mmend98
  • mmend98
The development studio behind the newest video game, Super Ostrich Racers, needs your help. Super Ostrich Racers is an exciting, fast-paced adventure game where your ostrich runs through 20 different levels while collecting coins. They need you to develop the number of coins and points for each level and provide data for the programming team. Create the data to fill in the tables below. The Coins table must be an arithmetic sequence and the Points table must be a geometric sequence. The common difference or ratio cannot equal 1 or 0. Provide reasons and justification of how you know the Co
Mathematics
chestercat
  • chestercat
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mmend98
  • mmend98
mmend98
  • mmend98
Create the data to fill in the tables below. The Coins table must be an arithmetic sequence and the Points table must be a geometric sequence. The common difference or ratio cannot equal 1 or 0. Provide reasons and justification of how you know the Coins sequence you created is arithmetic and how you know the Points sequence is geometric. Level Coins 1 2 3 Level Points 1 2 3 Planning is crucial in the early stages of this project. Demonstrate how a recursive process will allow you to find the number of coins and points on all levels up to level 5. The development team has asked you to jump ahead of them in the project. Create the sequence formulas, an, for the coins and the points based on the level in the game. Then describe how the formula can be used to find the coins and values on level 15. Use complete sentences. If the game only has 20 levels, explain how to find the value of the series for the coins and the points. Use complete sentences and arrive at final values. The programming team needs to understand the parameters for the game, in order to start coding it. Explain any restrictions to the domain and range of your sequences
mmend98
  • mmend98
this is what I have so far I need help on question 4 and question 5
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ganeshie8
  • ganeshie8
lets fix the mistakes in parts 1-3 first
mmend98
  • mmend98
ok
ganeshie8
  • ganeshie8
In part 1, below highlighted word should be "difference" right ? because "ratio" for an arithmetic sequence makes no sense |dw:1439525121495:dw|
mmend98
  • mmend98
k fixed it
mmend98
  • mmend98
what is next
ganeshie8
  • ganeshie8
good, lets see part 2
mmend98
  • mmend98
k
mmend98
  • mmend98
Is part 2 all correct?
ganeshie8
  • ganeshie8
nope, it is totally wrong
mmend98
  • mmend98
dang haha
ganeshie8
  • ganeshie8
you're correct about the recursive formulas but the numbers are wrong
mmend98
  • mmend98
okay
ganeshie8
  • ganeshie8
|dw:1439525341712:dw|
ganeshie8
  • ganeshie8
where does that \(9\) come from ?
mmend98
  • mmend98
let me see
mmend98
  • mmend98
I honestly don't know haha
ganeshie8
  • ganeshie8
|dw:1439525998794:dw|
mmend98
  • mmend98
its so hard to write these formulas on pages so is there anyway i could change my arithmetic series column to match this
mmend98
  • mmend98
I changed them to 3,6,9
mmend98
  • mmend98
and 2 4 8
ganeshie8
  • ganeshie8
Ahh okay, please attach the updated pdf so that it will be less confusing
mmend98
  • mmend98
kk
mmend98
  • mmend98
1 Attachment
mmend98
  • mmend98
ganeshie8
  • ganeshie8
parts 1,2,3 look okay now but your teacher can easily guess that you have copy pasted that stuff from internet
ganeshie8
  • ganeshie8
|dw:1439526431634:dw|
ganeshie8
  • ganeshie8
you seriously need to rephrase that into ur own words
mmend98
  • mmend98
ok
mmend98
  • mmend98
just completed that
ganeshie8
  • ganeshie8
okay good, whats the part 4 ?
mmend98
  • mmend98
i havent completed it yet. let me attach the question
ganeshie8
  • ganeshie8
can you copy paste only the part 4 question here
mmend98
  • mmend98
If the game only has 20 levels, explain how to find the value of the series for the coins and the points. Use complete sentences and arrive at final values.
ganeshie8
  • ganeshie8
remember, the word `series` refers to `sum`
mmend98
  • mmend98
ok
ganeshie8
  • ganeshie8
so basically you need to find the sum of first 20 terms
ganeshie8
  • ganeshie8
look up your notes for "sum" formulas of arithmetic series and geometric series
mmend98
  • mmend98
do i use this formula ?
ganeshie8
  • ganeshie8
yes, what formula ?
mmend98
  • mmend98
1 Attachment
ganeshie8
  • ganeshie8
there is another formula, look it up
mmend98
  • mmend98
this one
mmend98
  • mmend98
1 Attachment
ganeshie8
  • ganeshie8
nope
mmend98
  • mmend98
haha which one do i use. do i use the same formula for question 3?
ganeshie8
  • ganeshie8
for arithmetic series, it should look something like below : \[S_n = \dfrac{n}{2}[2a+(n-1)d]\]
mmend98
  • mmend98
ahh how do i put my numbers into this
mmend98
  • mmend98
if u don't mind putting them in i will calculate
ganeshie8
  • ganeshie8
do you know that exactly are we finding here ?
mmend98
  • mmend98
what?
mmend98
  • mmend98
we are trying to find the value of the series for the coins and the point
ganeshie8
  • ganeshie8
we want to find below sum : \[3+6+9+\cdots (\text{upto 20 terms})\]
ganeshie8
  • ganeshie8
whats the first term ?
