36 results for "chapter".
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Exam (9 questions) in Engineering Statics
End of chapter exercises for Engineering Statics: Open and Interactive
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Exam (13 questions) in Engineering Statics
End of chapter exercises for Engineering Statics: Open and Interactive
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Exam (8 questions) in Engineering Statics
End of chapter exercises for Engineering Statics: Open and Interactive
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Exam (11 questions) in Engineering Statics
End of chapter exercises for Engineering Statics: Open and Interactive
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Exam (13 questions) in Engineering Statics
End of chapter exercises for Engineering Statics: Open and Interactive
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Exam (6 questions) in Engineering Statics
End of chapter exercises for Engineering Statics: Open and Interactive
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Exam (1 question) in Andrew's workspace
Example exercise for Eng Fun Textbook
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Exam (19 questions) in Engineering Statics
End of chapter exercises for Engineering Statics: Open and Interactive
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Exam (10 questions) in Engineering Statics
End of chapter exercises for Engineering Statics: Open and Interactive
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Exam (11 questions) in Engineering Statics
End of chapter exercises for Engineering Statics: Open and Interactive
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Question in rhaana's workspace
Based on Chapter 8, quite loosley.Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix.
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Exam (1 question) in Rachel's workspace
No description given
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Question in Andreas's workspace
This is the question for week 9 of the MA100 course at the LSE. It looks at material from chapters 17 and 18.
Description of variables for part b:
For part b we want to have four functions such that the derivative of one of them, evaluated at 0, gives 0; but for the rest we do not get 0. We also want two of the ones that do not give 0, to be such that the derivative of their sum, evaluated at 0, gives 0; but when we do this for any other sum of two of our functions, we do not get 0. Ultimately this part of the question will show that even if two functions are not in a vector space (the space of functions with derivate equal to 0 when evaluated at 0), then their sum could nonetheless be in that vector space. We want variables which statisfy:
a,b,c,d,f,g,h,j,k,l,m,n are variables satisfying
Function 1: x^2 + ax + b sin(cx)
Function 2: x^2 + dx + f sin(gx)
Function 3: x^2 + hx + j sin(kx)
Function 4: x^2 + lx + m sin(nx)
u,v,w,r are variables satifying
u=a+bc
v=d+fg
w=h+jk
r=l+mn
The derivatives of each function, evaluated at zero, are:
Function 1: u
Function 2: v
Function 3: w
Function 4: r
So we will define
u as random(-5..5 except(0))
v as -u
w as 0
r as random(-5..5 except(0) except(u) except(-u))
Then the derivative of function 3, evaluated at 0, gives 0. The other functions give non-zero.
Also, the derivative of function 1 + function 2 gives 0. The other combinations of two functions give nonzero.We now take b,c,f,g,j,k,m,n to be defined as \random(-3..3 except(0)).
We then define a,d,h,l to satisfy
u=a+bc
v=d+fg
w=h+jk
r=l+mnDescription for variables of part e:
Please look at the description of each variable for part e in the variables section, first.
As described, the vectors V3_1 , V3_2 , V3_3 are linearly independent. We will simply write v1 , v2 , v3 here.
In part e we ask the student to determine which of the following sets span, are linearly independent, are both, are neither:both: v1,v2,v3
span: v1,v1+v2,v1+v2+v3, v1+v2+v3,2*v1+v2+v3
lin ind: v1+v2+v3
neither: v2+v3 , 2*v2 + 2*v3
neither:v1+v3,v1-2*v3,2*v1-v3
neither: v1+v2,v1-v2,v1-2*v2,2*v1-v2 -
Question in Calculus Math 5A
Identifying the correct rule to use
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Exam (10 questions) in Dave's workspace
No description given
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Question in LSE MA100 (Bugs fixed, September 2018)
This is the question for Lent Term week 10 of the MA100 course at the LSE. It looks at material from chapters 39.
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Question in LSE MA100 (Bugs fixed, September 2018)
This is the question for Lent Term week 9 of the MA100 course at the LSE. It looks at material from chapters 37 and 38.
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Question in LSE MA100 (Bugs fixed, September 2018)
This is the question for Lent Term week 8 of the MA100 course at the LSE. It looks at material from chapters 35 and 36.
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Question in LSE MA100 (Bugs fixed, September 2018)
This is the question for Lent Term week 7 of the MA100 course at the LSE. It looks at material from chapters 33 and 34.
The following is a description of parts a and b. In particular it describes the varaibles used for those parts.
This question (parts a and b) looks at optimisation problems using the langrangian method. parts a and b of the question we will ask the student to optimise the objective function f(x,y) = y + (a/b)x subject to the constraint function r^2 = (x-centre_x)^2 + (y-centre_y)^2.
The variables centre_x and centre_y take values randomly chosen from {6,7,...,10} and r takes values randomly chosen from {1,2,...,5}.
