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65) bhavana

	Circle	Ellipse	Parabola	Hyperbola
Equation (horiz. vertex):	x² + y² = r²	x² / a² + y² / b² = 1	4px = y²	x² / a² - y² / b² = 1
Equations of Asymptotes:				y = ± (b/a)x
Equation (vert. vertex):	x² + y² = r²	y² / a² + x² / b² = 1	4py = x²	y² / a² - x² / b² = 1
Equations of Asymptotes:				x = ± (b/a)y
Variables:	r = circle radius	a = major radius (= 1/2 length major axis) b = minor radius (= 1/2 length minor axis) c = distance center to focus	p = distance from vertex to focus (or directrix)	a = 1/2 length major axis b = 1/2 length minor axis c = distance center to focus
Eccentricity:	0	c/a	1	c/a
Relation to Focus:	p = 0	a² - b² = c²	p = p	a² + b² = c²
Definition: is the locus of all points which meet the condition...	distance to the origin is constant	sum of distances to each focus is constant	distance to focus = distance to directrix	difference between distances to each foci is constant

some thing specially for goiitians! try printing it and pasting in ur room! i promise u wont evr forget these basic formulas which sometimes tend to slip from our minds!

Scalar or Vector?
To explain the difference we use two words: 'magnitude' and 'direction'. By magnitude we mean how much of the quantity is there. By direction we mean is this quantity having a direction which defines it. Physical quantities which are completely specified by just giving out there magnitude are known as scalars. Examples of scalar quantities are distance, mass, speed, volume, density, temperature etc. Other physical quantities cannot be defined by just their magnitude. To define them completely we must also specify their direction. Examples of these are velocity, displacement, acceleration, force, torque, momentum etc.

Vector Addition
Parallelogram law of vector addition
If we were to represent two vectors magnitude and direction by two adjacent sides of a parallelogram. The resultant can then be represented in magnitude and direction by the diagonal. This diagonal is the one which passes through the point of intersection of these two sides.

Resolution of a Vector
It is often necessary to split a vector into its components. Splitting of a vector into its components is called resolution of the vector. The original vector is the resultant of these components. When the components of a vector are at right angle to each other they are called the rectangular components of a vector.

In the figure above the green vector has been resolved into two vectors: blue and red. These vectors are at right angles to each other. The are the rectangular components of the green vector.

Rectangular Components of a Vector
As the rectangular components of a vector are perpendicular to each other, we can do mathematics on them. This allows us to solve many real life problems. After all the best thing about physics is that it can be used to solve real world problems.

Note: As it is difficult to use vector notations on the computer word processors we will coin our own notation. We will show all vector quantities in bold. For example 'A' will be scalar quantity and 'A' will be a vector quantity.

Let A_x and A_y be the rectangular components of a vector A

then

A = A_x+ A_y this means that vector A is the resultant of vectors A_x and A_y

A is the magnitude of vector A and similarly A_x and A_y are the magnitudes of vectors A_x and A_y

As we are dealing with rectangular components which are at right angles to each other. We can say that:

A = (A_x + A_y)^1/2

Similarly the angle Q which the vector A makes with the horizontal direction will be

Q = tan^-1 (A_x / A_y)

here's the answer to ur second question-

since 1mole of O2 req. 2 moles of C hence 3 moles of oxygen(as i mentioned earlier) require 6 moles of C. that is 6*12=72 gms. of C.

do rate me if my answer sounds appropriate..

since acc. 2 the reacn. 2moles of c are required for 1 mole of oxygen gas, hence 24 gm c=2 moles of c and 96gm O2=3moles of O2 hence C will act as a limiting reagentand will be totally consumed in the reaction. now since it requires only one mole of O2 hence 2 moles of O2 will b left hat is 2*32=64gm oxygen will be left after completion of reaction..

well i havent been in touch wid this topic for quite a long time so 4give me if i m mistaken but i think my solution will surely help u out!

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