Trig
What is the tangent of 2pi/3 radians (exactly)?
The negative square root of 3
What is the area under the curve of the graph of f(x) from x=1 to x=5?
(Write f(x) on board)
52
A rectangle has a perimeter of 320 meters and its length L is 3 times its width W. Find the area of the rectangle.
Area = L W = 120 * 40 = 4800 meters 2
If a circle has a circumference of pi, what is it’s diameter?
1
What type of pie is seen in the picture below?
Get image
Pecan
What is the measurment of the two angles present in the right triangle seen below? (in degrees)
(Draw Picture on Board)
Angle 1 is 36.87 degrees
Angle 2 is 53.13 degrees
On what interval is the function f(x) increasing? On what interval is f(x) decreasing?
(Write f(x) on board)
Increasing: (0,2)
Decreasing: (-infinity,0)u(2,infinity)
What is the area of an equilateral triangle of height 20 units?
400/3*√(3) = 230.940 unit 2
Find the surface area of a cylinder with a height of 4 and a radius of 8.
SA = 192pi or 603.185
This type of pie is commonly eaten in the fall, and the fruit used in this pie can also be used to make a delicious cider.
Apple
A sailor’s boat lies 700 meters from the bottom of a cliff. The sailor looks up at a lighthouse on to of the cliff with an angle of elevation of 50 degrees. How tall, in meters, is the cliff? (Assume the height of the light house is negligible compared to the height of the cliff)
700tan(50)= 834.2275 meters
Find the area between the curves of f(x) and g(x)
(Write equations on Board)
24
Given the length (in feet) of side AB and the internal angle D of the parallelogram below, find the length of side BC given that the area of the parallelogram is equal to 1000 feet 2.
(Draw image on board)
length of BC = 1000 / [ 15 sqrt (2) / 2] = 94.28 feet
AC is tangent to circle O at point C. What is the length of OC?
Draw image on board
16 units
This type of pie’s main ingredient is the berry that the state of Maine is most well known for producing
Blueberry
A plane currently flying at an altitude of 6 miles above the surface of the earth is located a ground distance of 100 miles from the runway of the nearest airport (located straight ahead). The plane is forced to make an emergency landing due to a fire that sparked toward the rear if the cabin. What must the angle of depression of the plane’s descent (in degrees) be if it is to land just at the edge of the runway? (Assume the curvature of the earth is negligible)
3.43 degrees
A cone shaped tank has a base radius of 40 feet and a height of 120 feet. The tank is being filled with water at a rate of 60 ft^3/min. How fast is the water level rising when the height if the water is 10 feet?
27/5pi feet per minute or 1.72 feet per minute
In the figure below, triangle ABC is a triangle inscribed inside the circle of center O and radius r = 10 cm. Find the lengths of AB and CB so that the area of the shaded region is twice the area of the triangle.
(Draw figure on board)
first solution
AB = 20 cos (15.8) = 19.24 (2 decimals) and CB = 20 sin (15.8) = 5.45 (2 decimals)
second solution
AB = 20 cos (74.2) = 5.45 (2 decimals) and CB = 20 sin (74.2) = 19.24 (2 decimals)
NASA’s OSIRIS-REx mission was designed to travel to an asteroid called Bennu and bring a small sample back to Earth for further study. To achieve its mission, the spacecraft needed to make contact with 26 cm2 of asteroid Bennu’s surface and collect millimeter-size particles using its "contact-pad samplers." These are 1.5-centimeter diameter circular pads of Velcro-like stainless steel. There are 24 pads on the mechanism designed to collect the samples.
How many pads needed to make contact with Bennu's surface to meet the mission requirement?
15 pads
This pie, although not the desert kind, is commonly eaten in Ireland and Britain. It is especially common for people to eat this “pie” on St. Patrick’s day?
Shepherd’s Pie
Where are the vertical asymptotes located on the graph of
(Write Equation on Board)
(Answer must be in the form of (radian + radian*k where k is an integer)
Vertical asymptotes are located at pi/8 + k*pi/4
The region bounded by the graph of (write equation on board), x = 0, and y = 5 is revolved around the vertical line x = -1. What is the volume of the solid generated by this revolution (round your answer to the nearest hundredth place)?
58.64 units cubed
The distance between the centers of two circles C1 and C2 is equal to 10 cm. The circles have equal radii of 10 cm. O is the center of C2 and P is the center of C1. Find the overlapping area of the two circles. Approximate your answer to one decimal place.
Hint: Think about finding a portion of the area for one isolated circle first, then multiply that area by two.
(Draw image on board)
Area = 122.8 cm 2
Every day, Earth is showered in radiation from the Sun. The Sun also emits charged particles almost entirely in the form of ionized hydrogen and helium. These ions travel at speeds of about 400 km per second but rarely reach Earth's surface. That’s because they are deflected by Earth’s magnetic field due to the Lorentz force, given by the equation:
F = qvBsinθ
F = force (N)
q = charge of the particle in coulombs (C)
v = velocity of the particle in meters per second (m/s)
B = the magnetic flux density of Earth’s magnetic field in teslas (T)
θ in radians.
The charged particles can't cross Earth's magnetic field, so they follow it to Earth's North and South poles. The resulting concentration of charged particles is what creates auroras.
If Earth’s magnetic flux density is 60µT, what force would a hydrogen ion (q = 1.602E-19 C) observe at π/4 radians from the equator?
Force = 3E-18 N
This is the math club vice president’s favorite type of pie.
Key Lime Pie