Logs/Exponentials/ Inverse Trig
Trig
Motion
Related Rates
Halloween Trivia
100
d/dtt^2lnt
2tlnt+t
100
d/dx(tanx/(1+cosx))
No need to simplify as long as the answer is one fraction
Anything equivalent to
((secx)^2(1+cosx)-tanx(-sinx))/(1+cosx)^2
100
The position of a particle moving along a straight line at any time t is given by s(t) = t2 + 4t + 4. What is the acceleration of the particle when t = 4?
a(4) = 2
100
If x = 2, y = 1, and dx/dt = -4, find dy/dt for:
6y^2+x^2=2-x^3e^(4-4y)
dy/dt=8/11
100
The name of the villain in "The Nightmare Before Christmas"
Oogie Boogie
200
If y=e^(1/x)/x^2
Then y'=
y'=(-e^(1/x)-2xe^(1/x))/x^4
200
If f(x)=x^2sin(πx)
Then f'(x)=
2xsin(πx)+πx^2cos(πx)
200
If the position of a particle on the x-axis at time t is
s(t) = -5t2,
then the average velocity of the particle for 0 ≤ t ≤ 3 is
-15
200
A rectangle's length is always 3 times its width. If the shorter side is decreasing at a rate of 2 inches per minute, at what rate is the area decreasing? (include units)
The area is decreasing at a rate of 72 square inches per minute.
(Changing at -72 square inches per minute)
200
another name for a "lycanthrope"
werewolf
300
d/dt (4log_3t-ln(8t^2))
4/(tln(3))-2/t
300
d/dxcot(3x^2+5)
-6xcsc^2(3x^2+5)
300
A particle moves along the x-axis so that at any time t ≥ 0 its position is given by
x(t) = t3 – 3t2 – 9t + 1.
For what value(s) of t is the particle at rest?
only at t = 3
300
A person is standing 350 feet away from a model rocket that is fired straight up into the air at a rate of 15 ft/sec. At what rate is the distance between the person and the rocket increasing 20 seconds after liftoff? (calculators permitted, answers must be correct to at least 3 decimal places)
9.7618 (ft)/sec
300
The author of the 1818 novel, "Frankenstein"
Mary Shelley
400
d/dx3^(arctan(5x))=
3^(arctan(5x))(ln3)(5/(1+25x^2))
400
d/dxcsc^2(sinx)=
-2(csc^2(sinx))(cot(sinx))(cosx)
400
A bug begins to crawl up a vertical wire at time t = 0. The velocity v of the bug at time t, 0 ≤ t ≤ 8, is given by the function whose graph is shown above.
At what value(s) of t does the bug change direction?
t = 6 only
400
A light is mounted on a wall 5 meters above the ground. A 2 meter tall person is initially 10 meters from the wall and is moving towards the wall at a rate of 0.5 m/sec. After 4 seconds at what rate is the tip of the shadow moving towards or away from the wall?
The tip of the shadow is moving towards the wall at a rate of 5/6 m/sec.
400
Rotten Tomatoes lists this movie as the #1 scariest of all time
The Exorcist
500
If f(x)=(5x)^(3x^2-2x+8)
Then f'(x)=
lny=(3x^2-2x+8)ln(5x)
f'(x)=[(6x-2)ln(5x)+(3x^2-2x+8)(1/x)](5x)^(3x^2-2x+8)
500
If f(x)=sin(tansqrt(1+x^3))
Then
f'(x)=
f'(x)=cos(tansqrt(1+x^3))(sec^2sqrt(1+x^3))((3x^2)/(2sqrt(1+x^3))
500
A bug begins to crawl up a vertical wire at time t = 0. The velocity v of the bug at time t, 0 ≤ t ≤ 8, is given by the function whose graph is shown above.
What is the total distance the bug traveled from t = 0 to t = 8?
13
500
A tank of water in the shape of an inverted cone is being filled with water at a rate of 12 m3/sec. The radius of the tank is 26 meters and the height of the tank is 8 meters. At what rate is the depth of the water in the tank changing when the radius of the top of the water is 10 meters?
3/(25π) m/sec
500
The most popular Halloween costume in the US in 2023
Barbie