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RE: Dividing by variable when solving algebraic equation
October 26, 2016 at 11:12 am
(October 26, 2016 at 2:48 am)Alex K Wrote: I'm teaching my 11th graders quadratic functions right now, they are not amused. Question: you have 100 meters of fence to fence in a rectangular area, but one of the sides doesn't need a fence because there's a wall already. So the question is, how long and wide do you choose your corral to maximize the area.
How most physics questions used to sound to me:
A ball is falling from 25m. The mass of the ball is 2kg. Calculate the exact time of the plane landing in Bangladesh if the sun is seen on the north side of the sky and the course of Euro is 2$.
RE: Dividing by variable when solving algebraic equation
October 26, 2016 at 12:44 pm
(October 26, 2016 at 7:37 am)robvalue Wrote: I like questions like that though, because they show a simple application of maths to a real situation where guesswork would only get you so far.
For those that are interested, this is how you get the answer:
You have 100m of fence to make a rectangle against a wall, which forms one of the four sides. So if the length of the rectangle coming away from the wall is x, you'll be using x also for the side above it, leaving 100 - 2x for the third side, opposite the wall.
So the area is
A = x(100 - 2x) = 100x - 2x^2
To find the maximum, we differentiate with respect to x, to find the rate of change in the area. To differentiate Ax^n, you get Anx^(n-1)
dA/dx = 100 - 4x
At a maximum or minimum amount, the rate of change is zero. (Think of the top or bottom of a quadratic curve; the tangent becomes flat.)
0 = 100 - 4x
x = 25
To check this is indeed a maximum, we take the second derivative:
d2A/dx^2 = -4
This means it is a maximum, as its less than zero. The rate of change is lessening as you approach and go over the point. Less than zero is a minimum.
So with x = 25, the side opposite the wall is 100 - 2*25 = 50
Once you get to the formula for A in terms of x, there's an alternate method that doesn't involve using calculus. You can complete the square instead, and then pick the relevant value for x to give what is obviously the maximum value for A.
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RE: Dividing by variable when solving algebraic equation
October 26, 2016 at 3:47 pm
(October 25, 2016 at 9:58 pm)FallentoReason Wrote:
(October 25, 2016 at 9:54 pm)Fireball Wrote: Could I have an example?
Any equation where the constant is positive will do.
E.g. x^2 + 4
Let's test where it intersects the x axis:
x^2 + 4 = 0
=> x^2 = -4
therefore, x = 2i
Thanks! Next time, I'll pour more coffee down the inside of my neck before I ask a question. I taught algebra for a couple of years. My brain obviously had checked out for parts unknown while reading this thread.
If you get to thinking you’re a person of some influence, try ordering somebody else’s dog around.
RE: Dividing by variable when solving algebraic equation
October 26, 2016 at 4:01 pm
(October 26, 2016 at 11:12 am)Vic Wrote:
(October 26, 2016 at 2:48 am)Alex K Wrote: I'm teaching my 11th graders quadratic functions right now, they are not amused. Question: you have 100 meters of fence to fence in a rectangular area, but one of the sides doesn't need a fence because there's a wall already. So the question is, how long and wide do you choose your corral to maximize the area.
How most physics questions used to sound to me:
A ball is falling from 25m. The mass of the ball is 2kg. Calculate the exact time of the plane landing in Bangladesh if the sun is seen on the north side of the sky and the course of Euro is 2$.
RE: Dividing by variable when solving algebraic equation
October 27, 2016 at 1:32 am
irrational Wrote:I know for all you math masters out there, this is basic stuff.
I'm far from a being a math master myself. For me at least, I think math is cool and am interested in gaining a basic understanding of it. That being said, I thought your post was pretty cool. I've often found that when I'm struggling with a problem, it is due to my lack of familiarity with the basics, such as having an incomplete understanding of particular terms in definitions or being a bit rusty in fundamental algebra, trig, or calc concepts (etc.). Furthermore, I've learned to value the instances where I have the humility to crack open the books, engage in research, or pick another person's brain: this helps me avoid the trap of using the same problematic thinking, which got me confused in the first place.
P.S. Thanks for the cool thread and good luck with your math endeavors, sir.
Thanks! Next time, I'll pour more coffee down the inside of my neck before I ask a question. I taught algebra for a couple of years. My brain obviously had checked out for parts unknown while reading this thread. 
