Mathematics

Accuracy up to how many decimals...........? 32 + 42 = 52 9 + 16 = 25 1.(3/4)2 + (4/4)2 = (5/4)2 0.752 + 12 = 1.252 0.5625 + 1 = 1.5625 2.(3/5)2 + (4/5)2 = (5/5)2 0.62 + 0.82 = 12 0.36 + 0.64 = 1 O.K. Fellas, let’s notice a difference here. 3.(3/3)^2 +(4/3)^2 = (5/3)^2 1^2 + 1.3^2 = 1.6^2 1 + 1.69 = 2.56 Difference => 2.69 – 2.56 = 0.13 Accuracy =>0.13/2.69=.048 4.(3/3)^2 +(4/3)^2 = (5/3)^2 1^2 + 1.33^2 = 1.66^2 1 + 1.7689 = 2.7556 Difference => 2.7689 – 2.7556 = 0.133 Accuracy => 0.133/2.7689 = 0.00…

So I was confused if I should post this to math or to brain teasers, if I posted in the wrong spot I apologize, I got this probability question and I couldn't figure out the answer could some help me with the needed formula to solve it. The question is: given a binary string that contains 11 digits what is the probability that there is exactly four 1s in the number. I can solve half of it, I know that 11 digits means 2^11 or 2048 total numbers, but I can't figure out how to find out how many contain exactly four 1s through a formula.

How to get ,The Area of Trapezium from Triangle Lot of mathematicians have proved Pythagoras theorem in their own ways. If you google it you will indeed found hundred of ways. Meanwhile I was also sure that maybe one day I could find something new out of this incredible Pythagoras theorem and Recently I got something which I would like to share with you. To Prove: Deriving the equation of area of trapezium using Arcs Proof: There is a triangle ABC with sides a b and c as shown in the figure. Now, Copyrighted©PiyushGoel

Hi all, this is my first post here and I wanted to run something by people who are more knowledgeable than I. In the past couple days I've decided that I need to teach myself more advanced mathmatics as it is of great importance to my studies in physics, astronomy and biology. In school we never went past algebra 1 and geometry and that has proven to be a hindrance. So I decided to brush up on the basic math that I learned in school and then move on to more advanced maths. I decided to make up a bunch of problems to solve while waiting for my books to arrive and I ran into my old nemesis, finding square roots of large numbers. I was taught prime factorization, which didn'…

When I first came accross the mystery of Buffon’s needle, it was presented as a mystery because, apparently, nobody could understand why it would result in the value of pi or what the problem of scattered needles had to do with a circle. You might actually do the experiment and find that the results really did statistically converge to pi as the sample size grew larger or you might find the mathematical solution would indeed result in a probability that is exactly equal to pi. You might notice that there is a cosine of the angle between the needle and the lines on the table involved. You might even be able to construct a circle to describe how the cosine functio…

Could anyone walk me through on this equation and what proves its validity?

How would one use a quadratic formula with time as a variable? For example, what the intersections between two circular functions would be when T=0 compared to T=5 if the radius of the functions increases over time? Also, is there a general equivalent of the quadratic formula for circles? I would like to basically have a simple equation that gives me the coordinates of an intersection (x, y, z) for a given value of x, y, and time. After that, the derivative of an intersecting function is going to be treated as an axis for a change in slope of the other function over time (the slope will 'reverse' over the perpendicular line to the other function's derivat…

The space that we are used to is 3D and we construct it (the model) by ensuring that the 3 planes (x=0:y=0:z=0) are orthogonal to each other. How do we move on from there if we want to build a model with 4 such planes ,all presumably orthogonal to each other in the same way? To my untrained eye it seems that the new( 4th) plane will have "nowhere to go" ie ,if it is orthogonal to the x=0 plane then it feels like it should be identical to the y=0 or the z=o plane which already occupy those areas("area" is a poor choice of word ,but I hope the meaning is clear) How do we "shoehorn " this extra plane into the model when it f…

Zero Element Equivalency Can this be considered a field? Can this be considered a solution for division by zero? Can this sufficiently create varying amounts of zero? Allow that there exists an integer zero element ( -0 ). 0 =/= (-0) |0| = |-0| 0 |=| (-0) Where |=| is defined as “Zero Element Equivalency”, where any two unique or similar additive identities are considered equal because they share the same absolute value and cardinality but may or may not possess different multiplicative properties. Allow that : 0: possess the additive identity property and possess the multiplicative property of zero. …

X^0 is 1. such as 10^0 =1, since 10/10 =1, and 10^1/10^1 = 10^(1-1) = 10^0. How about 0^0.

If I have some function like y = kx/(1+x) How do I take the derivative of dln(y)/dln(x) ln is natural log... Can someone do like a step by step kind of a thing...

What is the Infinitesimal sign?

