Complex numbers Questions and Answers

Given that 3i is a zero factor the following polynomial function completely Use the Conjugate Roots Theorem if applicable f x x 21 26x 18x 315

The stock market crash In 1929 led to the beginning of the extensive regulation of trading stock on stock exchanges True or False

Find an equation of the inverse relation 3 x y 5 Choose the correct equation below OA y x 5 O C y 5x O B y x 5 OD x y 5

1 The formula for calculating the sum of any finite geometric sequence is a 9

A boat is being pulled toward a dock as shown in the figure to the right If the rope is being pulled in at the rate of 4 feet per second how fast is the distance between the dock and the boat decreasing when it is 5 feet from the dock Boat The distance between the dock and the boat is decreasing by the boat is 5 feet from the dock Round to the nearest thousandth as needed Rope 5 ft 4 Dock feet per second when

3 Plot the polar coordinate point 5 4 X 17 Clear All Draw Dot 3 Give equivalent coordinate points for 5 4 criteria r 0 and 27 0 4T r 0 and 2 0 0 r 0 and 0 0 2T r 0 and 2 0 0 5 7 on the graph below 57 X according to the following

5 17 10 9 3 8 14 14 10 28 Question 11 What is the median for the following set of numbers 5 17 10 9 3 8 14 14

Consider the function f x 3x 4x 2 a State the y intercept s of the graph of the function 0 2 b State the x intercept s of the graph of the function

The sum of two numbers is 76 The difference of the two numbers is 22 What are the two numbers Let be the larger number and y be the smaller number Write an equation that expresses the information in the sentence The sum of two numbers is 76 Write an equation that expresses the information in the sentence The difference of the two numbers is 22 Solve the system you have written above The larger number a is Question Help Video 1 Video The smaller number y is

1 Lines 1 and 12 12 are parallel lines Determ

E Mary Watson has 50 000 to invest in a 4 year certificate of deposit that earns interest at a rate of 3 75 compounded monthly or 3 50 compounded daily Based on annual yield which is the better investment

The formula T 2 32 relates the time T in seconds for a pendulum with the length L in feet to make one full swing back and forth What is the length of a pendulum that makes one full swing in 2 2 seconds Use 3 14 for x O 2 feet O 4 feet O 11 feet O 19 feet

2 Determine whether the following series converge or diverge If it converges find its su a b n 1 00 n 1 32n 1 6 5n 1 24n 3 5 4

At the beginning of an experiment a scientist has 200 grams of radioactive goo After 60 minutes her sample has decayed to 6 25 grams What is the half life of the goo in minutes Find a formula for G t the amount of goo remaining at time t G t How many grams of goo will remain after 44 minutes You may enter the exact value or round to 2 decimal places

To find the distance AB across a river a surveyor laid off a distance BC 356 m on one side of the river It is found that B 115 10 and C 15 10 Find AB 5 10 356 m 15 10 2007 The distance AB across the river in Simplify your answer Do not round until the final answer Then round to the nearest whole number as needed

31 The function f x x x 0 x0 x 0 A is continuous everywhere B is continuous except at x 0 C has a removable discontinuity at x C D has an infinite discontinuity at x 0 E has x 0 as a vertical asymptote

C a d Write the vector a in terms of the other vectors b

25 Classify each of the following as true or false for all values of x and y If false show a counterexample that makes it false a x x b c x y y xl x y x yl

Let 1 2 16 8 1 1 0 1 0 and P 010 0 0 100 Given that P diagonalizes A then compute the matrix A2661 A a pr i i

Lateral Area Surface Area Blank 1 Blank 2 7 ft B 84 3 ft squared feet squared feet round to tenths 4 ft

Arrange the pattern blocks as shown in this figure Add additional pattern blocks so that the completed design has rotation symmetry of 90 180 and 270 Sketch the completed design on the given axes

