Mathematics

The other day I was going through a post that said "Applied Mathematics involves mathematical models as well as creativity".

Hello all, I was practicing some problems and I come across this question : Is triangle ABC with sides a, b and c acute angled? Triangle with sides a2, b2, c2 has an area of 140 sq cms. Median AD to side BC is equal to altitude AE to side BC. Which one is the right answer? And How? Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked. BOTH statements (1) and (2) TOGETHER are sufficient but NEITHER statement ALONE is sufficient to answer the question asked. EACH statement ALONE is sufficient to answer the que…

What does this symbol mean? I pointed to it using the red color. http://www5.0zz0.com/2016/12/22/18/706933985.jpg

Very Interesting Number Nine Two Numbers (10 a+b) and (10 x+y) For two digits numbers, numbers can be written in four ways like this 1. (10 a+b) and (10 x+y) 2. (10 a+b) and (10 y+x) 3. (10 b+a) and (10 x+y) 4. (10 b+a) and (10 y+x) Multiple with each other  (10 a+b)*(10 x+y) = 100 ax + 10 bx + 10 ay +by  (10 a+b)*(10 y+x) = 100 ay + 10 by + 10 ax + x b  (10 b+a)*(10 x+y) = 100 bx + 10 ax + 10 by + a y  (10 b+a)*(10 y+x) = 100 by + 10 ay + 10 bx + ax Subtract each one respectively 1.100 ax +10 bx + 10 a y + by - 100 a y - 10 by- 10 ax - x b = 90 ax + 9 bx - 90 a y – 9 by = 9(10 ax+bx-10 a y- by) 2.100 ax +10 bx + 10 ay + by – 100 bx – 10 ax-…

Today we will see how Piyush Goel discovered something while playing with numbers. Here is the story . One day while sitting idle, and having nothing important to do he was just scribbling on paper. he was writing random numbers and thinking how could link them. To his amazement he discovered this: he wrote down 0, 1, 2, 3, 4, 5. Next to each number he wrote their respective squares, viz. 0,1, 4, 9, 16, 25. Then start subtracting each successive square from the next bigger square. It looks something like this: (1-0), (4-1), (9-4), (16-9) and (25-16). What is the result? he got 1, 3, 5, 7, 9. Now again subtract each successive number from the next one in th…

So a few days ago I was randomly solving some inverse trigonometric problems, and obviously I wasn't paying attention, and this question came on to me. Any clue why? Never really got it. Thanks in advance.

Let's say the collection of numbers A contains all number higher than 3 and lower than 4, including infinitesimals. This group is infinite. Let's say that group B contains all numbers higher than 3 and lower than 5. This group is also infinite. My question is if group B contains more numbers than group A? Although B is a more ''extensive'' infinity, i.e. technically includes double the amount of numbers than infinity A, either one of them are infinite and therefore nothing can have a higher value than any one of them. I would imagine this has been asked a trillion times over the course of history but I don't know of a definite conclusion.

Symmetry of Digit "2" In Squaring If we square 11, it is very simple put 1(2*1) (12) get 121 same as square 12 put 1(2*2)(22) get 144 again for 13 we get 169 and for 14 we get 1 8 16=196 and so on. When we go deep, we find that there is symmetry of two types (2, 4, 6, 8, 10, 12, 14, 16, 18, 20 …. Diff is always 2) & (1, 4 , 9 , 16, 25, 36, 49, 64, 81, 100 ) diff. is 3 5 7 9 11 13 15 17 19 and diff. of 3 5 7 9 11 always 2, so there is true symmetry . Up to 19 it is right but at 20 how we can put 1 20 100 just because of symmetry. 112 = 1 2 1 122 = 1 4 4 132 = 1 6 9 142 = 1 8 16 = 100 + 80 + 16 = 196 152 = 1 10 25 = 100 + 100 + 25 = 225 162 …

Hello, everyone This is my first forum. I need help to find the nth term of Fibonacci series with the golden ratio. Can anyone help me to know about golden ratio and its equation? and how to find Fibonacci series from it.

