## Simple interest

The basic concept of interest is based on the excess amount borrowed by the borrower in relation to the borrowed amount, in addition to the amount and amount of principal and interest paid on the amount paid to the principal in the fixed period of time. The amount made is known as compound. Interest on milling is calculated as simple and compound interest, and for a year, both the interest rate and compound interest are equal when the rate of interest is yearly.

## Simple interest

When calculating interest only for the time being, the principal is called simple interest.

### Finding the Principle on the Rate of Seduction Interest

When the rate of simple interest is different for different years, in such a situation, certain calculations are needed to calculate the principal. Using these sources, saving time in the examination building, along with the Accuracy also It comes

1 -  If the rate of ordinary interest goes from 1% to 2% and in time t is more than m

Principal amount   =
$\frac{M}{r2-r1}\times&space;\frac{100}{t}$

2 -  If the interest rate r1% for time t1 on any money, then rate r2% for time t2

### Finding simple interest on N times of principal

When a wealth gets N times of N times or N times of interest in time, then they experience some difficulty in finding the rate of simple interest because they are N times of themselves and due to the N times of interest, I do not care about it, so its concept is understood as follows

1- If any funding at the rate of simple interest becomes n times in T
rate of interest         =            $\frac{(n-1&space;)\times&space;100}{t}$

2- If any money at the rate of simple interest becomes n times of interest in time

rate of interest        =             $\frac{n\times&space;100}{t}$

## Reflection of light and snail law

A ray of light runs through a straight line, but when the ray of light

goes through a transparent medium to another transparent medium,

then it gets distracted by its path. In the second medium, the beam,

either towards the first medium, either bends towards the

perpendicular or away from the perpendicular

If the light beam goes from one medium to another, it is called

"refraction" from its path, if the refracted ray bends toward

the relation relative to the incident ray, then the second is called

the dense relative to the medium, but if the refracted ray is an

incident ray Removed from the relative angle, then the other

medium is called the relative viral of the first

Light refraction has two rules
1 Incident ray, refracted ray and perpendicular to the point of

view are all in the same plane

2 For any two of the medium and for the light of certain colors

(wavelength), the ratio of sin to the angle of incidence and the

angle of refraction remains constant.

If the angle of incidence is i and the angle of refraction then

$\frac{sin&space;I}{sin&space;R}=costant$

This rule is called the snail rule. This determinant is called the

refractive index of the second medium relative to the first medium

, if we first display the medium 1 and the second medium 2, the

refractive index is displayed from 1N2.

## Analytic method of vector addition

If two vectors display the results from two adjoining side drawn from any point of a parallelogram in the direction of the result, then the result and direction, the parallelogram that is drawn by the diagonal has been drawn from the same point to add the vector Parallel quadratic rules
Assuming vector $\vec{A}$ and $\vec{B}$ are bent at opposite $\theta$ angle, they are displayed in the direction of the parallel quadrilateral OPQS in the direction of OPQS and OP and the OS, then according to the rule of parallelogram, resultant $\vec{R}$ of $\vec{A}$ And $\vec{B}$ will be represented by the diagonal OQ in the result and direction. In order to find the result of the resulting $\vec{R}$, we increase the side OP and pull the vertical QE from the point Q, thus

Thus, in the right angled triangle OEQ

$(OQ)^{2}&space;=&space;(OE)^{2}&space;+&space;(QE)^{2}&space;=&space;(OP+PE)^{2}&space;+&space;(QE)^{2}$

$=&space;(OP)^{2}&space;+&space;(PE)^{2}&space;+&space;2(OP)(PE)&space;+&space;(QE)^{2}$

NOW

$(PE)^{2}&space;+&space;(QE)^{2}&space;=&space;(PQ)^{2}$

SO

$(OQ)^{2}&space;=&space;(OP)^{2}&space;+&space;(PQ)^{2}&space;+&space;2(OP)(PE)$

IN Right-angled triangle

$COS\theta&space;=&space;\frac{PE}{PQ}$
OR

$PE&space;=&space;PQCOS\theta$

So the final equation will be

$(OQ)^{2}&space;=&space;(OP)^{2}&space;+&space;(PQ)^{2}&space;+&space;2(OP)(PQCOS\theta&space;)$   ,  NOW

OP =A , PQ= OS = B , OQ = R ,,    SO

$R^{2}&space;=&space;A^{2}+&space;B^{2}&space;+2AB&space;COS\theta$

$\left&space;[&space;R=\sqrt{A^{2}&space;+B^{2}&space;+2ABCOS\theta&space;}&space;\right&space;]$

To find out the direction of the resulting $\vec{R}$, say that the angle of $\vec{R}$ vector $\vec{A}$ is formed by $\theta$

$Tan&space;\theta&space;=&space;\frac{QE}{OE}&space;,=&space;\frac{QE}{OP+PE}$   NOW  , OP = A , PE = BCOS$\theta$

To find the value of QE, in triangle PEQ

$SIN\theta&space;=&space;\frac{QE}{PQ}$

$\left&space;[&space;Tan\theta&space;=&space;\frac{Bsine\theta&space;}{A+bcos\theta&space;}&space;\right&space;]$

Special cases

(1) when both the vector are in same direction

Again  equation

$R&space;=&space;\sqrt{A^{2}+B^{2}+ABCOS\theta&space;}&space;=&space;\sqrt{A^{2}&space;+B^{2}+2AB}&space;=&space;A+B$   and

$Tan\theta&space;=\frac{b&space;\times&space;0}{a+b}&space;=0&space;,&space;\alpha&space;=0$
Thus the result of result $\vec{A}$ is equal to yoga of both vector $\vec{A}$ and $\vec{B}$ and in $\vec{A}$ and $\vec{B}$ same direction

(2) when the both vector are at right angle to each other

$R=\sqrt{A^{2}+b^{2}+2ABcos\theta&space;}&space;,=\sqrt{A^{2}+B^{2}}$

$Tan\theta&space;=\frac{Bsin90}{A+Bcos90}&space;,&space;=\frac{A}{B}$

(3) When both the vectors are in opposite direction

Again  equation

$R=\sqrt{A^{2}+B^{2}+2ABcos180^{\circ}}&space;=&space;\sqrt{(A-B)^{2}}&space;=A-B,B-A$

$Tan\theta&space;=\frac{Bsin180^{\circ}}{A+Bcos180^{\circ}}&space;=0&space;,nad&space;,\alpha&space;=0,or&space;180^{\circ}$
Thus the result of the resultant vector $\vec{R}$ is equal to the difference of the result of both vectors and in the direction of the large vector
It is clear from the above that the result of the result of both vector is maximized, then both vectors are in the same direction and this is minimal when they are in the direction