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NUMBER THEORY AND GEOMETRY
Number Theory and Geometry
Number Theory and Geometry
Question 3
We know that
Having finite order m, let f be an element of ?G,??.
Since fm =e , fm (1) needs to be 1 . By the second claim, f m (1)=f(1) m , so it follows that ...

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Algebra Assignment
Part 1
Completing the Square
If a quadratic function is one of the form (x ± a)2 = c, then we can solve it by taking the square root of each side. In an equation of this form, the left hand side is a perfect square: the square of a linear ...

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Algebra
Algebra
Part 1
1) f(x) = 4
When x = -2
f(-2) = 4
When x = -1
f(-1) = 4
When x = 0
f(0) = 4
When x = 1
f(1) = 4
When x = 2
f(2) = 4
x
-2
-1
0
1
2
f(x)
4
4
4
4
4
The graph of this equation is a horizontal line intercepting the y-axis at point (0,4). Since the line is parallel to ...

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Mathematics
Mathematics
Mathematics
Question 1
x + y + z -4 = 0
2x - 3y + 4z -33 = 0
3x - 2y - 2z -2 = 0
Solution:
Solving with the Cramer's rule = 35
= 70
= -105
= 175
Now X = = 2
Y = = -3
Z = = 5
Question ...

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SIMULATION CASE STUDY
Simulation Case Study
[Name of the Institute]
Simulation Case Study
1)
Inventory= total units produced by workers
The raw materials, work-in-process goods and completely finished goods that are considered to be the portion of a business's assets those are ready or will be ready for sale. Inventory represents one of the most important ...

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Mathematics
Mathematics Solution
Graphing Quadratic Equations.
Quadratic Equations are graphed as parabolas. So in order to construct a parabola, we will first simplify the equation if necessary and then find the vertex before proceeding for calculating the values of 'y' to the corresponding values of 'x'.
Question 1
Y = -(x2+4)+6
Y = -(x2+8x+16) + 6 ...

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Math project
Math project
Introduction
The housing prices made people understand the real situations prevailing in the market. House prices certainly depend upon various factors depending on the luxury and facilities available to the residents. It also depends upon the clean area and also on the environment facilities available to him. In ...

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CONTROL SYSTEM ANALYIS
Control System Analysis
Assignment number 01
The non linear systems are often linearized by making the use of approximation technique. The non linear equation of motion can be linearized as following.
The original non linear equation which is given as:
u? = Xuu + Xww - gcos(?0?) + XdEdE
To linearized this equation ...

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CONTROL SYSTEM ANALYSIS
Control System Analysis
[Name of the Institute]
Control System Analysis
Assignment 01
The given perubed equations for the longitudinal dynamics of aircraft are
?u? (t) = Xu ?u + Xw ?w - g (?0??) + XdEdE +Xuu0(t)
?w?(t) = Zuu0(t) + U0q - g (?0 ?? ) + ZdE dE + Zu ...

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CANAL OPERATING CALCULATIONS
Canal Operating Calculations
Part (i)
Question (a)
The linear length of the canal track associated with the proposed angle of the incline
Answer:
Question (b)
The velocity of the moving canal lock
Answer:
We know that
Hence
Taking and
The result from the velocity formula,
Will also yield the same velocity
Question (c)
The water saving ...