Complex numbers Questions and Answers

The eigenvector 2i 1 i of the matrix 5 2 a 2 3i b 2 3i c 2 3i d 3 2i e 3 2i f 3 2i g 3 2i h 2 3i 4 1

Find a function of the form y graph matches the function shown below A 9 8 A sin kx or y A cos kx whose y 7 6 5T 4 3 2 T 6 5 3 2 1 4 2 3 4 5 6 A 2 3 4 5T 6T 7 Leave your answer in exact form if necessary type pi for

if A1 A2 An are the eigenvalues of a matrix A Mn R and f a real polynomial function show that det f A f 1 f 2 f An

As shown in the following figure ABC is an equliateral triangle while DEFG is a square Given that D G F lie on AC AB BC respectively Find the value of a and b B F D b

Find the Laplace transform of the following function given by Larsin ar dr f 1 e 21 3

What is the probability that either event will occur A B 00 7 30 P A or B P A P B P A or B Enter as a decimal rounded to the nearest hundredth

Is the signal given in 2 a single or double signal If not what are the odd and even components 4 3 x t 2 1 2 2 2 3 10

Question 2 Represent the sample space using set notation 2 pt A bag contains one red marble one green marble and one blue marble You randomly pick a marble O marble red green blue O red green blue O marble red

12 Simplify the following expression x 7x 3x 2 O4x 2x O7x4 3x 2x O7x 2x Ap L

5 If a rectangular solid has the dimensions 5n x 4n xn what is the best way of stating the volume of the solid in terms of n Volume length x width x height Volume cubic units

ham turkey chicken O chicken ham turkey meatball O sandwich ham turkey O turkey chicken Question 4 Evaluate the expression 16C6 turkey and chicken 2 pts

Farmer has 7 500 meters of fencing and wants to enclose a rectangular plot that borders on a river If Farmer does not fence the side along the river what is the largest area that can be enclosed X 7 500 2x X

3 Jamie s parents gave him some money the year He spends 15 each month on paper pens and other supplies The graph shows his money decreasing as he spends from month to month 8 marks 100 y 80 60 40 20 0 2 4 6 8 10 X 8 15 in a moth X2 X1 Je 90 60 41 10 2 10 0 How much money did Jamie s parents give him at the start of the What is the slope of the line What is the equation of the line In how many months will Jamie have spent all the money antire school year of 9 months

Find the present value that will grow to 26 000 if interest is 9 compounded quarterly for 12 quarters Round to GCOCOON as needed

Decide if the given vector field is the gradient of a function f If so find f Remember to use absolute values where appropriate If an ane does not exist enter DNE 1 1 1 f x y z In x In y ln z x c If not explain why not 1 7 is the gradient of a function y 1 1 is not the gradient of a function because the curl of the field is not equal to zero xyz 1 1 k is not the gradient of a function because the field is not path independent xyz 1 1 is not the gradient of a function because the field has no potential function X y 1 1 4 m is not the gradient of a function because 7 7 dre 7 dr 0 for every c closed curve C

Calculate the average rate of change on the interval 1 x 3 O 1 02 O 0 5 4

3 A church steeple is 72 m high Find the angle of elevation to its top from a point 200 m away on level groun 4 James has designed a new roofing frame for his barn as shown below It is made of two symmetrical right triangles Determine the length of each side required to build the triangular wooden frame 50 50 ISA D

12 Convert the following word sentence as a mathematical statement involving a polynomial and then solve it The sum of the least and greatest of three consecutive odd integers is 134 What are the integers Write your answer on a sheet of paper or in the space provides

1 Use the 180 degree rule to find angle A 40 7 2 Use the Pythagorean theorem to find the missing side A b 3 6 5 cm 4 cm 2 mar 6 marks

he fox population in a certain region has a relative growth rate of 5 percent per year It is estimated hat the population in the year 2000 was 16200 a Find a function that models the population t years after 2000 t 0 for 2000 P t b Use the function from part a to estimate the fox population in the year 2008 Round to the nearest fox foxes

A professor wants to choose four students to go to the board If there are 25 students in class how many different groups of four could be chosen

