Algebra
[(a^-3b^-3c^-5)/(a^-3b^-3c^8)]^0
1
Using Calculus, mathematicians have determined an "Optimal Stopping Theory" algorithm that tells us when we should stop searching for things like apartments, candidates for a job, and even partners, and just cut our losses and settle.
Without knowing anything about what the apartment, candidate, or partner is like, and just knowing when they showed up in the order of explored resumes, the algorithm is able to find the best option XX% of the time.
37%
Use the quotient rule for exponents to divide:
(8k^3)/( 4k^6)
2/(k^3)
Sofia Kovalevskaya grew up around calculus: literally.
Her family couldn't afford wallpaper and covered her nursery walls with a professor's lecture notes on derivative calculus. Years later her tutor was amazed by how quickly she picked up the concepts, and as her memories flashbacked she said "the concept of limit appeared to me as an old friend.”
So it might be no surprise that she won the Paris Academy's Grand Prix for solving a problem in Nonlinear Dynamics, a branch of Calculus that famously bested Isaac Newton.
In particular, this problem, known as the "mathematical mermaid or water nymph" studied how to model spinning objects like tops. It can also be used to model the motion of which Winter Olympic sport?
Figure Skating
Write this in polynomial form
(4x^4 + 5x^2 + 6)/(3x^2)
(2x^2)/3 + (5x)/3 + 2x^(-2)
Use the power rule to simplify:
(3x^3y^4)^3
27x^9y^12
Use the quotient rule for exponents to divide:
(x^2y^5)/(xy^7)
x/(y^2)
In topology, this shape is known as a Torus. Mathematically it is equivalent to all of the following EXCEPT:
a) a donut
b) a coffee cup
c) a game of pac-man
d) a classic pretzel
d) a classic pretzel
Write this in fraction form AND write a Calculus scenario for when it would useful to have it in fraction form
6x^(-3)
Useful for when we want to manipulate algebra (ex: in the optimization unit, when we wanted to set the derivative equal to 0 and solve for x, this is easier to do as a fraction than it is as a polynomial where we would need roots.
6/(x^3)
3x^2+8x-7+5x^2-9x-2
8x^2-1x-9
Use the quotient rule and the negative exponent rule to simplify:
(8x^6y^2)/(2xy^2)
4x^5
Steve Jobs said "There are more PhDs working on this film than any other in movie history" about this 1995 movie, which was the 1st entirely computer-animated feature film.
The graphics for the movie were created by polygon surface subdivision approximations and would take an animator a week to synch an 8-second shot.
Toy Story
Use the exponent rules to simplify:
(4xy^3 * 3x^-4y)^2
Use the exponent rules to simplify:
(144y^8)/(x^6)
Simplify:
17dq^3r^2 * 2d^3qr^3
34d^4q^4r^5
Simplify:
(7y^-2x^2)^4
(2401x^8)/(y^8)
Use the quotient rule for exponents to divide:
(a^-3b^-3c^-5)/(a^-3b^-3c^8)
1 / (a^6bc^3)
Use the power rule to simplify:
(4x^2yz^3)^2
16x^4y^2z^6
Use the exponent rules to simplify:
(x^3y^4)^3*(3xy^2)^2
9x^11y^16
Finish this proof:
xn = xn -->
xn * 1 = xn so
1 = xn / xn so
1 = ??????
xn = xn -->
xn * 1 = xn which means
1 = xn / xn so, by using exponent division rules
1 = xn-n = x0
For Toy Story 5, Pixar recently developed a new way of animating hair described by Thomas Jordan here:
"Each curl knows the others, so they can ricochet and collide with each other, in addition to interacting better with Blaze's shoulders and clothes"
Which extension of Calculus from our unit does this sound most similar to?
This is most similar to the Day 2 of R&J where R and J's feeling depend both on the interactions and reactions between themselves and each other
Use the quotient rule for exponents to divide:
(3x^10y^9)/(8x^4y^4 * 2x^4y^3)
(3x^2y)/(16)
Use the product rule for exponents to multiply:
3x^4 * 2x^3 * 3x^2
18x^9
Use the exponent rules to simplify:
(2b^2c^3 * 3bc^5)^3 / (6b^3c^10)
36b^6c^14