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Solve the equation √3sinπœƒβˆ’cosπœƒ=0 for βˆ’180°≀π‘₯≀180Β°


Solve the equation 8sin^2π‘₯βˆ’7=2cosπ‘₯ for 0≀π‘₯≀360Β°, giving your answers to 1 decimal place.


Prove:

a. (sinπ‘₯+cosπ‘₯)^2 ≑1+2sinπ‘₯cosπ‘₯

b. (1+sinπ‘₯+ cosπ‘₯)^2 ≑2 (1+sinπ‘₯) (1+cosπ‘₯)

c. (6βˆ’cos^2πœƒ)/(sin^2πœƒ+5) ≑1


Create a program that will allow user to enter two numbers. Using a function, compute and display for its summation.

Create a project to model students with firstname, lastname, age, gender and student number. Create two constructors, one to be used as default and another to include all attributes. Add a class attribute to keep count of all registered students. Use the class attribute to generate student numbers with the following format 22201XYZ, where XYZ is the current count provided by the class attribute. Implement the respective getters and setters for each attribute. Now given a list of student information create the respective objects and print out their details see samples below, make sure the student class has a toString method.


Sample Run1



2



John Doe 29 M



Kelly Daniela 40 F



Output1:



Full names : John Doe



Age : 29



Gender : M



Student Number : 22201001


A – 41 nC charge is placed in between two-point charges, 32 nC and 24 nC. The negative

charge moves from point a to b. What is the change in potential energy?


Solve the following equations by Elimination method, Substitution method and Graphing method.


1. 2π‘₯ + 3𝑦 = 8


5π‘₯ βˆ’ 3𝑦 = βˆ’1


2. 2π‘₯ +5y = 19


x βˆ’ 2y = βˆ’4


3. 𝑦 = 5 βˆ’ 2π‘₯


4π‘₯ + 3𝑦 = 13


4. 𝑦 = 2π‘₯ βˆ’ 3


𝑦 = βˆ’ 2/3π‘₯ + 5


Write a class that contains variables that hold your hourly rate of pay and the number of hours that you worked. Display your gross pay, your tax please refer in the table below and your net pay (gross pay – tax).

Β 

Gross pay Tax

----------------------------------------

Below 2000 | No tax

2001 - 3000 | 5%

Above 3000 | 10 %




explain why it is necessary to know what information failure means when classifying goods as merit or demerit goods


Suppose that A, B, and C are sets such that A βŠ† B and B βŠ† C. Show that A βŠ† C.

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