MATHEMATICS ENCYCLOPEDIA

If the given expression is Find the value of m-n Solving the above expression

Projectile  is the name given to a body which, after having been given an initial velocity, is allowed to move under the influence of gravity alone. A body projected from a height h with velocity u at an angle θ with the horizontal

Projectile  is the name given to a body which, after having been given an initial velocity, is allowed to move under the influence of gravity alone. A body projected from the ground with a velocity u at an angle θ with the horizontal.

Projectile is the name given to a body which, after having been given an initial velocity, is allowed to move under the influence of gravity alone. A body projected horizontally with a velocity u from a height h Horizontal and vertical distances covered in time t are Differentiating above equations with respect to time t, we get the horizontal and vertical velocities Equation of trajectory Time of flight  Horizontal range Magnitude of resultant velocity at time t  The angle α which the resultant velocity vector subtends with the vertical is given by 

AB and CD intersect each other at O. Given ∠EOA = 90°, ∠EOC = x, ∠BOC = y and ∠BOD = 2y + 30. Find the value of x and y and ∠AOD Since CD is a straight line, therefore the sum of 2y + 30 and y must be 180 degree Hence, 2y + 30 + y = 180 3y + 30 = 180 3y = 150   y = 50° Also AB is a straight line therefore the sum of angles EOA, EOC and BOC must be 180 degree. Hence, 90 + x + y = 180 90 + x + 50 = 180  x + 140 = 180 x = 40° Therefore, x = 40° and y = 50°.

Find a, b and c from the following figure below Since CD is a straight line, therefore the sum of angles 4x, 3x and 5x must be 180° Hence, 4x + 3x + 5x = 180 →  12x = 180 →  x = 15 ° Now, we see that following are the equal angles because they are vertically opposite, hence  a = 5x  b = 3x  c = 4x Therefore,    a = 5x = 5*15 = 75°   b = 3x = 3*15 = 45 °  c = 4x = 4*15 = 60 °

The magic hexagon, the following is the only known magic hexagon ever. There are no other magic hexagon of any size. Size of the magic hexagon Properties of the magic hexagon

The number of significant figures in any measurement indicates the degree of precision of that measurement.  The degree of precision is determined by the least count of the measuring instrument. Suppose a length measured by a meter scale  ( of least count = 0.1 cm ) is 1.5 cm, then it has only two significant figures, namely 1 and 5.  Measured with a vernier callipers ( of least count = 0.01 cm ) the same length 1.53 cm and it then has three significant figures. Measured with a screw gauge ( of least count = 0.001 cm ) the same length may be 1.536 cm which has four significant figures.  It must be clearly understood that we cannot increase the accuracy of a measurement by changing the unit .  For example, suppose a measurement of mass yields a value 39.4 kg. It is understood that the measuring instrument has a least count of 0.1 kg.  In this measurement, three figures 3, 9, 4 are significant. If we change 39.4 kg to 39400 g or 3...

The internationally accepted standard units of the fundamental quantities.

Narcissistic number is a number that is the sum of its own digits each raised to the power of the number of digits. Narcissistic numbers also known as Armstrong number , plus perfect number , plusperfect digital invariant Examples 153 = 1 3 + 5 3 + 3 3 370 = 3 3 + 7 3 + 0 3 407 = 4 3 + 0 3 + 7 3

Here we would solve a dot puzzle Consider the figure below Connect all the dots without lifting the pen with only 4 straight lines and the lines do not overlap. Here are some examples already done for you but not been solved because some dots left to be crossed. You could see that some dots have been left to be crossed by the line. So do you think you could solve it. Let us try one more time. Now, what do you see, the puzzle has been solved with the required conditions. Find out some more solutions to this question.

Slope of a line A line in a coordinate plane forms two angles with the x-axis , which are supplementary.  The angle θ made by the line l with positive direction of x-axis and measured anti-clockwise is called the inclination of the line. Obviously 0° ≤ θ ≤ 180°. We observe that line parallel to x-axis, or coinciding with x-axis, have inclination of 0°.  The inclination of a vertical line ( parallel to or coinciding with y-axis ) is 90°. If θ is the inclination of a line l, then tanθ is called the slope or gradient of the line l. The slope of a line having inclination 90°  is not defined. The slope of a line is denoted by m. Thus m = tanθ, θ ≠ 90°. It may be observed that slope of x-axis is zero and slope of y-axis is not defined . Slope of a line when coordinates of any two points on the line are given  Let P ( x, y ) and Q ( x, y ) be two points on a line l with inclination θ. Then slope is given by ...

Have you ever wondered what is the speed of light ? Well this one of the most interesting questions in the world of Mathematics and Physics . The speed of light in vaccum is a fundamental constant . The most interesting fact about this speed is that if an object moves with this speed in one frame, it has the same speed in any other frame. This the key fact on which the special theory of relativity is based . The speed of light is defined to be exactly 299,792,458 m/s. Perhaps the first attempt to measure the speed of light was made by Galileo . Two experimenter A and B, each having a lantern and a shutter, stands on two small hills.  The shutter can cover or uncover the lantern. Initially, both the lanterns are covered . One of the persons A uncovers his lantern. The second person B uncovers his lantern when he sees the light from the lantern of A. The first person A covers his lantern when he sees the light from the lantern of B.  The time el...

Maria Agnesi ( 1718-1799 ) was the first woman to write a Mathematics handbook and the first woman appointed as a Mathematics Professor at a university. She was an Italian Mathematician, pholosopher . She was a sleep walker and could do mathematical problems in her sleep. Often in the morning she would find that she had sleepwalked to her desk and completed a problem she had been unable to solve the last night.

Question of the suspension bridge The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m . Find the length of a supporting wire attached to the roadway 18 m from the middle . Think of the problem as a real problem that you have to calculate the length of the wire. It is a very interesting problem that helps one to understand where mathematics is used in real life situation. It would be easy to visualize the problem if we have a diagram. So, let us draw a diagram. Now let us plot a coordinate graph for this diagram If we now solve using the coordinates of the parabola would get the answer.  Let us take the point ( 50, 24 ) and solving we get  Again using the point ( 18, y ) and solving we get  This is the length between...