approach

The problem is as follows: Two buggies one orange and the other blue are passing through an intersection with constants speeds of $v_{orange}=6\,\frac{m}{s}$ and $v_{blue}=6\sqrt{3}\,\frac{m}{s}$ respectively. Find the minimum approach in meters between the orange and blue buggies. The...

Hello. I want to show that, for an absolutely convergent series \sum_{n=1}^{\infty}a_n, we have \left|\sum_{n=1}^{\infty}a_n\right|\leq\sum_{n=1}^{\infty}|a_n|. Let M be an positive integer. I begin with the triangle inequality \left|\sum_{n=1}^{M}a_n\right|\leq\sum_{n=1}^{M}|a_n| and taking...

I want to self-educate myself in philosophy and I need advice on how and where to start. I want to be a specialist in differential geometry and relativity and also harness the power of logic and reason to put sound philosophical arguments together about what's around me. I'm hoping someone could...

How approach this integral? I have assumed z=nx and hence Then derivative gives #dz=ndx#. Now it becomes this Integral from #\frac{n} {n+1}# to 1 ##\frac{arctan(z)dz} {n arcsin(z)}##. After this I am not able to proceed further.

Solve deer hunting probability A hunter knows that a deer is hidden in one of the two near by bushes, the probability of its being hidden in bush-I being 4/5. The hunter having a rifle containing 10 bullets decides to fire them all at bush-I or II. It is known that each shot may hit one of the...

The problem is as follows: $\textrm{Prove:}$ $\sin 2\omega+\sin 2\phi+\sin 2\psi= 4 \sin\omega \sin\phi \sin\psi$ $\textrm{Given this condition:}$ $$\omega +\phi+ \psi= \pi$$ In my attempt to solve this problem I did what I felt obvious and that was to take the sine function to the whole...

0 = \left ( \begin{matrix} 0.z_1 \\ 0.z_2 \end{matrix} \right ) 0.z1 = 0 0.z2 = 1 P_1 0 = (1, 0) ~ \left ( \begin{matrix} 0.z_1 \\ 0.z_2 \end{matrix} \right ) = 1 \cdot 0.z_1 + 0 \cdot 0.z_2 = 0.z_1 P_2 0 = (0, 1) ~ \left ( \begin{matrix} 0.z_1 \\ 0.z_2 \end{matrix} \right ) = 0...

I volunteered abroad in rural Ethiopia and a village in a remote mountainous area of China. I plan to return to both places and teach for as long as I can make it work. I want to focus on STEM, but first I would like to reteach myself math and science from pre-school all the way to college-level...

So a common situation is that the parents know their child needs a lot of help, but they aren't willing to pay for more than one session a week. For instance I am working with a kid now who is in a "precalculus" class but has weaknesses in his prealgebra. They are willing to pay for me once per...

A triangle has an average angle of 60 degrees. A quadrilateral has an average angle of 90 degrees. A figure with 24 sides has an average angle of 165 degrees. As the number of sides approaches infinity, what does the average angle measure approach?

My cousin was doing some maths, but he did not have any idea how to resolve it. I don't know equation, so I post it here and hope someone kindly help him figure out whether there is an equation that can approximate the value of X. Here are the results, but with an unknown value x: When...

Hi. If you pick any two number, say for instance 5 and 7 and you keep adding them together (much like the Fibonacci Sequence) you get this: 5, 7, 12, 19, 31, 50, 81, 131, ... and so on. The ratio between the last two numbers always approaches the golden ratio, no matter which set of...

In preparation to return to school to pursue a B.S. in Mathematics, I was planning to purchase the texts of some prerequisite courses and work through them (namely Pre-Calculus and Calculus 1 & 2). Are there any better approaches that anyone could recommend? Or anything to supplement this...

(ex) The Fine Arts High School Piano club has 30 students, some from Grade 11 and the remainder from Grade 12. Each pair of students from the club must play a piano duet together over the course of the year. When two grade 11 students play together, they need 2 hours of practice time. When a...

Here is the problem. (ex) Determine the y-intercept of a line with a slope of -2 that is tangent to the curve y = x^2/3 - 4x - 3. I solved it in two ways. I am going to write them down. (1) with calculus dy/dx = 2x/3 - 4 Since m=-2 and dy/dx=m, solving for x gives x=3. Then...

Why does (1+x)^(1/x) = e as x approaches 0, as shown in this graph? https://www.desmos.com/calculator/d1bvs8tqlu 1 to the power of anything, including infinity, should be 1. 1*1*1*1*1*...=1 It's just repeating itself. It's like saying 1+0+0+0+0... nothing will ever change. So why...

"Mathematics considers natural numbers as points on a number line. I think it is a bit lopsided. Natural numbers are not just a series of points on a number line with an interval of 1. Let's try to build another series of intervals 3 ^ 0.5. ......" Andrey Shvets: The proof (?) of Fermat's theorem

Does anyone ever question the core data analytics of technology? My company has just released a free download that eliminates known issues associated with traditional techniques. The InoraRAE has a simple interface and calculates fast, accurate results, making it more meaningful and useful...

My company has just released a free software download that eliminates known issues associated with traditional techniques. The InoraRAE has a simple interface and calculates fast, accurate results, making it more meaningful and useful than any linear regression tool before it. It is available...

Hi, I have a problem where I have four non-linear differential equations. They are big and ugly, but I think they can be summarised as follows: dA/dz = f(A,B,C,D) dB/dz = f(A,B,C,D) dC/dz = f(A,B,C,D) dD/dz = f(A,B,C,D) I would like to integrate these equations over the range of z=0...