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The eigenvalues of a $2\times2$ matrix can be expressed in terms of the trace and determinant. $\lambda_\pm = \frac{1}{2}\left(\textrm{tr} \pm \sqrt{\text...
I fail to understand why the Jacobian matrix is used to transform Cartesian coordinates to polar coordinates. If I'm not misunderstanding, it is assu...
Suppose I'm given 2 sides and an angle for a triangle. How do I use those sides to determine whether the measurements can give 0, 1, or 2 triangles? ...
![Find absolute extrema of the function $ \ f(x)=1-|x-1| , \ \ x \in [-9,4] \ $ on the closed interval](https://edu.smbbmcl.edu.pk/uploads/find-absolute-extrema-of-the-function-f-x-1-x-1-x-in-9-4-on-the-closed-interval_720.jpg)
Find absolute extrema of the function $ \ f(x)=1-|x-1| , \ \ x \in [-9,4] \ $ on the closed interval. Answer: $f(x)= \begin{array} (2-x) , \ \ if \ x \in ...
Whenever I take a definite integral in aim to calculate the area bound between two functions, what is the meaning of a negative result? Does it simly mean...
1.Find all positive integers solution $xy+yz+xz = xyz+2$ 2.Determine all p and q which p,q are prime number and satisfy $p^3-q^5 = (p+q)^2$ Thx for the an...
While finding inverse $\mathcal{Z}$ transform of $\frac{1}{z^2(z+1)}$ i split it into three parts using partial fractions: $$\frac{a}{z} + \frac{b}{z^2}+\...
I have a question regarding First Order Logic. I have to express the property "x is a Prime" in First Order logic. So far I have the following solution: $...
I've heard all these terms thrown about in proofs and in geometry, but what are the differences and relationships between them? Examples would be awe...
Let $\langle K, +, * \rangle$ be our field. By definition, we know that every non-zero element, i.e every element except the additive identity, has an mul...
