Lets say, few independent events are happening. $E_1, E_2,...,E_n$. The probability of each of these events happening is given as $P_1,P_2,...,P_n$. Each ...

I need an exact answer for $x$ in the following algebraic expression: $$ x^{4/3} - 2\sqrt{2}x^2 + 2\sqrt{2} = 0 $$ I don't need or want an approximat...

I am working on volumes of prisms, using $\pi$, diameter, and radius; however, I haven't done any problems with cross-sectional areas before... Also,...

Find T(V) by using the standard matrix and the matrix relative to B and B' $T: R^3 -> R^2, T(x,y,z) = (x-y + 0, 0 + y-z), v = (2,4,6)$ $B = {(1,1,...

In a classroom, there are 8 desks equally arranged in two columns (i.e. each column has four desks). Each desk can accommodate 2 people and there are eigh...

A Farmer fenced a rectangular area with $75$ metres of chicken wire. The rectangle is twice as long as it is wide. What are its dimensions?

So my assignment states the following: $$\text{Let}\;\;f(x) = -\sin(x),\,\;\text{where}\;\,x \in \left[-\dfrac{\pi}{4}, \dfrac{\pi}{6}\right]$$ Ok, so I k...

How to find the formula for the sum of fractions like this? $$\frac{1}{1\times 2}+\frac{1}{2\times 3}+\ldots+\frac{1}{n\times (n+1)}=$$

1.Consider the set of all $n×n$ matrices with real entries as the space $\mathbb R^{n^2}$ . Which of the following sets are compact? (a) The set of all or...

If, say, we know that $x=1$, is then the expression $x=\pm 1$ mathematically incorrect? I ask this because when we use $\pm$ sign in the discriminant form...