Mid point Problem

Today we were given an assignment to find the midpoint of two places in the world that we like or would like to live in, visit etc. I had a hard time figuring which place to chose since i was blessed to travel to a lot of places around the world, so these were my top three results. New York Manhattan my dream town (which iv never been to) Paris (which is beautiful) and Belgrade (which i live in) so i settled to New York and Serbia. First thing to find is the latitude of the longitude of the places at hand.

 We take the two latitudes and longitudes which are 44.789489 and 20.432335 for Serbia Belgrade and 40.790077 and -73.958716 for New York Manhattan and we take the y's and x's and we add it together and divide by 2.
44.789489+40.790077/2=42.789783
20.432335+-73.958716/2=-26.7631905

 And the mid point was in the ocean somewhere as shown bellow:

Test Reflection

When I've got handed my test back I was pleasantly surprised at the answer i got right. There was nothing bellow a 7/8 which for me is a victory, and I was even more enlightened when I saw a 6/6. All in all the studies I did before hand all came into use and reflected on my test.

But now comes the part in which I have to talk about the changes I would make if I could go back and time and redo the whole test. One of my biggest problems was not reading a question fully but just guessing what the teacher wanted from me. One example of this (and the only example) was instead of me doing surface area, I had to do perimeter and of course Iv got that question as a redo to which i lost one point, one perfectly good point, which could of turned out to be 8/8 but did not because I haven't read the questions thoroughly.

My second change would be, writing the units, weather they be kilometers, centimeters and so on. But this is one essential thing I forgot to do which might have cost me a point or might have not.

Google Sketch Up Geometry

1) First off we decided to do the length of the slope.sa
2) We figured out that in order to find the slope we need to find the height and the base
3) After studying the shape we figured out that the rise is 1.5m by seeing that the height is 3m then 1.5 is half so another would get us the the place we wanted also indicating that its height is 1.5
4) The run how ever is 3m we saw this because the whole base was 6m while half was 3m and the point where the run was located was half point (plus there was more evidence showing that this was 3m)
5) A^+B^=C^ --> 2.25 +9.00= 11.25=C^ while C would be 11.25 square rooted= 3.35
6) Surface area- Divide object up, number separate Surfaces, calculate each one, add together to find the total m^2
7) We found the volume of the shape by multiplying the width times the length times the height

Triangle Problems

The pictures say it all! 

How to Find the Circumference of a Circle

To explain how to find the circumference of a circle i will show it in steps making it easier to understand it.   

Step 1: Draw a circle and when you do make a triangle within the circle to the have point making this your radius.

Step 2: we are going to calculated the the height and base of the triangle that we have drawn into our circle

Step 3: Could also be in step 2 but this is find the formula of what were trying to do which is this: B*H (base times hight) over 2 

Step 4: We change the B within the formula making it C (circumference) because we are looking for the circumference not the base

Step 5: We notice that Diameter times pie=c So we could also change formula once more making it now: D*pie*r over two. The same exact formula just a little less loose and we also gained a little bit of knowledge knowing what times what equals the circumference 

Step 6: Looking back at step five we see that the diameter is made up of radius times radius (across the circle) then we write this in as r(2)

Step 7: The formula looks like this (the finalized look until we eliminate the two's) 2r*pie*r over 2

as i mentioned above the dimeter is now replaced with 2r

Step 8: We eliminated both of the twos leaving us with r*pie*r 

Step 9: Notice that there are 2 r's so we put both of them together making it r(2)

Step 10: Final step we take the what we got, which is r2*pie and we flip it around because thats the mathematical way its written, but mathematically look at it it really does not matter, giving us our final formula:

Pie*r2

Google Earth Math

Pythangorean Theorem

A,B,C just by itself is the length but if you take those letters and square it then its a equal area and if you cube it is a volume.

A=1km(to the second power) plus B=0.5(to the second power) equals C(to the second power) 

After doing this you want to add all the numbers by its self (or in other words you would want to square it) which would give you something that looks like this problem bellow:

1+0.25=C(to the second power) now in order to find your answer while using this theorem (which is one of the most right theorem that's been around for thousands of years) you would add 1 with 0.25 giving you 1.25 and now we know that

C(to the second power)=1.25

but we want to know what C alone is which means we would have to find the square root of it. The answer being: 

C=1.12

Now to plug it back in or check it if you will you would take 1.12*1.12 which will give you 1.25-0.25 (which comes from the B)=1

1.25-0.25=1

10 Problems for the Game

1)Easy: the estimated raise in your population if your square root was 45

2)Easy: you have a meteoroid storm heading straight for your planet do you want to use your $45 dollars (or how ever much) to raise new technology to block the meteoroid from hitting your planet or do you choose to decrease in population by 5-10% because a meteorite hit the surface (people are happy with your decision and they give you 10 dollars in total

3)Hard: 2x+10y=50 (something that will have money+population and resources all together)

4)Easy: x+5=30 Maybe this can be calculated as resources

5)Medium: 7z*3a (over) 7z*1

6)Have a question asking what are real numbers and how could they be used in this game as money or any other way

7)After the question about real number should come a one about rational numbers because (if i can say so my self) they are one of the most confusing and forgettable in the whole table

8)There should be a ultimate question won if you get right will give you 100% population 100% money and 100% resources. if you miss you only end up with 5% population and nothing else. This may be like an dangers eclipse of some sort.

9)Medium-hard:Simplify the square root of 10/11 if you do what ever the number is you will get the money

10) A retrieve question which can help you out when you have no more things to relay on

Radical Expressions

Solve the following:
1a) square root of 45 (extra information)
How i solved this is by first looking at the the square roots closest to the number 45. The one before it is 36 (6*6) while the one over it is 47 (7*7) When i finish this step i had to see which one 45 was closer to in this case its a no brainer. From 45 to 47 its 2 numbers from 36 to 45 its 9. So I knew after i did this that the estimated number were looking for (the square root has to be larger then .5 because its over the half way line. So my estimate was 6.7 and then to get a little fancier (closer to 45 or atleast thats what i think) i just added a 3 so the final answer would be 6.73. Now to check your work just take,
6.73*6.73= 45.2929 which is pretty close to 45

1b) Simplify square root of 45
This may sound confusing but it's really easy to do. You find two numbers that can go into 45 but at least one has to have a square root. So it would be the square root of 9 times the square root of 5. This is when the square rooting comes in. Square root of 9=3. There is no whole number square root to 5 so we just leave it 5 making our problem 3 times the square root of 5

2) Simplify square root of 12 divided by the square root of 3
starting of you would first divide 12 with 3 which would give you 4 which in our math world is perfect because 4 has a square root which is 2. Coming to our answer fast and easy.

One Idea For Math Game

One idea that came to mind when thinking about our game was, what will the people who are out do. Somehow everybody has to be involved no matter how long we play or who loses, but of course people have to go out, its in the nature of the game. So I though of a think called second chance. Once a player has come to the lowest point he can get he can choose a hard card (only) and he can go all in or choose to stay out, it all depends on his choice. If the player gets the answer right he gets 1 of everything. By this I mean population (people) houses, and resources putting him back in the game. However if he messes the question up he loses everything and is out of the game. I also just thought of a card where a player (if he gets it incorrect) must lend 2% of his population to another player. These aren't all the way thought out, but would certainly make the game better (in my opinion)