You are sent to the local tea shop to pick up 9 drinks You purchase 5 sweet teas and 4 unsweetened teas Unfortunately you forgot to label them If you pick 3 drinks at random find the probability of each event below Give your answers as simplified fractions a All of the 3 drinks picked are sweet teas b Exactly one drink is sweetened

Using 26 flavors how many different milkshakes can you create using seven of the flavors

In how many ways can 3 books be choosen from a group of nine Your answer is

3 Find the equations of the vertical asymptote s the horizontal asymptote algebraically if they exist for the functions below a f x x x 1 b r x x2

z 2 2 3i karma k say s n n karek klerinden biri a a dak lerden hangisidir A 3 i D 2 3 i B 3 i C 2 3 E 1 3i

7 7 2x7 4y7 2z 3 k and C is the line from 1 1 1 to 4 4 4 4 Use the Fundamental Theorem of Line Integrals to calculate dr TO x F dr exactly

lect the correct answer from each drop down menu etermine the number and type of solutions for the following quadratic equations using the discriminant 2 x Equation 6x 5 11 242 50 4x 8x100 15x 2 7x 8x Number and Type of Solutions

L is perpendicular to y 2x The equation is Type an equation Use integers or fractions for any numbers in the equation Simplify your answer 8

21 Find the slope intercept form for the equation of the line which passes through the point 3 13 and has a slope of 2 Oy 2x 7 y 2x 7 y 2x 19 Oy 2x 19

1 Simplify 01 10 2 5 4 O x2 x 5 4 0 4x x 5

21 Is the following equation a rational equation 5 12 2 4 1 O yes O no

20 Add 17 8d 9d 7 9d 7 Answer 17 9 80 11 9d 7

The focal length of a magnifying glass is modeled by the equation where t is the distance from the eye to the glass s is the distance from the glass to the object viewed an f is the focal length of the glass Identify the equation that properly solves for s 08 8 8 82 Don 8

Fill in the blanks to correctly complete the sentence To obtain the graph of f x x 2 3 7 shift the graph of y x to the left units and down units To obtain the graph of f x x 2 3 7 shift the graph of y x to the left down units units and

1 For the functions f x x and g x a fog x and its domain b gof x and its domain a fog x Do not rationalize the denominator Its domain is Type your answer in interval notation b gof x Do not rationalize the denominator x 2 Its domain is find the following

Given functions f and g find a fog x and its domain and b gof x and its domain f x 1 X 8 g x 1 X a fog x Simplify your answer The domain of fog x is Type your answer in interval notation b gof x Simplify your answer The domain of gof x is Type your answer in interval notation

For the function f x 2x 6 f 7 FL 3 M Si

3 Solve 60 5 12 Answer x Round your answer to nearest hundredth if necessar

3 Simplify if possible 153 22 3 2 4 Simplified

2 What would you expect the range of the function to be if Dom f 0 85 Ran f Select

2 The most simplified form of 10 3 2 is O202 y r y 625y 19 O 5z8y5 O 20 272 3 6z y 20 27 y 625y

4 Simplify the following if possible 8 6 13ry 11xy Simplified 1 x

5 What would the y intercept of the function tell you in terms of age and height Would you expect such a point to exist The y intercept tells us Select Select Select expect such a point to exist because

7 Given the formula F mk solve for m Make sure to use appropriate parenthesis m

Graph the following function 1 7 g x Use the graphing tool to graph the function Click to enlarge graph 2101 F16 12 811 41 20 16 12 8 8

7 The following are the initial volume and pressure for a gas in a flexible container V 5 4 liters P 4 6 atmospheres If the pressure is changed to 4 5 atmospheres what will be the change to the volume O The volume would change to about 6 89 liters O The volume would change to about 5 79 liters O The volume would change to about 7 22 liters O The volume would change to about 5 52 liters

8 2 20 15 Solve the equation by graphing it on your graphing calculator Verify the graph by solving the equation algebraically What are the values for that make the equation undefined Enter one of the values for which is undefined in the space provided

10 Solve for 2 If the equation choose no real solution has no solution O 7 6 O 9 2 O 4 8 O 17 9 O no real solution

The terminal side of an angle in standard position passes through P 15 8 What is the value of sin O sin e sine 197 O O sin e 15 O sin 8 8 17 15 T 17