We have the ordered set of variables (a,b,c) defined to be randomly chosen from one of the following pythagorean triplets: (3,4,5) , (5,12,13) , (8,15,17) , (7,24,25) , (20,21,29). The a and b variables here are the same as those in the objective function. They are defined in this way because the minimum will occur at (centre_x - (a/c)*r , centre_y - (b/c)*r) with value centre_y - (b/c)r + (a/b) * centre_x - (a^2/bc)*r , and the maximum will occur at (centre_x + (a/c)*r , centre_y + (b/c)*r) with value centre_y + (b/c)r + (a/b) *centre_x + (a^2/bc)r. The minimisation problem has lambda = -c/(2br) and the maximation problem has lambda* = c/(2br).
We can see that all possible max/min points and values are nice rational numbers, yet we still have good randomisation in this question. :)
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Question in LSE MA100 (Bugs fixed, September 2018)
This is the question for Lent Term week 6 of the MA100 course at the LSE. It looks at material from chapters 31 and 32.
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Question in LSE MA100 (Bugs fixed, September 2018)
This is the question for Lent Term week 5 of the MA100 course at the LSE. It looks at material from chapters 29 and 30.
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Question in LSE MA100 (Bugs fixed, September 2018)
This is the question for Lent Term week 4 of the MA100 course at the LSE. It looks at material from chapters 27 and 28.
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Question in LSE MA100 (Bugs fixed, September 2018)
This is the question for Lent Term week 3 of the MA100 course at the LSE. It looks at material from chapters 25 and 26.
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Question in LSE MA100 (Bugs fixed, September 2018)
This is the question for Lent Term week 2 of the MA100 course at the LSE. It looks at material from chapters 23 and 24.
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Question in LSE MA100 (Bugs fixed, September 2018)
This is the question for Lent Term week 1 of the MA100 course at the LSE. It looks at material from chapters 21 and 22.
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Question in LSE MA100 (Bugs fixed, September 2018)
This is the question for week 10 of the MA100 course at the LSE. It looks at material from chapters 19 and 20.
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Question in LSE MA100 (Bugs fixed, September 2018)
This is the question for week 9 of the MA100 course at the LSE. It looks at material from chapters 17 and 18.
Description of variables for part b:
For part b we want to have four functions such that the derivative of one of them, evaluated at 0, gives 0; but for the rest we do not get 0. We also want two of the ones that do not give 0, to be such that the derivative of their sum, evaluated at 0, gives 0; but when we do this for any other sum of two of our functions, we do not get 0. Ultimately this part of the question will show that even if two functions are not in a vector space (the space of functions with derivate equal to 0 when evaluated at 0), then their sum could nonetheless be in that vector space. We want variables which statisfy:
a,b,c,d,f,g,h,j,k,l,m,n are variables satisfying
Function 1: x^2 + ax + b sin(cx)
Function 2: x^2 + dx + f sin(gx)
Function 3: x^2 + hx + j sin(kx)
Function 4: x^2 + lx + m sin(nx)
u,v,w,r are variables satifying
u=a+bc
v=d+fg
w=h+jk
r=l+mn
The derivatives of each function, evaluated at zero, are:
Function 1: u
Function 2: v
Function 3: w
Function 4: r
So we will define
u as random(-5..5 except(0))
v as -u
w as 0
r as random(-5..5 except(0) except(u) except(-u))
Then the derivative of function 3, evaluated at 0, gives 0. The other functions give non-zero.
Also, the derivative of function 1 + function 2 gives 0. The other combinations of two functions give nonzero.We now take b,c,f,g,j,k,m,n to be defined as \random(-3..3 except(0)).
We then define a,d,h,l to satisfy
u=a+bc
v=d+fg
w=h+jk
r=l+mnDescription for variables of part e:
Please look at the description of each variable for part e in the variables section, first.
As described, the vectors V3_1 , V3_2 , V3_3 are linearly independent. We will simply write v1 , v2 , v3 here.
In part e we ask the student to determine which of the following sets span, are linearly independent, are both, are neither:both: v1,v2,v3
span: v1,v1+v2,v1+v2+v3, v1+v2+v3,2*v1+v2+v3
lin ind: v1+v2+v3
neither: v2+v3 , 2*v2 + 2*v3
neither:v1+v3,v1-2*v3,2*v1-v3
neither: v1+v2,v1-v2,v1-2*v2,2*v1-v2 -
Question in LSE MA100 (Bugs fixed, September 2018)
This is the question for week 8 of the MA100 course at the LSE. It looks at material from chapters 15 and 16.
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Question in LSE MA100 (Bugs fixed, September 2018)
This is the question for week 7 of the MA100 course at the LSE. It looks at material from chapters 13 and 14.
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Question in LSE MA100 (Bugs fixed, September 2018)
This is the question for week 6 of the MA100 course at the LSE. It looks at material from chapters 11 and 12.