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Example of metric space but not norm

Let (u,v)=u^2-v^2,y(u,v)=2uv.


Find the the Jacobian determinant,J(u,v).

Write a c program to make a queue from user input and check whether prime number present or not in the queue and find frequency of the prime number.



Hints


Make a menu which will having following menu options


-insert queue data


-insert in which position


-delete queue data


-show queue


-show prime numbers in queue


-show frequency of prime number in queue




Determine which of the following


pairs of functions are independent. Using the Jacobian matrix



a) u= x cos y and v=x sin y;



b)u= x + y and v= y/x+y;



c)u=x-2y and v=x^2 +4y^2-4xy+3x-6y;



d)u= x + 2y and v= x^2-y^2+2xy-x

The following consecutive readings were taken with a level and a 4-metre leveling staff on a continuously sloping ground at common intervals of 30 m:

0.855 (on A), 1.55 m, 2,335, 3.825, 0.455, 1.380, 2.055, 2.855, 3.455, 0.585, 1.015, 1.850, 2.755, 3.845 (on B).

 

The RL of A was 380.500. Make entries in a level book and apply the usual checks. Determine the gradient of AB.



Write a function named mybstmirror() that takes a reference to the root node of a binary tree and creates


a new tree (with its own nodes) that is the mirror image of the original tree. For example: if root is a reference to the root of the tree on the left below, then the return value of mybstmirror(root) would


be a reference to the root of the tree on the right below.



Node mybstmirror(Node root)

Write a program that uses loops to print out a design of following using asterisks:

* * * * *

* *

* * * * *

* * * * *

* *

* * * * *


* * * * *

* * * * *


* * * * *

* * * * *

The program should only use the following print statements:

print(“* * * * *”)

print(“* *”)

print(“\n”)


Tshego won R165000 and decided to deposit 65% of this amount in an account earning 8,25% interest per year, compounded every four months. What is the accumulated amount after five years?

Write a program that prints the value of 120.456789 rounded to the nearest digit, tenth, hundredth, thousandth, and ten-thousandth. [Hint: This should make use of formatted output.]


Given the slope-intercept form equation, y = mx+b. Write a program that asks the user to enter values for the respective variables (m, x, and b). Use those variables to calculate the results of the equation. Then print out the values for m, x, b, and y.


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