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question 2

0 votes

1. Given:

 

image

 

1.1. Find Z

1.2. Convert Z into polar form. Show all steps. θmust be positive

1.3. Represent Z and ALL calculated values in 1.2 on the Argand diagram

 

2. Solve for x if:

image

 

3. Solve for x if:

 

image

 

4. Given:

 

Z = (2.4 |86.3° ) image

Use de movire’s theorem to calculate for Z. Leave the answer in a+jb form.

 

5. Given:

 

Z= -3 -j3

 

5.1. Find Z

5.2. Convert Z in polar form. θ must be positive. Show all steps

 

6. Solve for x if:

image

 

7. Make y the subject of the formula if:

image

 

8. Determine the length and breadth of a rectangle if the length of a rectangle is 3m more than its breadth and the area of a rectangle is 54m².

 

9. Given:

 

A + 4b + 8c =0

2a - 5b = -2 + 6c

B - 4c = -3

 

Solve for c by the use of cramer’s rule

10. Make P the subject of the formlua:

 

image

 

11. The hypotenuse of a right angles triangle is 10mm longer than the longest of the two sides. Calculate the lengths of the sides if the shortest side is 50mm long.

 

12. Solve for x if:

image

 

13. Given:

 

| 1        2         3|

| 4        -1         -2|

| -3       -4         -5|

 

13.1. Calculate the value of the detrminant

13.2. What is the minor of -5

13.3. What is the co-factor of -2

 

14. Solve for x by using the determinant if:

 

x + y = 10

X - y = 2

 

15. Given:

 

2x -- 2y - Z =  3

4x + 5y - 2Z = -3

3x + 4y - 3Z = -7

 

15.1. Solve for the value of Z by using Cramer’s Rule.

15.2. Determine the value of the cofactor of -3.

 

16. Given:

 

image

 

Make y the subject of the formula.

 

17. Solve for x:

image

18. The sum of two numbers is 10. The difference of their squares is 50. Calculate the two numbers.

 

19. Solve for x and  if:


image

 

20. Given:

 

image

 

Convert z into polar form. Show ALL steps. θ may only be positive.

 

21. Given:

 

Z = 15.9 |49,7°

 

Express z in a+jb form. Show all steps.

 

22. Given:

 

2x + 3y - z = 4

3x + y + 2x = 13

X + 2y - 5x = -11

 

Solve for the value of x with the aid of Cramer’s Rule.

 

23. Given:

 

image

 

Determine the value of x and y.

 

24. Given:

 

image and image

 

24.1. Determine the polar for of image and image

24.2. Evaluate: image

25. Simplify:

 

image

asked Mar 17, 2017 in ALGEBRA 1 by anonymous

12 Answers

0 votes

5)

Step 1:

The rectangular form is image

Find image

image

Step 2:

Convert Z in polar form.

image

Conversion from rectangular to polar equation :

image and image

image

Solution:

The value of image

Polar form is image

answered Mar 17, 2017 by Anney Mentor
0 votes

4)

Step 1:

The polar form is image

Conversion from Polar to rectangular form :

image and image.

Substitute image in the rectangular form.

image

The rectangular form is image

Step 2:

De Moivres Theorem:

If image is a complex number, then

image where image is a positive integer.

De Moivres theorem: .

Then,

image

Solution:

image

answered Mar 17, 2017 by Anney Mentor
0 votes

8)

Step 1:

The length of a rectangle is 3 m more than its breadth.

Consider the rectangle breadth is x.

Then, the equation is image

The area of a rectangle is image

Find the length and breadth of a rectangle.

The are of the rectangle is image

Substitute image

image

The length of the rectangle is always positive then consider the x value is positive.

Substitute image in image

image

Solution:

The length and breadth of a rectangle is image

answered Mar 17, 2017 by Anney Mentor
0 votes

9)

Step 1:

The system of equations are

image

Rewrite the equations are

image

Convert the equations into matrices form image,

where image is coefficient matrix, image is variable matrix and image is constant matrix.

image

Solve the equations by using Cramer's Rule.

image

Since image Cramer's Rule is applicable.

Step 2:

image

image

image

image

Solution:

image

answered Mar 17, 2017 by Anney Mentor
0 votes

Question numbers

1, 2, 6, 7, 10, 12, 16, 17, 19, 20, 23, 24, 25 images are not loaded please check once.

answered Mar 17, 2017 by Anney Mentor
0 votes

11)

Step 1:

The hypotenuse of a right angles triangle is image longer than the longest of the two sides.

The shortest side is image long.

Find the lengths of the sides.

Consider the right angle triangle,

Let longest side is image and hypotenuse is image

image

Pythagorean theorem image

image

Solution:

image

answered Mar 18, 2017 by Anney Mentor
0 votes

13)

Step 1:

The matrix is image

Find the determinant.

image

Determinant value of the matrix is image

Step 2:

The co factor of image

image

The co factor of the image

Solution:

Determinant value of the matrix is image

The co factor of the image

answered Mar 18, 2017 by Anney Mentor
0 votes

14)

Step 1:

The system of equations are

image

Convert the equations into matrices form image,

where image is coefficient matrix, image is variable matrix and image is constant matrix.

image

Solve the equations by using Cramer's Rule.

image

Since image Cramer's Rule is applicable.

Step 2:

image

Solution:

The value of image

answered Mar 18, 2017 by Anney Mentor
0 votes

15)

Step 1:

 The system of equations are

image

Convert the equations into matrices form image,

where image is coefficient matrix, image is variable matrix and image is constant matrix.

image

Solve the equations by using Cramer's Rule.

image

Since image Cramer's Rule is applicable.

image

Step 2:

The co factor of image

image

The co factor of the image

Solution:

The value of image

The co factor of the image

answered Mar 18, 2017 by Anney Mentor
0 votes

18)

Step 1:

Find the two numbers.

Consider the two numbers are image

The sum of two numbers is image

The difference of their squares is image

Rewrite the equation is

image

Solve the two equations

image

The two numbers are

image

Solution:

image

answered Mar 18, 2017 by Anney Mentor

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