Distances
3 miles per hour
Let u = [2,-3] and v = [5,2]
What is u + v?
[7,-1]
Angle Theta is an acute angle in a right triangle.
The opposite side length is 3
The adjacent side length is 4
The hypotenuse length is 5
What is the sine of that angle?
sin = opposite/hypotenuse = 3/5
What's the next number in the sequence?
1,2,4,8,16,???
32. Each number doubles the previous number
He is the director of the original Star Wars (1977)
George Lucas
What is the length of the hypotenuse of a triangle whose legs are 3 and 4 units long?
5 units
Let u = [5,-2]
What is 3*u?
[15, -6]
A parallelogram has an angle of 60 degrees. What are the other three angles?
60, 120, 120
9 = 72
8 = 56
7 = 42
6 = ???
30
Fill in the blank!
"But <blank>! What light from yonder window breaks?"
soft
(from Romeo and Juliet)
I walk 2 miles north and 3 miles west. How far am I from my original position?
The square root of 13mi, or about 3.6mi.
What is the angle made between the following vectors?
u = [4,2]
v = [-2, 4]
90 degrees! Notice u dot v = 0
A trapezoid has angles 45 and 60. What are the other two angles?
120 and 135
What is the next number in the sequence?
1,1,2,3,5,8,13,???
21 (This is a famous sequence, the Fibonacci Sequence, where to find the next number you add the previous two)
He wrote The Origin of Species.
Charles Darwin
Fill in the blank!
A unit of distance, not time, Han Solo says of the Millenium Falcon, that it made the Kessel Run in less than 12 <blank>
Parsecs
What is the vector in the opposite direction of [2,-3] but with the same length?
[-2,3]
A triangle has angles 2x, 2x, and 3x. What is x?
180 = 2x+2x+3x
180 = 7x
x = 180/7 = 25.7
What's the next number in the sequence?
-1,2,7,14,23,???
34. Each number is the index squared minus 2
This sea separates Greece from Turkey.
The Aegean Sea
An Astronomical Unit (AU), is the measure of the distance between what two celestial objects?
The Sun and the Earth.
What is the vector of length 1 in the direction of [3,-4]?
(1/5)*[3,-4] = [3/5,-4/5]
What are the acute angles in a 3-4-5 triangle?
cos^-1(3/5) = 53.1
cos^-1(4/5) = 36.9
5 people are in a room, and each person shakes hands (or elbow bumps?) with every other person. How many total handshakes (or elbow bumps) are there?
10
The Cartesian Coordinate System is named for this French mathematician (and philosopher)
Renee Descartes