Hello everyone!

Today started off with an in depth study of our homework. The first question we looked at was well... number 1...

The point of doing number one was to show how to find a good domain in a problem that does not give any concrete numbers to work with. The example was talking about the number of daylight hours per day. Mr.K then dived right into the in depth analysis of the problem. We discussed the day with the most daylight (Summer solstice), the day with the least light (Winter solstice) and the days which the amount of daylight is equal to the amount of night (cannot remember what they were called). With this information in hand and the assumption that we are in Saskatchewan and at the equator to simplify this we delved into finding a suitable domain and range. Since the cycle comes full circle from summer solstice to summer solstice it was decided that a year would be a fair domain. For range we estimated that the daylight would shift by three hours off dead even at the solstices (at this point we also realized that this is a sine or cosine graph pretty much straight out of last years questions). So we found the domain and range and the shape of the graph which satisfied the question. But Mr.K is not satisfied with teaching us merely the rudiments of what we need to know so to the weather network statistics page we went and we observed all the different patterns Winnipeg goes through.

The second question that we moved onto goes as follows:

An open box is made by cutting squares of side x from teh four corners of a sheet of cardboard that is 8.5 by 11 inches and then folding up the sides.

a) Express the volume of the box as a function of x.

No without crunching numbers terribly much we came up with the domain. We knew that it could not be 4.25 inches or more because we'd lose the third dimension therefor losing the volume and you cannot cut 0 or less because you cannot cut negative distances and if you don't cut at all you don't have a third dimension and therefor no volume.

From there we continued to make x useful and make it the size of our cut. From there we deduced that the 8.5 inch side must be 8-2x because two sides will be cut from it and same with the 11 inch side as shown in the diagram below.




Then using what we know about volume, we found the function that related x to the volume. All we had to do is multiply the L x W x H. So our function ended up as f(x) = x(8.5-2x)(11-2x). (Though the slides show it as 8 - 2x).

Then Mr.K got rid of a wasp.

We then moved onto the golf ball question which ended up looking very similar to many questions we have answered in the past years and we quickly caught the drift of it. The only thing that was a little bit tricky was the fact you had to look back in your work for the answer (view slide 2).

The last question that we handled from our homework was as follows:

A wire 6 meters long is cut into twelve pieces. The pieces are welded together to form the frame of a rectangular box with a square base.
a) Define a function that relates the height of the box to the length of one edge of the base.
Well first off we knew that all the sides of the base and top must be the same because it is a square and the four sides connecting the squares must be the same length as well, so our equation for the perimeter became 4H + 8L = 6.
b) Define a function that relates the total surface area of the box to the length of one edge of the base.
Well we quickly came up with a formula for the surface area 2L^2 + 4LH = SA.
But we had to express it in terms of one length of the base. So finagling with our first equation we isolated H and substituted it in and took it as solved (slide 3).

From this point on we were just drawing graphs...
The only one that was tricky was the graph of f(x) = sqr(-x-2). Within it you have to factor out the -1 in both terms or else when you do your flip then translation it will be wrong.

Remember to do your homework! If I can this weekend I'll update this to try out a JAVA applet I'll create (found a couple stumbling blocks). Have a good weekend!

The next scribe is......







John D!