real solutions math

(which are pulling the striking molecules due to attraction). where a' is a constant of proportionality. If we put a N 2 = a, we find that Hence, in the ideal gas equation we must replace p by the sum of the observed pressure for a real gas and the drop caused by intermolecular attractions, i.e. ^ p Using this result in Eq. (3.4), we fin..

solution

Trigonometric Functions and Identities LEVEL-I 1. Here L.H.S. $\sin^{2}12^{\circ}+\sin^{2}21^{\circ}+(\sin^{2}39^{\circ}-\sin^{2}9^{\circ})+(\sin^{2}48^{\circ}-\sin^{2}18^{\circ})$ $\Rightarrow\sin^{2}12^{\circ}+\sin^{2}21^{\circ}+\sin(48^{\circ}).\sin(30^{\circ})+\sin(30^{\circ}).\sin(66^{\circ})$ ..

solutions

LEVEL II 1. We know from Napier's analogy that : $\qquad\qquad{\displaystyle \tan\left(\frac{B-C}{2}\right)=\frac{b-c}{b+c}\cot\frac{A}{2}}$ $\qquad\qquad{\displaystyle \tan\left(\frac{A-B}{2}\right)=\frac{a-b}{a+b}\cot\frac{C}{2}}$ $\qquad\qquad{\displaystyle \tan\left(\frac{C-A}{2}\right)=\frac{c-a}{c+a..

mathematical notes

1 Solution of quadratic equations Ax 2 + Bx + C = 0 has two solutions, which either are both real or are complex conjugates: 2 Numerical solution of equations There are many numerical techniques for finding the root of f(x) 0, i.e. the value of x for which the equation is t..

relativity real

1. State the domain and range of {(1,2), (2,4), (3,6), (4,8),(5,9)}. 2. If $R=\{(x,y):x,y\in W\; and\;2x+y=4\}$ write (i0 Domain of R; (ii) Range of R; (iii) R as a set of ordered pairs. 3. State true or false. (i). In a relation the domain an drange should be equivalent sets. (ii) In a relation neither the domain or the range can..

for real image

$p(2,3)$ in the line mirror $y=x$ is the point $Q$ and the image of $Q$ in the line mirror $y=0$ is the point $R(x,\ y)$. Find the co-ordinates of $R$. 2. The equations of perpendicular bisector of the sides $AB$ and $AC$ of a $\triangle ABC$ are $x-y+5=0$ and $x+2y=0$ respectively. If the point $A$ is $(1,\ -2)$, find the equation of line $BC$. 3..

real image

$x^{2}+y^{2}=1$. 8. Find an equation of a circle through the origin, making an intercept of $\sqrt{10}$ on the line $y=2x+{\displaystyle \frac{5}{\sqrt{2}}}$ and subtending an angle of $45^{\mathrm{o}}$ at the origin. The centre of the circle is in the positive quadrant. 9. If $x+y\sqrt{-1}=\tan(u+v\sqrt{-1})$, where $x,y,u$ and $v$ are all r..

real numbers

In the previous classes, we have learnt the representation of natural numbers, integers, rational numbers, terminating and non-terminating decimals on the number line. Also, we have learnt representation of irrational numbers on the number line. Here, in this chapter we shall learn Euclid's division algorithm, fundamental theorem of arithme..

Solution

="font54" style="font-style: italic;"> x sin a) dx J oosx J cosx J, . - '' . : - = cos a jdx + sin a Jtan x dx = (cos a) x + sin a log | sec x \ + c 4. Let x-a = t => x = t + a and dx = dt "..

Solutions

The greatest common factor is 8 6Ans : Given equation is xy + 3y 2x 6 = 0 arrange them in an order now. We get xy 2x + 3y 6 = 0 x (y 2) + 3 (y 2) = 0 (x + 3) (y 2) = 0 So here (x + 3) and ( y 2) are the factors 7Ans: Given that. 5(A) +6(O) =$40 Each orange is $3 So we get 5(A) + 6(O) = $40 5(A) + 6(3) = 40 5(A) + 18 ..

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