The Big Bang Theory Mystery Cache
Please note Use of geocaching.com services is subject to the terms and conditions
in our disclaimer.
Calc, physics, numbers, oh my. This straightforward work came straight from Sheldon Cooper's board. If you like numbers, you may enjoy this.
The cache is NOT at the posted coords. You just need to figure out the .000 for the N and W. The rest is correct. Good Luck.
Solve the following calculus and physics problems. Obtain an answer for each, and then determine the letter that corresponds with each answer. The letters will provide you with a message regarding the coordinates.
1. Find the area of the region bounded by the graphs of the algebraic functions f(x)=x^(2)-4x and g(x)=0.
2. Find the area of the region between y=x^(2)-1, y=-x+2, x=0, and x=1.
3. Find ‘b’ such that the line y=b divides the region bounded by the graphs of y=9-x^(2) and y=0 into two regions of equal area.
4. An electric cable is hung between two towers that are 200 feet apart. The cable takes the shape of a catenary whose equation is y=75(e^(x/150)+e^(-x/150)). Find the arc length of the cable between the two towers (in feet).
5. Find the arc length of the graph of (y-1)^(3)=x^(2) on the interval [0,8].
6. Evaluate ∫(x^(2)*ln(x))dx.
7. Find the volume of the solid formed by revolving the region bounded by f(x)=2-x^(2) and g(x)=1 about the line y=1.
8. Find the volume of the solid formed by revolving the region bounded by the graphs of y=√(x) and y=x^(2) about the x-axis.
9. Find the volume of the solid formed by revolving the region bounded by the graphs of y=x^(2)+1, y=0, x=0, and x=1 about the y-axis.
10. A manufacturer drills a hole through the center of a metal sphere of radius 5 inches. The hole has a radius of 3 inches. What is the volume of the resulting metal ring (in cubic inches)?
11. Find the volume of the solid of revolution formed by revolving the region bounded by y=x-x^(3) and the x-axis (0≤x≤1) about the y-axis.
12. A pontoon is designed by rotating the graph of y=1-x^(2)/16, -4≤x≤4 about the x-axis, where x and y are measured in feet. Find the volume of the pontoon in cubic feet.
13. Find the volume of the solid formed by revolving the region bounded by the graphs of y=x^(3)+x+1, y=1, and x=1 about the line x=2.
14. Find the average value of f(x)=tan(x) on the interval [0, π/4].
15. If f’’(x) is positive on the interval [0,4], what can be said about f’(x) and f(x) on the interval?
16. A 50.0-kg circus acrobat drops from a height of 2.00 meters straight down onto a springboard with a force constant of 8.00*10^(3) N/m. By what maximum distance (in m) does she compress the spring?
17. A 1.00-kg block is shot horizontally from a spring and travels 0.500 m up along a frictionless ramp before coming to rest and sliding back down. If the ramp makes an angle 45 degrees with respect to the horizontal, and the spring was originally compressed by 0.120 m, find the spring constant (measured in N/m).
18. A uniform ladder 10.0 m long and weighing 50.0 N rests against a smooth vertical wall. If the ladder is just on the verge of slipping when it makes a 50 degree angle with the ground, find the coefficient of static friction between the ladder and ground.
19. Estimate the fractional change in the volume of Earth’s oceans due to an average temperature change of 1 degree Celsius. Note that ᵝwater=2.07*10^(-4)((degrees Celsius)^(- 1)).
20. An ideal gas absorbs 5.00*10^(3) J of energy while doing 2.00*10^(3) J of work on the environment during a constant pressure process. Compute the change in the internal energy of the gas (in J).
21. Using a small pendulum of length 0.171 m, a geophysicist counts 72.0 complete swings in a time of 60.0 s. What is the value of g (in m/s^(2)) in this location?
22. A circuit provides a maximum current of 20.0 A at an operating voltage of 1.20*10^(2) V. How many 75 W bulbs can operate with this voltage source?
23. What is 2+2?
Answers:
-4/π*ln(√(2)/2) ≈ 0.441 … S
13/6 …W
4π …A
29π/15 …X
150(e^(2/3)-e^(-2/3)) ≈ 215 …F
2π/3 …C
x^(3)/3*ln(x)-x^(3)/9+C … V
3π/10 …S
7.784 …B
3π/2 …I
740 …D
1/27(40^(2/3)-4^(3/2)) ≈ 9.073 …I
4π/15 …S
0.420 …N
9(1-4^(-1/3))≈3.330 …O
64π/15 …I
3.00*10^(3) …E
The graph of f(x) is concave up and the graph of f’(x) is increasing on the interval. …E
The graph of f(x) is concave down and the graph of f’(x) is decreasing on the interval. …U
4 …N
2*10^(-4) …S
32/3 …T
9.73 …V
16π/15 …E
158π/45 …W
32.0 …E
0.560 …V
256π/3 …X
481 …E
P.S. Do not confuse π with n-- π is pi, not lowercase N! Also, * is 'multiplied by'.
Additional Hints
(Decrypt)
Whfg n wbxr sebz Furyqba... N arhgeba jnyxf vagb n one naq nfxf, "Ubj zhpu sbe n qevax?" Gur onegraqre ercyvrf, "Sbe lbh? Ab punetr."
Treasures
You'll collect a digital Treasure from one of these collections when you find and log this geocache:
Loading Treasures