## word problem, Mathematics

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tom has 150 feet of fencing to enclose a rectangular garden. if the length is to be 5 feet less than three the width, find the area of the garden

#### 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

#### Ratio, which ratio is largar. 1. 15:16 or 24:25

which ratio is largar. 1. 15:16 or 24:25

#### Solving trig equations, Solving Trig Equations : Here we will discuss on s...

Solving Trig Equations : Here we will discuss on solving trig equations. It is something which you will be asked to do on a fairly regular basis in my class. Let's just see the

#### Simple harmonic motion, prove that the composition of two simple harmonic o...

prove that the composition of two simple harmonic of the same period and in the same straight line is also a simple harmonic motion of the same period.

#### Sum of a number of terms in g.p., We know that the terms in G.P. are:...

We know that the terms in G.P. are: a, ar, ar 2 , ar 3 , ar 4 , ................, ar n-1 Let s be the sum of these terms, then s = a + ar + ar 2

#### Numerical methods, Consider the following interpolation problem: Find a q...

Consider the following interpolation problem: Find a quadratic polynomial p(x) such that p(x0) = y0 p’(x1) = y’1 , p(x2) = y2 where x0 is different from x2 and y0, y’1 , y2 a

#### Expressing the interest rate as a decimal fraction, Total Contribution per ...

Total Contribution per Year for next 10yeras =\$1000+\$800 =\$1800 So Total Future fund Vaule  =\$1800*(1+1.073+power(1.073,2)+ power(1.073,2)+ power(1.073,3)+ power(1.073,4)+ power

#### Absolute mean deviation-measures of central tendency, Illustration 1 I...

Illustration 1 In a described exam the scores for 10 students were given as: Student Mark (x) |x-x¯| A 60

#### Diffrentiation, y=f(a^x)   and f(sinx)=lnx find dy/dx Solution) dy/dx...

y=f(a^x)   and f(sinx)=lnx find dy/dx Solution) dy/dx = (a^x)(lnx)f''(a^x), .........(1) but f(sinx) = lnx implies f(x) = ln(arcsinx) hence f''(x) = (1/arcsinx) (1/ ( ( 1-x

#### Determine the taylor series, Example : Determine the Taylor series for f(x)...

Example : Determine the Taylor series for f(x) = e x about x=0. Solution It is probably one of the easiest functions to get the Taylor series for. We just require recallin

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