Hi everybody, We all know that in mathematics, any wave can be thought of as the plot of a circle in the 2D coordinate plane (considering 2D waves only). A wave [math]W[/math] may be represented as: [math]W(x,t)=Acos(kx-\omega t)[/math] Where [math]W(x,t)[/math] is the function of the wave's position [math]x[/math] and time [math]t[/math], which gives the displacement from the x-axis, [math]k[/math] is the wavenumber, [math]\omega[/math] is the angular frequency of the circle; [math]\omega=2\pi f[/math], where [math]f[/math] is the frequency of the wave. Thus the wave [math]W[/math] is a curved line, consisting of points of the form [math](x,Acos(kx-\omega t))[/ma…

Take a simple function f(x)=x^2, or the equation y=x^2 This clearly lies on a plane with two dimensions. There is one variable x that determines the solution y. In terms of ?vector space? this function needs +x, -x, and +y However if you zoom out far enough when x is in the order of magnitude 1x10^5, the plane begins to disappear. Eventually, but a lot before x=infinity, this function loses the positive x axis, the negative x axis, and the positive y-axis. Simply it becomes a line x=0. Let me call this a declining function, as dimensions decline with increase in scale. Conversely, if you start with something that measureably resembles a line…

Please read and check the following two short proofs, which I presume to be inaccurate given what is proven, as I am looking to know what is wrong as the case may be. Thank you in advance!: 1) Let [latex]q_1, q_2, q_3,[/latex] … be an enumeration of [latex]A = \mathbb{Q} \cap (0,1)[/latex]. 2) Select a real number [latex]r \in (0,1)[/latex] uniformly at random. Note: A common way of doing this cited by mathematicians is the theoretical flipping of a coin infinitely many times followed by some trivial 'clean-up' given that there are two binary expansions of each dyadic rational, e.g. 0.1 = 0.01111111... 3) Let [latex]B = \math…

36 / 6(2+2+2) = ?? What is the right answer?? 1 or 32 ?? My friend told me, "use BODMAS.. ==> 36/6*6 ==> 6*6= 36 "

I'm running analytics and need help setting up my formula. I remember from my calculus days there is a formula to find the optimal output but I cant remember, here is what I'm looking for: I have a total rev per patient and I have total number of patients seen. Ive noticed as the number of patients increase the rev per patient decreases. I'm trying to find the optimal number of patients seen to have the highest rev per patient. rev per patient tot patients 248.89 906 240.19 851 227.03 947 252.67 896 276.60 772 261.…

Im working on a little problem for an idea im having. If you stand on earth and look out over the ocean. Your field of vision would be almost 180 degrees. But lets say 150 degrees for this example. Being 6 feet above sea level puts your distance to the horizon 3 miles out. This means that by trigonometry you can draw a triangle with 3 miles on two sides and the angle between them being 150 degrees. This would make the line between them be 5.8 miles. Ive been wondering. By math, how much of earth curvature would be seen on each side of the middle where the curvature from your point of view would be zero ? Earth will curve down to the sides in respect to the di…

Here is my formula for the area of n layers of appolonian gasket(assuming no circles past the nth layer): $$πR^2 - (πR^2 - (\sum_{0}^{n} x_n*πr_{n}^2))$$ Here R is the radius of the outer circle, r is the radius of an inner circle, x is a function that represents the number of circles in a given layer and n is the number of layers. I know this is right as far as calculating area is concerned but how would I actually represent this if I wanted to show someone else this formula? The reason I only have $πr_{n}^2$ once is because here is what the sum would be like for a successive number of layers. If I assume I have this kind of Apollonian gasket: th…

Hi, I am a math tuition teacher. Now my students are preparing for their final exams. They are little slow in math problems. Actually i need to check the answers fast. So i tried many online calculators. Finally found an online percentage calculator to calculate problems. But it is confused for me how it works and gives the result. Could someone explain me?

