Recent Changes

{bee.gif}
{cooltext422503332.png}
Cya Suckas, Chhyeaaaaa{calculusjoke.jpg}

{bee.gif}
{cooltext422503332.png}
{calculusjoke.jpg} Cya Suckas, Chhyeaaaaa

c. Your y variable is the section of wire corresponding to the 12ft pole and the z variable is the wire corresponding to the 28ft pole. W is the amount of wire of y and z combined. You want to find the minimum amount for W. The distance between the two poles is 30ft, so the one section between the 12ft pole and stake is variable x and the section between the stake and the 28ft pole is 30-x.
d. W=y+z
y^2
e. make sure that you have an equation thaty^2=12^2+x^2
so
y=sqrt(x^2+144) and
z=sqrt(x^2-60x+1684)
With these variables, you can differentiate withinsubstitute in to solve for W
Thus, W=sqrt(x^2+144) + sqrt(x^2-60x+1684)
e. W is differentiable, so,
dW/dx=(x/sqrt(x^2+144))+((x-30)/sqrt(x^2-60x-1684)
Set the Rules of Differentiationequation equal to zero to find your intervals.
f. use thex=9 and x=-22.5 Since -22.5 is an impossible number (for this example), your intervals to confirm that the values are maximums or minimumsfrom (0, 9)(9,30)
W(0)=53 W(9)=50 and W(30)=60
So, W(9) is the minimum value, optimizing the use of the wire.
Video
Practice Sites

b. Draw a sketch:
{wire.JPG}
c.
d.
e.Your y variable is the section of wire corresponding to the 12ft pole and the z variable is the wire corresponding to the 28ft pole. W is the amount of wire of y and z combined. You want to find the minimum amount for W. The distance between the two poles is 30ft, so the one section between the 12ft pole and stake is variable x and the section between the stake and the 28ft pole is 30-x.
d. W=y+z
y^2
e. make sure that you have an equation that you can differentiate within the Rules of Differentiation
f. use the intervals to confirm that the values are maximums or minimums
Video
Practice Sites

Completion of Wiki??
Hi Zach and Alyssa,
I noticed example 3 of your wiki is not complete. Could you please update your wiki with a solution so that I do not have to lower your grade for this project. Thanks!!

{6a00d83451c56869e200e54f06ee6a8833-640wi.jpg}
{6a00d83451c56869e200e54f06ee178833-640wi.jpg}
{sat.JPG}

OptimizationZack and Alyssa
{Calc_Wordle.JPG} {aaaaaa.jpg}{Calc_Wordle.JPG}
{aaaaaa.jpg}
Formal Definition
Optimization, or applied maximum and minimum, has no definite formal definition. It is solving for the absolute maximum or minimum of a function used to find real life applications. For example, a packaging company may want to make a box with X amount of volume, but with the minimum amount of packaging to minimize cost. Finding the dimensions of the box would be the proccess of optimization.