THE FUTURE OF PREMIUMS Mid Project Update TRAC Dev Workshop, January 16, 2013.
The dev project
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Transcript of The dev project
The DEV ProjectBy Matt
Problem 1
Graph: x³+9x²-64x-576 x³+7x²-50x-336
Given: x=-6
To solve this problem you have to get the numerator and denominator to simplest forms
Since there are four proportional terms we can group the numerator so we start of by factoring out the GCF
After doing that we end up with this because both sides are multiplied by (x+9)
Because of difference of squares we are able to simplify it even more
Since the denominator is not proportional we must long divide using -6(given)
To long divide you must find out what you have to multiply by x to get x³( its x²) then multiply that by the rest of the polynomial then subtract the new from the old and repeat
We come out with this
Reduced to
Now we must get what we need for the graph out of the equations
Factored Standard
Vertical Asymptote: -6,7 in denominator of factor form when we put 0 in for xHorizontal Asymptote: 1 in standard form taking highest power then dividingX int: -9,8 in numerator in factor form when we put 0 in for xY int: 12/7 taking to lowest powers from standard form and dividingHole: -8 in factored form when numerator and denominator are the same
The Graph
Question 2
• Mark has 200 feet of fence he want to make a fence around his garden and use his house as one of the sides to make the garden bigger. What is the maximum area Mark can have?
• Find domain and range when done
We must start of by making 2 equations that show perimeter and area
Since we have 200 feet of fence and we have 3 sides 2 of which are the same the equation is
200=2x+y
We must solve for a now
Start of by solving the Perimeter formula
200-2x=y
Put this equation in for y in the area equationA=x(200-2x)
A= -2x²+200x
To find the maximum value use the formula -b/2a to find the x of the vertex
-200/-4= 50Plug x into the equation to get the maximum
-2(50)²+200(50)=5000D:(-∞,∞)
No number x cannot equalR:(-∞,5000]
No minimum value and already found the maximum
Question 3
Distribute(x+4)(x-4)(x+6)(x-10)(x+2)
Start of by distributing (x+4) to (x-4)Then you should get
Which simplifies to
Distribute (x²-16) to (x+6)
You should get
Distribute (x³+6x²-16x-96) to (x-10)
You should come out with
Simplify to
Distribute (x⁴-4x³-76x²-256x+960) to (x+2)
Comes out to
Simplifies to
Question 4
Factor 10x²+82x+27=x²-2x
Get it Equal to Zero
Subtract x² then add -2xWhich should get you 9x²+84x+27=0
Set it up
(9x+ )( + )You must then find to numbers that multiply to
get 27 but add to get 84x
You should come up with (9x+3)(x+9)
X=3/9X=9