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How do you find a parametric representation for a specific surface?
I trying to find a parametric representation of the plane which goes through the origin and contains the vectors $i-j$ and $j-k$. I found the cross produc...
Apr 15, 2026
Archive: News
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How would you use this position equation to calculate the max height?
A ball is thrown upwards from the top of a 192-foot-tall building with an initial speed of 64 feet per second. The height of the ball as a function of tim...
Apr 15, 2026
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Finding kernel and range of a linear transformation
We are given: Find $\ker(T)$, and $\textrm{rng}(T)$, where $T$ is the linear transformation given by $$T:\mathbb{R^3} \rightarrow \mathbb{R^3}$$ with stan...
Apr 15, 2026
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Methods for efficiently factoring the cubic polynomial $x^3 + 1$
$$x^3 + 1$$ factors as $$(x^2 - x + 1)(x + 1) .$$ It would have taken me a few minutes to identify this. What are the various approaches to determining ra...
Apr 15, 2026
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Inverse of diagonalizable matrix is diagonalizable
Let $A \in M_n(\mathbb C)$ be invertible. Prove that $A$ is diagonalizable if and only if $A^{-1}$ is diagonalizable. This is what I have for one directio...
Apr 15, 2026
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Why $\cosh(y)$ cannot be zero in this example?
" Find the points $z \in \mathbb{C}$ at which the function $g(z) = \cos(\bar{z})$ satisfies the Cauchy-Riemann equations. " So I've written $g(z) = g(...
Apr 15, 2026
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Method of generating random numbers that sum to 100 - is this truly random?
I am writing a computer program that involves generating 4 random numbers, a, b, c, and d, the sum of which should equal 100. Here is the method I first c...
Apr 15, 2026
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Is there a listing of natural numbers with their properties?
I am looking for a category of natural numbers (about <1000 is enough) with its properties. Here's some examples : 2 - It is the first prime numbe...
Apr 15, 2026
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Solving Systems of Linear Differential Equations by Elimination
For a homework problem, we are provided: $\frac{dx}{dt}=-y + t$ $\frac{dy}{dt}=x-t$ Putting these into differential operator notation and separating the d...
Apr 15, 2026
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Meanings of the terms "conjunct" and "disjunct" in a logic?
This sentential logic problem is stated as: Suppose that $A \models B$, where $A$ is a conjunction of literals and $B$ is a disjunction of literals. Show ...
Apr 15, 2026
