Calculus
Find the integral of 5x^4 with respect to x
(x^5) + C
What is the expected value of rolling a fair six-sided die?
The expected value is 3.5
Solve for x: 3(x−4)+5=2(x+1)+7
x=16
What is the measure of an angle in a regular pentagon?
108 degrees
What is 2 raised to the power of 5?
32
Determine the critical points of f(x) = x^3 - 6x^2 + 9x
Critical points are at x = 1 and x = 3
A bag contains 3 red, 2 blue, and 5 green balls. What is the probability of drawing a red ball?
The probability is 3/10 or 0.3
Simplify (x^3 - 27) / (x^2 - 9)
(x^2 + 3x + 9)/(x + 3).
Solve tan(x) = 1 for x in the interval [0, 2π]
x = π/4, 5π/4.
What is the derivative of x^2 + 3x - 4?
The derivative is 2x + 3.
Find the limit as x approaches 0 of (sin(2x)/x)
The limit is 2
A coin is flipped 4 times. What is the probability of getting exactly 2 heads
The probability is 3/8 or 0.375
Find the roots of 2x^2 - 4x - 6 = 0
x = 3 or x = -1
Find the area of a triangle with sides of length 7, 24, and 25.
The area is 84 square units.
How many ways can you arrange the letters in 'MATH'?
24 ways.
Solve the differential equation dy/dx = 3x^2, given y(1) = 5
y = x^3 + 4
Given P(A) = 0.5, P(B) = 0.3, and P(A and B) = 0.2, are A and B independent?
no, they aren't independent because P(A and B) doesn't = P(A) * P(B)
For f(x) = 2x^2 - 3x + 5, find the vertex
Vertex is at (3/4, 31/8)
solve the equation in the interval in the interval 0∘≤x<360∘
sin(x)+cos(x)=1
x=0∘andx=90∘
If a number is divisible by both 4 and 6, what are all the numbers it must be divisible by?
1, 2, 3, 4, 6, 12
Find the area under the curve of f(x) = x^2 from x = 0 to x = 3
The area is 9
Find the variance of the data set {2, 4, 6, 8, 10}
The variance is 8
If g(x) = x / (x - 1), find the inverse function g^(-1)(x)
g^(-1)(x) = x / (x - 1).
Solve the triangle if:
∠𝐴=38∘, 𝑎=40 units, 𝑏=52 units
Round the angles and side lengths to the nearest 10th 10th .
∠𝐴=38∘ ∠𝐵≈126.8∘ ∠𝐶≈15.2∘
𝑎=40 𝑏=52 𝑐≈17.0
OR
∠𝐴=38∘ ∠𝐵≈53.2 ∘∠𝐶≈88.8∘
𝑎=40 𝑏=52. 𝑐≈65.0.
S=[n=1∑∞](-1)^n/(n^2 + n)
(write on board)
S=−1