College Algebra, Mathematics

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What is number systems, NUMBER SYSTEMS: Numbers  are intellectual  witne...

NUMBER SYSTEMS: Numbers  are intellectual  witnesses  that belong  only  to  mankind. Example: If the H C F of 657 and 963 is expressible in the form of 657x + 963 x -

Theorem, Theorem, from Definition of Derivative  If f(x) is differenti...

Theorem, from Definition of Derivative  If f(x) is differentiable at x = a then f(x) is continuous at x =a. Proof : Since f(x) is differentiable at x = a we know, f'(a

Example of complex roots, Solve the subsequent IVP. y'' - 4y' + 9y = 0, ...

Solve the subsequent IVP. y'' - 4y' + 9y = 0, y(0) = 0, y'(0) = -8 Solution The characteristic equation for such differential equation is. As:  r 2 - 4r + 9 = 0

Ratio, There are only Chinese and Malay pupils in a hall.The ratio of the n...

There are only Chinese and Malay pupils in a hall.The ratio of the number of boys to the number of girls is 2:3.The ratio of the number of Chinese boys to the number of Malay boys

Square of a number added to 25 equals 10 times the number, The square of a ...

The square of a number added to 25 equals 10 times the number. What is the number? Let x = the number.  The statement, "The square of a number added to 25 equals 10 times the n

In terms of x what is the total number of miles they rode, Noel rode 3x mil...

Noel rode 3x miles on his bike and Jamie rode 5x miles on hers. In terms of x, what is the total number of miles they rode? The terms 3x and 5x are such as terms since they hav

Graphical understanding of derivatives, Graphical Understanding of Derivati...

Graphical Understanding of Derivatives: A ladder 26 feet long is leaning against a wall. The ladder begins to move such that the bottom end moves away from the wall at a const

Find the sum of all natural numbers, Find the sum of all natural numbers am...

Find the sum of all natural numbers amongst first one thousand numbers which are neither divisible 2 or by 5 Ans:    Sum of all natural numbers in first 1000 integers which ar

Show that positive integers is divisible by 6, Show that the product of 3 c...

Show that the product of 3 consecutive positive integers is divisible by 6. Ans: n,n+1,n+2 be three consecutive positive integers We know that n is of the form 3q, 3q +1

Addition rule - probability rule, The Addition Rule: Mutually Exclusive Eve...

The Addition Rule: Mutually Exclusive Events P(A or B or C) = P(A) + P(B) + P(C) This can be represented by the Venn diagram as follows:

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