mmend98
  • mmend98
correct
mmend98
  • mmend98
the first term is 3
ganeshie8
  • ganeshie8
so \(a=3\)
ganeshie8
  • ganeshie8
whats the common difference ?
mmend98
  • mmend98
3
ganeshie8
  • ganeshie8
so \(d=3\)
ganeshie8
  • ganeshie8
how many terms are there in the sum ?
mmend98
  • mmend98
20
ganeshie8
  • ganeshie8
so \(n=20\) plug them in the formula, the formula gives you the sum
mmend98
  • mmend98
ok let me calculate real quick
ganeshie8
  • ganeshie8
\[S_n = \dfrac{n}{2}[2a+(n-1)d]\] \[S_{20} = \dfrac{20}{2}[2*3+(20-1)*3]\]
mmend98
  • mmend98
s20=7.5?
mmend98
  • mmend98
sorry one sec
mmend98
  • mmend98
haha 750
mmend98
  • mmend98
s20=750?
ganeshie8
  • ganeshie8
try again
mmend98
  • mmend98
3420
mmend98
  • mmend98
geez
mmend98
  • mmend98
i think thats correct @ganeshie8
mmend98
  • mmend98
how do i change that formula for geometric series @ganeshie8
ganeshie8
  • ganeshie8
time to burn ur calculator
ganeshie8
  • ganeshie8
\[S_n = \dfrac{n}{2}[2a+(n-1)d]\] \[S_{20} = \dfrac{20}{2}[2*3+(20-1)*3]\] wolfram says that evaluates to 630 http://www.wolframalpha.com/input/?i=+%5Cdfrac%7B20%7D%7B2%7D%5B2*3%2B%2820-1%29*3%5D
mmend98
  • mmend98
okay now what is the formula for geometric
ganeshie8
  • ganeshie8
look up in your notes for "partial sum of geometric series formula"
mmend98
  • mmend98
this it?
1 Attachment
mmend98
  • mmend98
i am sorry for my slowness i just really am trying to get this done
ganeshie8
  • ganeshie8
nope, use this : \[S_n = a_1\dfrac{r^n-1}{r-1}\] where \(a_1\) = first term \(r\) = common ratio \(n\) = number of terms
mmend98
  • mmend98
okay so how would i plug this in
mmend98
  • mmend98
what would m common ratio be
ganeshie8
  • ganeshie8
|dw:1439528427488:dw|
mmend98
  • mmend98
k
ganeshie8
  • ganeshie8
plug them in and evaluate
mmend98
  • mmend98
okay.
mmend98
  • mmend98
Sn=2 (2^20-1)/(2-1)?
mmend98
  • mmend98
i don't think i plugged it in right lol
mmend98
  • mmend98
my answer was outrageous
ganeshie8
  • ganeshie8
what do you get ?
ganeshie8
  • ganeshie8
outrageous number for the sum is expected because this is a geometric series grows super fast
mmend98
  • mmend98
2,097,150
ganeshie8
  • ganeshie8
Perfect!
mmend98
  • mmend98
yes okay great.
mmend98
  • mmend98
I have question 5 now then i am done
mmend98
  • mmend98
The programming team needs to understand the parameters for the game, in order to start coding it. Explain any restrictions to the domain and range of your sequences.
ganeshie8
  • ganeshie8
for restrictions on domain, look at first column |dw:1439528857139:dw|
ganeshie8
  • ganeshie8
what numbers are allowed in that column ?
ganeshie8
  • ganeshie8
can you have 1.5 ?
mmend98
  • mmend98
no
ganeshie8
  • ganeshie8
or -2 ?
mmend98
  • mmend98
no
mmend98
  • mmend98
so how would i express that as my answer
ganeshie8
  • ganeshie8
domain is all the "inputs" that are allowed for the function to eat so whats the domain in our problem ?
mmend98
  • mmend98
the domain is 1,23,..?
mmend98
  • mmend98
There would be no restriction on the range. The domain for the points would be andy integer that is greater than or equal to 1, like 1,2,3,4,5,..etc.
mmend98
  • mmend98
would this work for my answer ? @ganeshie8
ganeshie8
  • ganeshie8
Looks good! the domain is all positive integers : 1, 2, 3, 4, 5,...
ganeshie8
  • ganeshie8
|dw:1439529213392:dw|
mmend98
  • mmend98
okay we are finished ! There would be no restriction on the range. The domain for the points would be any positive integer that is greater than or equal to 1, like 1,2,3,4,5,..etc.
mmend98
  • mmend98
Right?
ganeshie8
  • ganeshie8
there are rstrictions on range too
mmend98
  • mmend98
dang it
mmend98
  • mmend98
what are they haha
ganeshie8
  • ganeshie8
restrctions for range of arithmetic sequence : |dw:1439529300043:dw|
mmend98
  • mmend98
what does that mean
ganeshie8
  • ganeshie8
range is also positive integers, for arithmetic sequences the range is only the multiples of 3 for geometric sequence the range is only the powers of 2
ganeshie8
  • ganeshie8
please attach the updated the pdf if you want me check
mmend98
  • mmend98
k
mmend98
  • mmend98
1 Attachment
mmend98
  • mmend98
here it is @ganeshie8
ganeshie8
  • ganeshie8
Looks okay!
mmend98
  • mmend98
thanks i really appreciate you.. life saver
ganeshie8
  • ganeshie8
yw

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