I have a system of 1st order odes given by $$ \dot{x_1}(t) = \alpha_1 f_1(x_1,t) + \beta_1 u(t) \\ \dot{x_2}(t) = \alpha_2 f_2(x_2,t) + \beta_2 u(t) $$ They are constrained by an algebraic equation $$ x_1(t) + x_2(t) = k $$ where $\left( \alpha_1,\alpha_2, \beta_1,\beta_2 , k \right) \in \mathbb{R}$ are known constants (i.e. parameters). $f_1(t)$ and $f_2(t)$ are both unknown. Starting from a rich set of input-output **noise-free** data available from simulating a complex proxy system, what would be the best procedure to identify (even a subset of repeatable/characteristic properties) the unknown **_possibly time-varying_** functions $f_1…

Using equation with mathcad 15 I can't to output table and plot. What is wrong in my mathcad code? drop2.rar

if this is true why we need any numbers beyond 0 and 1? Feels like different scaling of the natural numbers. What would be the difference between the infinite numbers between 0 and 1 or the infinite numbers between 0 and 1 000

This is a question to the mathematicians on the forum: when you're trying to solve an open problem in pure mathematics, what are the first things you do? Do you test the conjecture with a few example problems? Do you look up recent theorems related to the question, or do you just dive right in?

I've just begun the study probability and I have a very basic question. If I roll a fair dice I know I have a one in six chance of getting a "1". What is my chance of getting a "1" if I roll it twice? (It could be either on the first roll or the second roll or both. I am just concerned with getting a "1" at some point.) What is my chance of getting a "1" if I roll it ten times? (Same thing: I'm just concerned with getting a "1" (could be more than one "1") at some point.) I realize this may be too basic of a question for this forum, but I'm hoping someone will have the time to help me out with this really simple question. Thank you.

Hi All, votefavorite I am trying to measure a curved profile of a surface(2D) to determine the surface availability at different rate of testing. I have attached an image for a rough picture. Actually I have a reference geometry and performed two tests to determine the behavior. They two had different profiles at top portion. So I considered an axis for reference geometry and drew radial lines with 15deg angle difference each and marked those points as 1 (15 deg anticlockwise from vertical axis),2(30 deg anticlockwise from vertical axis),3,... and measured length of the radial …

While trying to sleep last night I discovered a new triangle. I call it the Piangle. What's a Piangle? Maybe this will make it clear. The Piangle is an unraveled circle. Imagine cutting a radius, then draw some inner circles. Next unroll each outline to the right. This is a right triangle, so by the Pythagorean theorem the length of the hypotenuse is , which is or . The Piangle is not distorted, it's just an unrolled circle. It even has the same area as its corresponding circle. Its area is 1/2*b*h = = . Proof that I discovered this: the hypotenuse = ≈ 6.3…

Are there any formulas for finding the LCM of at least 2 numbers? All I know is tedious methods which give you a long amount of time of computing (not always? If yes, then what is it? If no then is it still possibe that we can find a formula?

Suppose you determine a point as the centroid for a single variable function is there a method to verify that the point is indeed the centroid?

In another thread on this subject it was stated that “we can establish a one-to-one mapping between any Rm and any Rn.” There is a relationship that occurs in R3 that I believe cannot be mapped to R2. The relationship exists between the sphere center and the surface curvature. I believe that because R2 has no third orthogonal plane or axis that this relationship does not exist in R2. This is best described as a relationship that exists between the tangent to a small circle on the surface of a ball and the gross position of the ball in 3-space. The illustrations show how this relationship can be seen. Mathematically, it is expressed as an identity…

I have a scenario that im trying to quantify, and wondering if there is a scientific/mathematical way of approaching it. Scenario: Under the previous process when purchasing goods for the values of $0 to $2,000 we were required to obtain one verbal quote. Now under the new process when we purchase goods for the same values we are required to obtain two verbal quotes. Example: Under the previous process one quote was obtained for $1,200, under the new process two quotes were obtained for $1200 and $980 Is there any way to quantify the benefit to the organization by following this new process. As under the previous process it would have cost $1,200 but by se…

In every R there exists an integer zero element ( -0 ) ( -0 ) =/= 0 |0| = |-0| ( -0 ) : possesses the additive identity property ( -0 ) : does not possess the multiplication property of 0 ( -0 ) : possesses the multiplicative identity property of 1 The zero elements ( 0 ) and ( -0 ) in an expression of division can only exist as: (0)/( -0 ) 0 + ( -0 ) = 0 = ( -0 ) + 0 ( -0 ) + ( -0 ) = 0 1 + ( -0 ) = 1 = ( -0 ) + 1 0 * ( -0 ) = 0 = ( -0 ) * 0 1 * ( -0 ) = 1 = ( -0 ) * 1 n * ( -0 ) = n = ( -0 ) * n Therefore, the zero element ( -0 ) is by definition also the multiplicative inverse of…

When calculating the circumference of a circle, we use 2πr. Since π is an irrational number, then for a unit circle, for example, the circumference must be an irrational length. However, the meter was origionally based on being one billionth the distance between the N. Pole and the Equator thus making the circumference of the Earth an integer in terms of meters. The meter was later changed to be based on the speed of light to again force the value of c in a vacuum to be an integer in meters/second despite an uncertainty of 4 parts in a billion. i.e. the uncertainty then becomes the length of the meter. It is the relationship of the speed of light to the cir…