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Evaluate(( ∇× (→r ))/r^2 )
QUESTION: ONE
you are required to develop an online complains management system for your local Municipality. The system must have the following specifications:
1.1. ABOUT US: This must load a page containing the history of the Municipality.
1.1.2. CONTACTS: This must be link to a page with all the conctac details of the Municipality.
1.1.3. COMPLAINS: This link must load a complains form which includes the text areas to insert the complain's name, conctact details, subject and the actual problem. Your form must have the sending button to submit the complain and a reset button.
1.1.4. Home: This link will always take you back to the Mission and Vision statement page.
1.2. The Home page must use frames to align and separate different sections of its contents. Every page visited on the site must target the main frame of the home page.
1.3. Include a Copyright protection statement as footer on every page which includes the publication date and the developer's name.
you are required to develop an online complains management system for your local Municipality. The system must have the following specifications:
1.1. ABOUT US: This must load a page containing the history of the Municipality.
1.1.2. CONTACTS: This must be link to a page with all the conctac details of the Municipality.
1.1.3. COMPLAINS: This link must load a complains form which includes the text areas to insert the complain's name, conctact details, subject and the actual problem. Your form must have the sending button to submit the complain and a reset button.
1.1.4. Home: This link will always take you back to the Mission and Vision statement page.
1.2. The Home page must use frames to align and separate different sections of its contents. Every page visited on the site must target the main frame of the home page.
1.3. Include a Copyright protection statement as footer on every page which includes the publication date and the developer's name.
Hello Please Help me in this problem Please T_T this is the problem.Please anyone can answer this
Create a program that will compute the prelim, midterm, final grades of the students. The program will input grades for quiz, recitation, project, and exam rating for each grading period (PRELIM/MIDTERM/FINALS). The class standing, class average and the prelim, midterm and final grades will be computed and displayed automatically. Display also the grade equivalent and if the grade of the student is greater than 75 then the remark will be “passed” otherwise “failed”. The program will continuously accept grades and terminate when you enter 0 or negative value. Use these formulas:
PRELIM:
CS= (Q+R)/2
PROJECT= P*40%
LECTURE= ((2*CS+PER)/3)*60%
PG= PROJECT + LECTURE
MIDTERM:
CS = (Q+R)/2
MPROJECT= PM*40%
MLECTURE= (2*CS+MER)/3*60%
CA= MPROJECT + MLECTURE
MG= (2*CA+PG)/3
FINALS
CS = (Q+R)/2
FPROJECT= PF*40%
FLECTURE= (2*CS+FER)/3*60%
CA= FPROJECT + FLECTURE
FG= (2*CA+MG)/3
Create a program that will compute the prelim, midterm, final grades of the students. The program will input grades for quiz, recitation, project, and exam rating for each grading period (PRELIM/MIDTERM/FINALS). The class standing, class average and the prelim, midterm and final grades will be computed and displayed automatically. Display also the grade equivalent and if the grade of the student is greater than 75 then the remark will be “passed” otherwise “failed”. The program will continuously accept grades and terminate when you enter 0 or negative value. Use these formulas:
PRELIM:
CS= (Q+R)/2
PROJECT= P*40%
LECTURE= ((2*CS+PER)/3)*60%
PG= PROJECT + LECTURE
MIDTERM:
CS = (Q+R)/2
MPROJECT= PM*40%
MLECTURE= (2*CS+MER)/3*60%
CA= MPROJECT + MLECTURE
MG= (2*CA+PG)/3
FINALS
CS = (Q+R)/2
FPROJECT= PF*40%
FLECTURE= (2*CS+FER)/3*60%
CA= FPROJECT + FLECTURE
FG= (2*CA+MG)/3
TASK H1: with each of the 4 marked statements immediately below, explain, in
plain English,
a) what the statement does and
b) its purpose in the program.
const int MAXSTACKSIZE = 5; - TASK H1.1 Explain this statement
const int BOTTOMOFSTACK = -1; - TASK H1.2 Explain this statement
typedef char StackElement; -TASK H1.3 Explain this statement
TASK H1.4 Explain this statement
typedef struct {
StackElement contents[MAXSTACKSIZE];
int top;
} Stack;
plain English,
a) what the statement does and
b) its purpose in the program.
const int MAXSTACKSIZE = 5; - TASK H1.1 Explain this statement
const int BOTTOMOFSTACK = -1; - TASK H1.2 Explain this statement
typedef char StackElement; -TASK H1.3 Explain this statement
TASK H1.4 Explain this statement
typedef struct {
StackElement contents[MAXSTACKSIZE];
int top;
} Stack;
Find the points of intersection of the conics (2)
(b) Let be the point which divides the line segment joining and
in the ratio such that . Find the equation of the line
passing through and parallel to the line (3)
(c) Under what conditions on , the spheres and
intersect each other at an angle of 45
0
. (3)
(d) Find the centre and radius of the circle
(2)
(b) Let be the point which divides the line segment joining and
in the ratio such that . Find the equation of the line
passing through and parallel to the line (3)
(c) Under what conditions on , the spheres and
intersect each other at an angle of 45
0
. (3)
(d) Find the centre and radius of the circle
(2)
Find the equation of the line which passes through and makes an angle
30
0
with the line (3)
(b) Find the distance of the line obtained in part (a), from the origin by expressing it
in the normal form. Also find the intercepts made by this line on the coordinate
axes. (3)
4
(c) Obtain the equation of the plane passing through the line and
which is perpendicular to the plane (3)
(d) Find the vertices, eccentricity, foci and asymptotes of the hyperbola
Also trace it. Under what conditions on the line will be tangent
to this hyperbola? Explain geometrically.
