2005 Free Response Question #5

I hate free responses...

Anyways! Sandy Beach has some problems that needs to be solved! :

Sand being removed:

Sand being added:

A. How much sand will the tide remove from the beach during this 6-hour period?
We use the equation R(t) for this one! Integral of 2+5sin(4pit/25) from 0 to 6. It should output an approximation of 31.816 cubic yards of sand removed.


B. Write an expression for Y(t), the total number of cubic yards of sand on the beach at time t.
Since the sand is being eaten [R(t)] at the same time it's being put on the beach [S(t)], we need to combine them to find out how much of the sand remains! Our new equation will be:

Y(t) = [S(t) - R(t)] + 2500

C. Find the rate at which the total amount of sand on the beach is changing at time t=4.
I don't think you include the +2500 in Y(t) for this one because it's asking for the rate of change of the sand... :/ Bleh, confused. Either way, if you plug in 4 into Y(t) without the +2500 then you'll get -1.908750647 which should be rounded out to about -1.909 cubic yards...??


D. For , at what time t is the amount of sand on the beach a minimum? What is the minimum value? Justify your answers.
Given that the boundary is 0 to 6, those are our endpoints i assume? I'm too lazy and confused to find the critical points... so using my magic calculator of magic, I found that our critical points are t= 0, 5.118, and 6! ... But I still don't know whether 5.118 is my minimum...

Now then~

*Brings out ipod and begins singing to Help! by the Beatles...*

What's On Your Mind?

PURPLE~

Which mindset do you think you are a part of when it comes to "intelligence"? According to the reading, what tells you that you are of this mindset?

Truth be told, I really don't believe in these kinds of theories or explanations. But for the sake of this assignment, I would assume that I belong in the fixed mindset because of all the obstacles I am avoiding. Not mainly because I think they are 'hard' or 'time consuming', but because I know that my mind can't take any more. I don't give up THAT easily, and criticism isn't always acknowledged, but I do put in effort, just not into the right subjects or matter. I enjoy challenges, but to my benefits or entertainment. Seeing others accomplish is actually encouraging rather feeling it as a threat. Overall, I don't really know whether or not if I'm more of the fixed mindset than growth mindset.


How has this mindset helped or hurt you in math?

I have no clue. Like I said, I don't really believe in these kinds of theories because they don't always apply to an individual. But if I had learned about this beforehand, I would have been discouraged from the beginning rather than attempting to better myself. I may be struggling, but it won't affect me so m


What is your reaction to finding out that the brain is just a big muscle that can be trained?

I've always known that the brain can be trained but not that I really paid mind to it. But I'm evil to my brain, I feed it dark knowledge and never bother to remember much information besides junk, music, art, and life changing quotes. Thus resulting into a bad trained brain with a wild imagination... with some sort of wisdom about this world. XD


How do you see this new piece of information affecting your future?

I don't and it won't. I can guarantee that. Either because I will pay no mind to it, forget it, or just believe que sera, sera. But if I do somehow believe in this, assuming my nature, I'll be discouraged. But we never know what tomorrow will bring us. Heck, I'm just glad if I get to open my eyes tomorrow...