Finding the value of X on the equation: $$4^x+6^x=9^x$$

 Introduction.

On the approach to find the value of x on the given equation we will use ingenious mathematical techniques in order to find the value of x. On this approach we will only use elementary algebra. 

Handwritten mathematical solution. Finding the value of x on the given equation $$4^x+6^x=9^x$$ This solution belongs to the area of Elementary Algebra.

 Background.

In the approach to the solution of this equation, you can learn some valuable forms to find the value of a x variable by certain ingenious algebraic moves.

Resolviendo la ecuación dada. | Usando solo algebra elemental e identidades pitágoricas vamos a resolver la siguiente ecuación: $$81^{Sen^2 x} + 81^{Cos^2 x}= 30.$$.

 El día de hoy vamos a resolver un problema de algebra elemental de nivel IMO(International mathematics olympiad) , que, aunque en principio se ve complicado, te darás cuenta a lo largo de la resolución de que no es así. Es más, para la resolución de la ecuación que vamos a estudiar, solo se necesita conocer conceptos tan básicos como productos notables, propiedad de potencias de igual base e identidades trigonométricas, por lo tanto todo lo necesario para resolver la ecuación, lo incluyo dentro la resolución del mismo de manera explicita. Este planteamiento tiene la caracteristica clásica de todo lo que se plantea en la IMO, te reta a conseguir soluciones muy creativas a los problemas matemáticos, sin necesidad de incurrir en las deep mathematics(matemáticas profundas). Bueno, sin mas que decir, te voy a enseñar a resolver esta ecuación :) .

La ecuación a resolver.

 La Solución.

This sheets on LaTeX were made it by me.

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Blessings for all of you, and thanks for your attention

#math #stem #science 

Handwritten mathematical solution to a given problem. | Solve the equation: $$81^{Sen^2 x} + 81^{Cos^2 x}= 30.$$.

 Background.

This is the handwritten solution to a IMO(International Math olympiad) type problem. This problem belongs to the elementary algebra area. So look at this creative solution that i found for this equation.

Rocket Science Principles. || A thrust and acceleration problem. #1.

 Today I decided to vary a bit the area of science I always work on, which is mathematics, and this time I decided to bring some content from physics, and more specifically from rocket science principles. Rocket science is the second area of science I like the most and the one I usually do best after mathematics.

This problem is about Thrust and acceleration in rockets, to be more precise, the problem is about calculating the thrust felt by a rocket at the moment of take-off from a launch pad, as well as calculating the respective initial acceleration at the launch pad. I found this problem very nice and interesting, because it shows principles of rocket science as fundamental as the concept of thrust and variation of the mass of the rocket as the fuel is depleted and the change of mass in the rocket-system takes place.

The problem to solve.

The solution.

These Sheets written on LaTeX were made by me.

Download this on PDF.

Blessings for all of you

#physics #rockets #science 

Handwritten physics problem about Rocket Science Principles. || A thrust and acceleration problem. #1

Background.

Hello ladies and Gentleman, first of all let me wish you a very nice day. This uploaded Handwritten sheet deal with principles of rocket science, and more specifically with a problem of thrust and acceleration of a Saturn V rocket.

On this problem i show how to use some fundamental definitions for the rocket science as Thrust, Velocity of the Exhaust, and change of mass. 

Blessings for all of you.

#Physics #math #science #rocketscience 

Mathematical Proof. | Using the Epsilon-Delta definition we are going to prove that the limit for the given function is 4.

 Today i will prove that the limit for the given f(x,y) is 4, using the Epsilon-delta definition for it. Also i will show you how to use the Distance Formula in order to find the necessary relations between epsilon-delta. At the end you will see how i found the proper epsilon to satisfy the epsilon-delta definition of ordinary limit and prove that the limit is L, that in this case of study is 4. This mathematical proof belongs to the areas of: Real Analysis and Multi-variable Calculus

Proposition.

The Mathematical Proof.

This sheets on LaTeX were made it by me.

Download This on PDF.

Thanks for your attention.

#math #science #Realanalysis  

Handwritten mathematical proof that belongs to the area of Real Analysis. #2

Background.

Hello ladies and Gentleman, first of all let me wish you a very nice day. This proof belongs to the area of Real analysis, and prove the existence of a Limit through the use of the epsilon-delta definition for limits with multiple variables.

Mathematical proof(Number Theory).| 8 is the largest integer number that divides all odd numbers of the form $$m^2-n^2.$$

Handwritten mathematical proof that belongs to the area of elementary number theory. #1