Find the dot product of the following two vectors:
a = 2i + 3j b = -5i
-10
How many cards need to be dealt from a standard deck of 52 cards to ensure that you will have at least 2 cards that share the same rank?
State the contrapositive of "if a number is even then the square of the number will be even"
and state if it is sometimes, always, or never true
If the square of a number is odd then the number will be odd
true
Where are the asympotes on a graph of y=sec(x)
(0 to 2pi)
90 and 270
or pi/2 and 3pi/4
If vector AB is <2,1> and the position vector of B is -5i, find the position vector of A
AB=OB-OA
OA=OB-AB = -7i - j
How can you confirm mathematically if two vectors are perpendicular?
Dot product = 0
How many arrangements of the word DUPLICATE have two vowels and three consonants?
7200
Disprove the following statement:
"No squares have perimeters equal to their areas"
a 4x4 square exists
Express as a sum or product:
cos(2x)cos(3x)
0.5cos5x + 0.5cosx
If A= 2 3 , find 5AI
0 -2
10 15
5 -5
Find the vector of magnitude 6 in the same direction as u=3i+4j
6/5 (3i+4j)
Using the digits 0,1,2,3,4,5 without repetition, how many odd four digit numbers can be formed?
144
An arc subtends an angle of 36 degrees at the centre of a circle. What is the size of the angle that is subtended by the same arc on the circumference of the circle?
18 degrees
Find the solution to cosx=0.5
30 + 2kpi, k=Z
(-30) + 2kpi, k=Z
Find im[(2+i)/(2-i)]
4/3
Find x if the vector 4i-5j is parallel to the vector <-10i, x>
12.5
Four students are to be chosen from a group of eight students for the school tennis team. Two members of the group, Sam and Tess, do not get along and cannot both be on the team. How many ways can the team be selected?
55
State the contradiction statement of the following:
"There exists an even prime number"
All prime numbers are odd
How many subsets of {1,2,3} exist?
8
empty, 1, 2, 3, 12, 13, 23, 123
If A is transformed to A' by 0 1
1 2
Find the matrix that will transform A' back to A
- ( 2 -1 )
-1 0
What does the vector projection of a in the direction of b represent geometrically?
The component of a that is parallel to b
Your friend offers you any of six books that she no longer wants. How many selections are possible assuming that you take at least one book?
2^6 - 1 = 63
Is 5n^2 + 3n + 7 odd or even? Briefly describe your process.
Sub n=2m and simplify. Will get 2()+1 therefore odd.
A triangle of area 5 is transformed by matrix
1 2
3 1
What is the area of the resulting triangle?
25
State the transformation matrix for a reflection in the line y=x
0 1
1 0