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Tuesday, September 9, 2008

The 9th of September

Whoa! Well, the reason why I'm doing this post later than usual is because I forgot about it until now. I decided to start this post at 3pm right after my school, but I decided to wait for the slides to get published so I would of had something to work with. Now, seeing as the slides did not get published, I should have originally done the post at 3pm, instead of 11pm. Sorry class, I should not have waited!

Today in class we pretty much just recapped on functions and graphs from our gr. 12 pre-calculus year. We were given a box with a width of 8 - 2x, length of 11 - 2x, and a height of x. We were asked to find the volume of this block. Even though x is not given we can find the volume quite easily because volume is length multiplied by width and multiplied by height. When the values are input to the equation it should look similar to this : V = (x)(8-2x)(11-2x). We were asked to input this into our calculators as a graph and find the zeros. I found that this graph has one zero at a value of 5.5

Our next problem was a word problem: "Find the function for the max profit when selling golf balls prcied at $3 and costing 60 cents. At this price you can sell 1000 golf balls. Decrease price by 10 cents for each decrease you sell 50 more gold balls." The equation should look something like this: profit = (price - cost)(# sold), The value I wrote this in was in cents, so $3 would be 300 cents. the filled in equation should be profit = ((300 - 10x) - 60)(1000 + 50x) where 300 - 10x is the price, 60 is the cost and 1000 + 50x is the #sold. The value of "x" should be the amount of times the price of the gold balls is decreased by 10 cents. After a bit of solving it should for from this: ((300 - 10x) - 60)(1000 + 50x) to this: (240 - 10x)(1000 + 50x). When graphed it should look like an upside down parabola. To find the x- value you need to find the roots but solving for x in each bracket, and finding the average of the two root values, which is the axis of symmetry where x should equal 2. To find the max profit you must find the max point of this upside down parabold, which is the y-value of the vertex. Since x is found you can put that into the equation and solve. (240 - 2(2))(1000 + 50(2)). This should workout to the max profit being 242000 cents if you decrease the cost of the $3 golf balls by 10 cents twice, so 20 cents to be specific giving you $2.80 gold balls.

The last review question is of a box that Mrs. Ingram drew and only one given equation being: 4h + 8L = 6. We were asked to find the surface area of the box, and write it as a function of (L). So on a box there are 4 surfaces that are equal, and another 2 that are equal, for a total of 6 surfaces. The area of a surface would be length multiplied by width for each surface. For the 4 equal sides, it would be 4hL and for the 2 smaller sides it would be 2L^2. The equation should then look like SA(L) = 2(L^2) + 4hL. Well, that "4h" looks familiar. It looks like it cam from an equation which was given already:
4h + 8L = 6. By a bit of massaging you can change that equation into 4h = 6 - 8L and then input 6 - 8L in the surface area equation as 4h. The surface area equation should look like this: SA(L) = 2(L^2) + (6 - 8L)L with a bit of solving you can change it into SA(L) = -6(L^2) + 6L and you're done, because that's as simplified as it's going to get.
Toward the end of class we plotted f(x) graphs, they were pretty simple such as: f(x) = x and f(x) = x^3 and those other simple ones. Then we briefly sketched transformations using a square root function. We didn't get to indepth in the area, but I believe we will continue our review on this for tomarrows class. That was pretty much all we did in class today, so our next scribe will be:

- Rence

So long for now. -Francis

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