Algebra
3x + 5 = 14
Solve for x.
x = 3
sin(x) / cos(x)
Simplify.
tan(x)
Find the average of:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34
8.8
derive: x
1
3xy = dy/dx
Solve in terms of y
y = Ce(3/2)x^2
2x(x - 5)(3x + 4)
Simplify.
6x3 - 22x2 - 40x
In a right triangle, if the opposite side is 7, the adjacent side is 5, and the hypotenuse is 13, what is the cosine of the angle?
5/13
What's the probability of flipping a coin and getting head 8 times in a row?
1/256
Integrate: x*x2+1
(x4/4)+x+c
What is the 6th axiom of a Vector Space?
Existence of an additive inverse vector in V.
(For all u values which exist in V, there exists a -u in V such that u + (-u) = 0 where -u is the inverse of u.)
Solve the system of equations.
2x + y = 12
x - y = 6
x = 6, y = 0
Simplify: sin(2x)/2sin(x)
cos(x)
A bag of skittles contains:
10 yellow skittles
6 orange skittles
5 green skittles
7 red skittles
2 purple skittles.
What's the probability of picking a red or green skittle?
12/30 or 2/5
derive: x3ln(x)
3x2ln(x)+x2
Use Cramer's Rule to solve the following system of equations.
-3x + 7y = 18
5x + 4y = -13
x = -3.47
y = 1.08
3x2 + 5x - 2
Factor.
(3x - 1)(x + 2)
sin(pi/6)+tan(pi/2)+cot(pi/3)+cos(2pi)
undefined
because tan(pi/2) is undefined
One hundred people line up to board a plane. Each of them has a boarding pass with an assigned seat. However, the first person lost their boarding pass and chose a random seat. After that, each passenger sits in their assigned seat if it's unoccupied. Otherwise, they sit in an unoccupied seat at random. What is the probability that the last person to board gets to sit in their assigned seat?
1/2
Integrate: (x2)/(x3+1)2
-1/3(x3+1) + c
Use a Matrix to solve the system of equations by simplifying to Row-Echelon Form.
R1 + R2 + R3 = E/Io
R1 + (1/2)R2 + R3 = E/Ia
R1 + R2 = E/Ib
R1 = E/Ib - 2E/Io + 2E/Ia
R2 = 2E/Io - 2E/Ia
R3 = E/Io - E/Ib
x2 - 5x - 6 = 0
Solve for x.
x = 6, x = -1
3sin2(x)-2sin(x)-1=0
pi/2
A cookie jar contains 10 cookies of 3 types. There are 5 chocolate chip cookies, 3 oatmeal raisin cookies, and 2 sugar cookies. Sparsh reaches into the jar and chooses a cookie at random and then, without replacing the first cookie, reaches into the jar again and chooses another cookie at random. What is the probability that both of the cookies Sparsh chooses are the same type?
28/90
Integrate: tan(x)/(sec3(x)+1)1/2
(-2/3)tanh-1(sec3(x)+1)1/2
Solve the following differential equation:
y'' = y' + x2
y = -(1/3)x3 - x2 -2x + C1ex + C2