Podcast
Questions and Answers
What is the sum of a symmetric matrix and a skew-symmetric matrix?
What is the sum of a symmetric matrix and a skew-symmetric matrix?
- A zero matrix (correct)
- A matrix that is only skew-symmetric
- An identity matrix
- A matrix that is only symmetric
What is the derivative of $\sin(x)\sin(x)$ with respect to $x$?
What is the derivative of $\sin(x)\sin(x)$ with respect to $x$?
- $2\sin(x)\cos(x)$
- $\sin^2(x)$
- $\cos^2(x)$
- $2\cos(x)\sin(x)$ (correct)
For $x = a(\theta + \sin(\theta))$ and $y = a(1 - \cos(\theta))$, what is $dx$ in terms of trigonometric functions?
For $x = a(\theta + \sin(\theta))$ and $y = a(1 - \cos(\theta))$, what is $dx$ in terms of trigonometric functions?
- $\sec^2(\theta)$
- $\tan(2\theta)$ (correct)
- $-a\sin(2\theta)$
- $a\cos(2\theta)$
In which intervals is the function $f(x) = 10 - 6x - 2x^2$ decreasing?
In which intervals is the function $f(x) = 10 - 6x - 2x^2$ decreasing?
What is the result of evaluating $\int (x-1)(x-2) dx$?
What is the result of evaluating $\int (x-1)(x-2) dx$?
What is the area of the parallelogram formed by vectors $\mathbf{a} = \mathbf{i} + \mathbf{j} - \mathbf{k}$ and $\mathbf{b} = \mathbf{i} - \mathbf{j} + \mathbf{k}$?
What is the area of the parallelogram formed by vectors $\mathbf{a} = \mathbf{i} + \mathbf{j} - \mathbf{k}$ and $\mathbf{b} = \mathbf{i} - \mathbf{j} + \mathbf{k}$?
Which of the following correctly represents the inverse of the product of invertible matrices A and B?
Which of the following correctly represents the inverse of the product of invertible matrices A and B?
Given x = a(θ - sinθ) and y = a(1 + cosθ), what is dx?
Given x = a(θ - sinθ) and y = a(1 + cosθ), what is dx?
For the function f(x) = x^2 - 4x + 6, in which interval is f decreasing?
For the function f(x) = x^2 - 4x + 6, in which interval is f decreasing?
What is the integral of (x+1)(x+2) dx?
What is the integral of (x+1)(x+2) dx?
Given sec^2(x) tan(y) dx + sec^2(y) tan(x) dy = 0, solve the differential equation.
Given sec^2(x) tan(y) dx + sec^2(y) tan(x) dy = 0, solve the differential equation.
If one defective item is randomly chosen from a stockpile containing items from machines A and B, what is the probability it was produced by machine B?
If one defective item is randomly chosen from a stockpile containing items from machines A and B, what is the probability it was produced by machine B?
If the function 𝑓(𝑥) = 𝑎𝑥 + 𝑏$ is continuous for $2 < x < 10$, what are the values of a and b?
If the function 𝑓(𝑥) = 𝑎𝑥 + 𝑏$ is continuous for $2 < x < 10$, what are the values of a and b?
Using the equation 𝐴² - 𝐴 + 2𝐼 = 𝑂, find the inverse of matrix A if 𝐴 = $\begin{bmatrix}4 & -2 \ 4 & -2 \end{bmatrix}$, 𝐼 is 2x2 identity matrix, and 𝑂 is the zero matrix.
Using the equation 𝐴² - 𝐴 + 2𝐼 = 𝑂, find the inverse of matrix A if 𝐴 = $\begin{bmatrix}4 & -2 \ 4 & -2 \end{bmatrix}$, 𝐼 is 2x2 identity matrix, and 𝑂 is the zero matrix.
In the relation 𝑅 = {(1,1), (2,2), (3,3), (1,3)}, which ordered pair should be added to make R the smallest equivalence relation?
In the relation 𝑅 = {(1,1), (2,2), (3,3), (1,3)}, which ordered pair should be added to make R the smallest equivalence relation?
Given the function 𝑓: 𝑅 → 𝑅 as 𝑓(𝑥) = |𝑥| for 𝑥 ∈ 𝑅, what type of function is 𝑓?
Given the function 𝑓: 𝑅 → 𝑅 as 𝑓(𝑥) = |𝑥| for 𝑥 ∈ 𝑅, what type of function is 𝑓?
If a function is both one-one and onto, what type of function is it?
If a function is both one-one and onto, what type of function is it?
What is the result when the determinant of a matrix is zero?
What is the result when the determinant of a matrix is zero?