This is the last missing piece I need to complete my compression algorithm, new one. Let's say I have 4 bits with 2 bits set as 1, 0011. The total number of permutations for this number is 0011, 0101, 0110, 1001, 1010, 1100, 6 cases. This can be computed using the calculation. 4! / ((2!)(4-2)!) = 6 Now I want to be able to find the nth sequence, for instance 1st number is 0011, second number is 0101. So if I say n=5, I want to be able to get the 5th permutation sequence 1010 from the initial 0011. How do I do this?

Hey all. I am trying to figure something out that I can't. Basically, for some reason I wanted to find the inverse of y = x7+x5. How the heck would you do that. I know it is probably possible, but how?

06:12, 06:16 06:12 1 The root digit; a point or a circle, not a duet. Black standard hover. 2 The fount. Opposite, and polar the line. 3 The minor triangular. Wit, a tutor of the second a quiver. 4 Major, or the square: a fix, a gradient a scale. Skeleton. 5 Minute integer; agent of a quartet. A note on a blank canvas a pin 6 Naught. screw. 7 The enigma; corrival for the root digit. Sinister asylum, the lens. 8 Eclipse number. Opulent mien a lever. 9 Bone immaturity. The phobia, temper; a nexus. 10 The flux, a cross of hue and tint, multiplied. The perfect blend; the fly. 06:16 2 (8) Band (.2). 3 (9) Bezel (.5). 1 (10) Lug (.1).

Apparently [latex]xe^{-x^2}[/latex] is an odd function. I found out the long way finding the integral sums to zero (btw, excluding trivial cases, is that a sufficient condition to conclude a function must be odd?). However, i am supposed to be able to tell this was odd by inspection (similarly for even functions). I'm sure they don't mean i need to be able to determine the parity of any function by inspection, but does anyone know of any hints and tricks for doing so? I'm starting to see a pattern where the parity of a Gaussian integral multiplied by a polynomial is equal to the parity of the polynomial. Any others?

Hey, I have a question about math. If you take : - 8 = 3/19 n (imagine the 3/19 as a fraction.) you need to find N. To do this you would flip the 3/19 to get 19/3 and put it of the other side of the equation. Getting: 19/3 * -8/1 = n Getting in the end the answer: -152/3 = n How does this give the answer?

WHEN I Was A Teenager I Used To Create Mathematical Patterns Using A Pyramid Design To See If Any Sums Or Calculations Had A Pattern. RECENTLY I wanted to learn Binary Code for Fibonnaci. I wanted to see If there was a secret Binary Code for Fibonnaci. The Pyramid Maths Works By Using The Pattern Of Fibonacci on the Bottom Row,, Then Adding Number Above On The Next Row. To Create The ​Number On The Row Below It.. So To Create A Row Above, You Add The Same Fibonacci Pattern To The Sequence Of Numbers On The Row Below It.. 0+1 is 1. So you Add The 0 On The Row below + The Beginning Number Of The Row Above In The Sequence To Create The Next Number In Sequence On The Row …

Using the linear regression method outlined in the following https://www.easycalculation.com/statistics/learn-regression.php I wrote some javascript to find the outliers of a given set. However I would like the method to work with curves and in 3d. Not sure of the forumlae in 3d. <script> function findLineByLeastSquares(values_x, values_y) { var sum_x = 0; var sum_y = 0; var sum_xy = 0; var sum_xx = 0; var count = 0; var x = 0; var y = 0; var values_length = values_x.length; if (values_length != values_y.length) { throw new Error('The parameters values_x and values_y need to have same size!'); } if (values_le…

Hi, Could you please help me to linear this, my model is non-linear so it cannot estimate. someone suggest me using the Taylor Expansion but I think it to hard to apply the Taylor expansion in my case Thanks you so much! Chung How to linear this equation.pdf