30
0
with the line (3)
(b) Find the distance of the line obtained in part (a), from the origin by expressing it
in the normal form. Also find the intercepts made by this line on the coordinate
axes. (3)
4
(c) Obtain the equation of the plane passing through the line and
which is perpendicular to the plane (3)
(d) Find the vertices, eccentricity, foci and asymptotes of the hyperbola
Also trace it. Under what conditions on the line will be tangent
to this hyperbola? Explain geometrically.
Find the reciprocal cone of the cone . (3)
(b) Find the equation of the cylinder with base curve
. (3)
(c) For what value(s) of α, the conicoid
has a unique centre? Give reason for your answer. (3)
(d) Find the angle between the lines . (3)
(e) Find the equation of the plane which passes through the line of intersection of the
planes and makes equal angles with
these planes.
(b) Find the equation of the cylinder with base curve
. (3)
(c) For what value(s) of α, the conicoid
has a unique centre? Give reason for your answer. (3)
(d) Find the angle between the lines . (3)
(e) Find the equation of the plane which passes through the line of intersection of the
planes and makes equal angles with
these planes.
a) Let a quadratic form have the expression x
2
+ y
2
+ 2z
2
+ 2xy + 3xz with respect to the
standard basis B
1 = f(1; 0; 0); (0; 1; 0); (0; 0; 1)g. Find its expression with respect to the
basis B
2 = f(1; 1; 1); (0; 1; 0); (0; 1; 1)g (3)
b) Consider the quadratic form
Q : 2x
2
4xy + y
2
+ 4xz + 3z
2
i) Find a symmetric matrix A such that Q = X
t
AX .
ii) Find the orthogonal canonical reduction of the quadratic form.
iii) Find the principal axes of the form.
iv) Find the rank and signature of the form. (5)
2
+ y
2
+ 2z
2
+ 2xy + 3xz with respect to the
standard basis B
1 = f(1; 0; 0); (0; 1; 0); (0; 0; 1)g. Find its expression with respect to the
basis B
2 = f(1; 1; 1); (0; 1; 0); (0; 1; 1)g (3)
b) Consider the quadratic form
Q : 2x
2
4xy + y
2
+ 4xz + 3z
2
i) Find a symmetric matrix A such that Q = X
t
AX .
ii) Find the orthogonal canonical reduction of the quadratic form.
iii) Find the principal axes of the form.
iv) Find the rank and signature of the form. (5)
a) Check whether the forms 2x
2
+ 3y
2
+ 5z
2
4xz 6yz and 4x
2
+ 3y
2
+ z
2
6xy 2xz
are orthogonally equivalent. (3)
b) Use Gram-Schmidt orthogonalisation process to find an orthonormal basis for the
subspace of C
4
generated by the vectors (1; i; 0; i), ( i; 0; 1; 2) and (0; i; 1; 1). (5)
c) Which of the following matrices are Hermitian and which are Unitary? Justify your
answer. (4)
A =
2
4
1 i 0
i 1 1 i
0 1 + i 2
3
5
; B =
2
4
1
p
2
0
1
p
2
0 1 0
p
2i 0
p
2i
3
5
2
+ 3y
2
+ 5z
2
4xz 6yz and 4x
2
+ 3y
2
+ z
2
6xy 2xz
are orthogonally equivalent. (3)
b) Use Gram-Schmidt orthogonalisation process to find an orthonormal basis for the
subspace of C
4
generated by the vectors (1; i; 0; i), ( i; 0; 1; 2) and (0; i; 1; 1). (5)
c) Which of the following matrices are Hermitian and which are Unitary? Justify your
answer. (4)
A =
2
4
1 i 0
i 1 1 i
0 1 + i 2
3
5
; B =
2
4
1
p
2
0
1
p
2
0 1 0
p
2i 0
p
2i
3
5
Let
A =
2
4
5 4 4
6 7 6
12 12 11
3
5
a) Find the adjoint of A. Find the inverse of A from the adjoint of A. (4)
b) Find the characteristic and minimal polynomials of A. Hence find its eigenvalues and
eigenvectors. (6)
c) Why is A diagonalisable? Find a matrix P such that P
1
AP is diagonal. (2)
d) Verify Cayley-Hamilton theorem for A. Hence, find the inverse of A
A =
2
4
5 4 4
6 7 6
12 12 11
3
5
a) Find the adjoint of A. Find the inverse of A from the adjoint of A. (4)
b) Find the characteristic and minimal polynomials of A. Hence find its eigenvalues and
eigenvectors. (6)
c) Why is A diagonalisable? Find a matrix P such that P
1
AP is diagonal. (2)
d) Verify Cayley-Hamilton theorem for A. Hence, find the inverse of A
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