Fall 2016 - Professor Kate Poirier

# Author: Sonam

A circle that contains all three vertices of the  triangle ABC is side to circumscribe the triangle. The circle is called the circumscribed circle or simply the circumcircle of the triangle. The radius of the circumscribed is called the circumradius.

#### Theorem – Every triangle has a unique circumscribed circle. The circumcenter is the center of the circumscribed itself.

https://ggbm.at/ekkyFwsN

### I .Do Now: read the following problem.             https://www.desmos.com/calculator/ecnyow98r1

Marry has decided to plants some flowers, so she can make packet money.  She will spend up to \$180 for the seeds. One rose seeds cast \$15,  one peony seeds cost \$5. She has enough space for plant 16 flowers. She wants to plants at lest 3 peonies and at lest 8 roses. If peonies earn\$40 for her and the roses earn \$60. how many of each type should marry to plant to maximize the amount of packet money she can make?

1.  From the problem, list all the constraints:

• She will only spend up to \$180 for the seeds.
• she has space only for 16 flowers.
• she wants plant at lest 3 peonies and 8 roses

2. Find variables:

let  x = # of roses  and  let y = # of peonies

### II.  Use Desmos to solve the problem by turning all the constraints into Inequalities.

1. Turn the first two boxes of Desmos Graphing Calculator into a text boxes.

Type in our variables      x = # of roses and let y = # of peonies

2. Turn the all constraints into inequalities and type then into the boxes of Desmos Graphing Calculator.

•   15x + 5y ≤ 180
•   x + y ≤ 16
•   y ≥ 3
•   x ≥ 8

3. Turn everything into same color, that will make the region that we’re looking for a little bit more clear, because it just the darkest region.

4. The four sets of intersection of the darkest region are the sets that satisfied of our constraints.

•       (10,6)
•       (11,3)
•       (8,3)
•       (8,8)

### III. Solve the problem by set up a function with two variables x and y.

1.   f(x,y) = x(60) + y(40)
2. Plug the four sets into the function.
• f(10,6) = 840
• f(11,3) = 780
• f(8,3)   =600
• f(8,8)  = 800

### IV. Conclusion :

As you can see when x = 10 and y = 6, Marry can make the maximum of money \$840. So she should plants 10 roses and 6 peonies.

I grew up in Tibet, I speak Tibetan, Chinese, and English. I came to United States five years ago.

Since I was in elementary school,  I am interested in History and Math. I love history because it tells you a lot of interesting stories happened long long time ago. And math, I did not really liked it  at the beginning, until Ms.Kang Ruo became my math teacher when I was forth grade. I liked the way she taught us Math, and I started like math after that too.

When I was in the high school, I believed that graphing calculator was a very helpful tool for my math class. other than that I also think Maple is a great tool  for solving advance  Math problems.

I hope I can get  best grates I can get from all the classes.  And become a qualified teacher at the end.

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