slide 3 -must use logarithms on both sides to solve for m -bring down the exponent and make it the coefficient (power law:. For example (32 )4. We would multiply 2 and 4. It is the same with logarithm. A logarithm is an exponent. So the exponent 13/3 is multiplied to the logarithm.) -once logm is isolated all that is needed to do is solve for m -a logarithm is an exponent -this is in base 10 because no subscript under log -going from logarithm form to its exponential
a) This question is another probability question. A tree drawn makes life much easier when it comes to solving this question. Refer to slide 3. To find the probability of him having work given that he was late you must:
STEP 1: Find probability of P(WL) and P(NWL)
-just like the other probability question -multiply probability of W and L -multiply probability of NW and L
STEP 2: Find on tree where there was a case that he was late
-case found on two branches -another given that question meaning P(W/L) -plug in values -work shown on slide 4
b) STEP 1: Circle on tree when case is NL
-2 branches circled - not a given that question because only one case needed to be satisfied which is NL
STEP 2: Add probabilities
-can either be P(WNL) or P(NWNL) -keyword or meaning to add -work shown on slide 5
STEP 1: Drawing tree This is a probability question so it is always helpful to draw a tree. Refer to slide number 3. The 1st branch consists of 2 cases which are he’s the father (F) or maybe he’s not (NF). The next cases branching out from those are whether the test was positive (P) or negative (N) in determining the last case.
STEP 2: Find the probabilities of the different cases -refer back to tree -find P(FP), we multiply the two values because we want the probability of him being the father (.2) and the test being positive (.99) -keyword is and meaning to multiply -same process for rest of cases
STEP 3: Find cases on branch where he tested positive: -question states the paternity test was positive -circle the branches where the outcome was a positive -the case of him testing positive is true in 2 branches, which are P(NFP) and P(FP) -whenever a case fits on more than one branch, it is a given that question -since you want to find whether he tested positive and is the father you are looking for P(F/P) -now all you need to do is plug in the values of P(FP) and P(NFP) -refer to slide 4 for the work
**MADE TYPO ON SLIDE WITH GRAPH, FULL PERIOD IS 362 NOT 352
a) Graph
Find day of max and min: -max is where x=0 because that is our starting point for this graph January 1 -to find day of min add up number of days from jan to june -we're making february only 28 days -after adding it all up our min should be on the 181th day!
Drawing graph: -x axis is days, y is temperature -when x=0 is January 1 -we're given the max and min -knowing max and min we know half a period, multiply by 2 to get full period of 362 -make your 4 ticks quickly for the days -full period is 362, 3/4 of a period is 271.5, 1/2 a period is 181, 1/4 a period is 90.5 -max temp of 37 and min temp of 15, we need to find the avg value -write down the max and min values on the y axis -avg value = (37+15)/2, which is 26! -so you should have a point on (0,37) which is the max and a point on (181, 15) the min -this is a cosine graph since it starts at its max point -pattern of a cosine graph is it will go to its max point then to its avg value then to its min back up to its avg value and up to its max
b)Equation:
A=amplitude can be found by finding the difference of the max and avg value or the difference of the average value and the min B=2pi/period C=phase shift is the number of units the graph moved from the original sine or cosine graphs on the x axis D=avg value
Cosine A= 11 B=2pi/362 c= no phase shift since it already starts at its max point D=26
Sine **sine and cosine are related by pi/2 units on the x axis**
A=-11 (negative sign flips the graph over so it goes from its min to avg value to max) B=2pi/362 C=-90.5 (sine graph starts on its avg value, 90.5 is the value of which the cosine graph is at its avg value so we must minus 90.5 to move the graph left) D=26
c)Finding the temperature on March 17
-first find the how many days from January to march 17 there is -that is 76 days -then all that is left to do is to plug it in plug it in -plugging the value into the cosine would be a faster way to get the answer since it has no phase shift
And you are now done this question XD.
Posted by kristina at 5:00 PM
My Last Piece of Work: REFLECTION
1)Why did you choose the concepts you did to create your problem set?
The concepts we chose had to deal with question we either hated or loved. What the important part of picking the questions was the mathematical "grit" as Mr. K called it. There had to be a level of difficulty present in the question that would make it somewhat a challenge. It wouldn't be very helpful to our learning if we used a question like what's log10. There wouldn't be much explaining going on with that.
2)How do these problems provide an overview of your best mathematical understanding of what you have learned so far?
Well from reading my explanations on how to solve the questions, it shows which questions I had difficulty with or not. I thought I explained the log questions the best because I feel most comfortable with that and I think...it shows in my explanation. In my other questions, I explained it as best I could but it does show I'm still flawed at understanding those question. However, I can tell from when I first learned this to redoing questions similar, I am doing much better at them. Some of these questions like the graphing one I hated and I still hate but I feel much more confident with them.
3)Did you learn anything from this assignment? Was it educationally valuable to you?
I didn't enjoy doing this assignment. It'd be wrong for me to like any homework assigned XD. Saying that though, it wasn't useless even though I had to force myself to work on it. Doing this was quite a valuable experience. Without it, I would never have opened my dust collected exercise book and looked/redid questions. If anything this has taught me, I'd rather solve a question than make one up because of the two solving is much easier.
Posted by Joyce at 4:47 PM
Wednesday, June 4, 2008
Reflection: Kristina
Why did you choose the concepts you did to create your problem set?
Well, we both chose the concepts together as we had problems on similar things. The first one that came to both our minds was definitely the Saskatchewan question and the like. I remember doing terribly bad on that type of question for the test and as soon as I heard of the DEV project, this question was an instant choice to put onto our project. Our other questions were also based on past questions that we've had significant difficulty on before. We definitely had to have a question involving probability or counting since those two units were two of the harder units for us. In the end, we ended up choosing two probability questions that were difficult for us. As for our last question two questions, we figured that a logarithm and a conics question would be suitable, considering that there were questions from those units that we found difficult at first glance, but then found them to be easy afterwards, so we wanted to show our newly found knowledge on those.
How do these problems provide an overview of your best mathematical understanding of what you have learned so far?
These problems help provide an overview of my best mathematical understanding since these used to be some of the harder questions for me, but after having going through them and picking at the little details as to how to solve them, I think that my understanding is shown very well. Specifically with the explanations and diagrams and such. I also remember trying to combine knowledge learned in grade 11 to one of our questions, which was the fish question (finding whether a line intersects another, or in this case a parabola), in order to show how much we understood how the question works.I've also gotten to show all the things I've learned how how I've improved on how these questions, compared to before. Did you learn anything from this assignment? Was it educationally valuable to you?
Saying that I didn't learn anything from this assignment would be a lie! I learned so much and it was a good review from previous units as well. It was a great educational experience and I think that it was very valuable to me. I also got to improve greatly on questions that I've done poorly in the past and I gained a greater understanding of certain concepts. If I hadn't been given the experience of doing this assignment, I would definitely feel more overwhelmed than I should be for the exam. There is also the fact that I've learned a bunch of neat html codes just by doing this assignment, although not really math related, I thought it was pretty cool. Heck, just learning how to put music onto the blog was fun enough for me! Well then, I'm done! *collapses*