Showing posts with label math. Show all posts
Showing posts with label math. Show all posts
Radial and Transverse Components of Velocity and Acceleration
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Post Author
Amna Mughal

Radial and Transverse Components of Velocity and Acceleration

Radial and Transverse Components of Velocity and Acceleration  A point in Polar coordinate system is represented by p(r, θ) where r is ...

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Prove that (a+b)/(an - bn) , if n is a positive even integer.
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Post Author
Amna Mughal

Prove that (a+b)/(an - bn) , if n is a positive even integer.

Prove that (a+b)/an-bn , if n is a positive even integer Proof: We prove it with the help of mathematical induction. CASE – I ...

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Prove that product of three consecutive integers is divisible by 6.
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Post Author
Amna Mughal

Prove that product of three consecutive integers is divisible by 6.

Proof: The product of three consecutive integers which are divisible by 6 is: ⟹ 6 /n(n+1)(n+2) We have to prove it by mathema...

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What is Curvature
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Post Author
Amna Mughal

What is Curvature

What is Curvature Curvature Definition: The rate of binding of a curve is called curvature and its reciprocal is called radiu...

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Tangential and Normal component of Velocity and Acceleration
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Post Author
Amna Mughal

Tangential and Normal component of Velocity and Acceleration

Tangential and Normal Component of Velocity and Acceleration

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Cartesian component of velocity and acceleration
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Post Author
Amna Mughal

Cartesian component of velocity and acceleration

Cartesian Component of Velocity And Acceleration 

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Velocity and Acceleration
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Post Author
Amna Mughal

Velocity and Acceleration

Velocity and Acceleration Velocity: Acceleration:  

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Position of moving particle
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Post Author
Amna Mughal

Position of moving particle

Position of Moving Particle Consider a particle in xy-plane moving along a curve AB . Let at any time 't' , the particle...

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Amna Mughal

Kinematics

Kinematics Mechanics The branch of science in which we deal with the action of force on bodies at rest or motion is called mechanics. ...

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Amna Mughal

Introduction to Topology

Introduction to Topology ·         Theory of Sets Topology is one of those branches of mathematics, where set theory is used extensi...

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Prove that if n is an odd integer then 8/n^2 -1.
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Post Author
Amna Mughal

Prove that if n is an odd integer then 8/n^2 -1.

Theorem: Prove that if n is an odd integer then 8/n^2 -1. Proof: We prove it by mathematical induction CASE-I For n=1 = n^2 -1...

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If a, b belongs to Z then show that (1) if a/b and b/a this implies a = ±b. (2) if a/b and b/c then a/c. (3) if a/b then a/bc. (4) if a/b then ac/bc. (5) if a/b and a/c then a/bx+cy for x,y belongs to Z. (6) if a/b1+b2 and a/b1 then a/b2. (7) a/o (8) 1/a
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Post Author
Amna Mughal

If a, b belongs to Z then show that (1) if a/b and b/a this implies a = ±b. (2) if a/b and b/c then a/c. (3) if a/b then a/bc. (4) if a/b then ac/bc. (5) if a/b and a/c then a/bx+cy for x,y belongs to Z. (6) if a/b1+b2 and a/b1 then a/b2. (7) a/o (8) 1/a

Theorem: If a, b belongs to Z then show that  If a/b and b/a this implies a = ±b.  If a/b and b/c then a/c. If a/b then a/bc. If a/b...

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Euclid's Theorem and Its consequence
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Amna Mughal

Euclid's Theorem and Its consequence

Definition: Set of integers is denoted by Z and defined as: Z = {0, ±1,  ±2,  ±3,... } Set of positive integers   Z+  = {1, 2, 3, ...

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If a and b are unit vectors and θ is the angle between them, then how do I prove that sin θ/2 = ½ |a-b|?
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Post Author
Amna Mughal

If a and b are unit vectors and θ is the angle between them, then how do I prove that sin θ/2 = ½ |a-b|?

If a and b are unit vectors and θ is the angle between them, then how do I prove that sin θ/2 = ½ |a-b|?

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Show that a is perpendicular to b iff |a + b| = |a - b|.
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Post Author
Amna Mughal

Show that a is perpendicular to b iff |a + b| = |a - b|.

Show that a is perpendicular to b iff |a + b| = |a - b|.

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Dot Product or Scalar Product and some important points
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Post Author
Amna Mughal

Dot Product or Scalar Product and some important points

Dot Product or Scalar Product

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Prove that the three points -2a + 3b + 5c, a + 2b + 3c and 7a - c are colinear, where a, b, c are non-coplanar.
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Post Author
Amna Mughal

Prove that the three points -2a + 3b + 5c, a + 2b + 3c and 7a - c are colinear, where a, b, c are non-coplanar.

Prove that the three points -2a + 3b + 5c, a + 2b + 3c and 7a - c are colinear, where a, b, c are non-coplanar.

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Prove that the four points 2a + 3b - c, a - 2b + 3c, 3a + 4b -2c and a - 6b + 6c are coplanar, where a, b, c are no-coplanar
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Post Author
Amna Mughal

Prove that the four points 2a + 3b - c, a - 2b + 3c, 3a + 4b -2c and a - 6b + 6c are coplanar, where a, b, c are no-coplanar

Prove that the four points 2a + 3b - c, a - 2b + 3c, 3a + 4b -2c and a - 6b + 6c are coplanar, where a, b, c are no-coplanar Prove t...

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Prove that the vectors 3a - 7b - 4c, 3a - 2b + c , a + b + 2c are coplaner, where a, b, c are non-coplaner vectors.
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Post Author
Amna Mughal

Prove that the vectors 3a - 7b - 4c, 3a - 2b + c , a + b + 2c are coplaner, where a, b, c are non-coplaner vectors.

Prove that the vectors 3a - 7b - 4c, 3a - 2b + c , a + b + 2c are coplaner, where a, b, c are non-coplaner vectors. Prove that the v...

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Prove that four points -6a + 3b + 2c , 3a - 2b + 4c , 5a + 7b + 3c and -13a + 17b - c are coplanar, where a,b,c are non-coplanar.
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Post Author
Amna Mughal

Prove that four points -6a + 3b + 2c , 3a - 2b + 4c , 5a + 7b + 3c and -13a + 17b - c are coplanar, where a,b,c are non-coplanar.

Prove that four points -6a + 3b + 2c , 3a - 2b + 4c , 5a + 7b + 3c  and -13a + 17b - c are coplanar, where a,b,c are non-coplanar. P...

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