Derivatives and Integrals
find the derivative of x9
9x8
what is k in the differential equation dy/dx = ky which we used to derive the exponential growth/decay function.
the constant of proportionality
acceleration is the derivative of what w.r.t time?
velocity
The full name of the character who famously proclaimed "The limit does not exist!" in Mean Girls.
Who is Cady Heron?
Big "Ten"? In that sports conference, there are currently 2 fewer than twice that number of member schools, or this many.
What is 18? (20x2 - 2)
Find the integral of 2cos(x)
2sin(x) + C
what is a solution to dy/dx = 0?
y = any constant
velocity is the derivative of what w.r.t time?
position
This singer known for "All Of Me" appeared in La La Land as Keith, the singer of a band that takes an approach to jazz reviled by Ryan Gosling's character Sebastian.
Who is John Legend?
The number of innings in a standard baseball game times the number of yards in a down in football.
What is 90? (9 x 10)
Find the indefinite integral of 4/(x-3)
4ln|x-3| + C
solve dy/dx = 3
3x + c
what is the formula for position in Newtonian kinematics?
x= x0 + v0t + .5(a)t^2
Who is Logan Lerman?
The number of minutes in a standard NBA game minus Michael Jordan's number.
What is 25? (48 - 23)
find derivative of ln(1+x2)sin(x)
2xsin(x)/1+x2 + ln(1+x2)cos(x)
solve dy/dx = (1/y)*x3
y = +- sqrt(2x^5/5 + c)
A ball is dropped from rest from a 50m high building. At which speed does it hit the ground?
31.3
Sydney Sweeney and Glen Powell starred as enemies-turned-lovers Bea and Ben in this 2023 rom-com that adapted the Shakespeare play Much Ado About Nothing.
What is Anyone But You?
The total number of players on a volleyball court (with both teams) times the number of penalty kicks one team takes if a soccer game is still tied after overtime.
What is 60? (12 x 5)
find derivative cos(3x+sin(x))/sin(x)
-sin(x)sin(3x+sin(x))(3+cos(x))-cos(3x+sin(x))cos(x)/sin^2(x)
find the solutions to dy/dx = (y-10)*sin(x)
y = Ce^(-cosx) + 10 & constant solution y = 10
Lets assume a ball was kicked off the ground at an angle of 30 degrees with an initial velocity of 30m/s
3.06
In 2023, she became the first Asian woman to win the Oscar for Best Actress for her performance in Everything Everywhere All At Once and also has acted in Wicked and Crazy Rich Asians.
Who is Michelle Yeoh?
This is the number of NBA teams times the number of WNBA teams.
What is 390? (30 x 13)