When will the following options be equal Solve algebraically where possible Population of country A was 35 million 2 years ago and was 30 million 13 years ago increasing at an annual percentage rate Population of country A was 35 million 2 years ago and was 30 million 13 years ago increasing at an annual percentage rate Population of country B was 30 6 million 2 years ago and was 24 million 13 years ago increasing compounded continuously Population of country B was 30 6 million 2 years ago and is increasing by 0 8 million people per year 14 54 6 ye 15 82 1 no

2x 4 2x 4 11 Draw a graph of f x additional point on the graph by first placi

A pizza pan is removed at 3 00 PM fro a At what time is the temperature of th b Determine the time that needs to e c What do

how much work is done in pushing a 200 LBS weight up a ramp that is 100 ft long and inclined at an angle of ten degrees from the horizontal course hero

Determine the arctan sin 0 38 Your Answer Answer Question 2 1 point sin tan x b x 2 1 T Saved round to 3 decimal places

The base of a triangle is eight more than twice the height The area of the triangle is 252 square feet Find the measures of the base and height of the triangle The base measures The height measures feet feet 0

9v 30v 25 If there is more than one solution separate them with commas If there is no solution click on No solution V 3 08 No solution

QUESTION 13 Z1 Find and write the quotient in 22 Z 2 21 Z 3 3i 031 3n 212 cos 237 37 2 63 cos 0 isin 0 9 COS isin 10000 join 01

QUESTION 11 se De Moivre s theorem to find the ind rm a bi 5 cos 105 isin 105 3 5 5 5 2 i

Find the volume under the surface z 3 2x y with a region enclosed by the x axis an the lines y 2x and x 2

Looking at the exponential form of an equation y a b Identify and match each part of the equation with its definition y a b III

Find the distance between the complex numbers in the complex plane 1 41 1 6i

ii iv i function x 1 x 1 X 1 Identify the values for m n a b 4 Graph g x m a x n b Identify the oblique asymptote iii Identify the vertical asymptote X Find the y intercept algebraically irovcovad P bus Hint Set the numerator equal to zero and solve 10 9 8 7 6 5 4 3 2 10 9 8 7 6 5 4 3 2 1 L 0 1 2 3 4 5 6 7 8 56 0 9 10 01 2 3 Removable Point of discontinuit 4 5 6 7 8 9

Use the method of variation of parameters to solve the initial value problem x Ax f t x a x using the following values A 1 5 2 f t 15 2 27 1 x 0 ALE

a Find the range of values of a for which the equation 2x 6a 7ax 2 has no real roots b Solve the following equation 4 5r 24 r 6 M

24 In the diagrams below lines m and n are parallel Give the sizes of the lettered angles 00 52 8 c d 40 u 80 105 k P q r m m n

a principal of 50 000 was invested at 9 interest rate for 10 years find the final balance for simple interest compound interest to be compounded yearly monthly and daily and continuously compounding interest

9 The equation that best models the linearized data for a particular data set is log y 0 0169217x 1 44908 Find the approximate value of y when x 26 Round your answer to the nearest whole number 02 077 0579 0760

An amount of 700 is deposited into an investment account at a rate of 1 8 This investment compounds monthly for 6 investment be worth A 779 77 B 868 49 C 1889 69 D 2044 81

Why is it a good idea to check all roots in the given equations elect one a Very large or small roots may not work b Fractional solutions cannot be graphed c Solutions containing radicals are not allowed Od Some roots may require imaginary numbers to solve the equations

What is the area of the largest rectangular space you can enclose with 176 f of fence Select one O a 1 936 ft O b 88 ft O c 44 ft O d 7 744 ft

Find the solution of XY 6 and 3X 2Y 12 Select one O a 3 2 O b 3 2 O c 2 3 d 2 3

the solution s of X2 y2 16 and X2 y2 34 ct one a 5 3 D 5 3 and 5 3 c 5 3 and 5 3 5 3 and 3 5

Solve for x x 4 1 2 1 02 2 2 2 8 0 10 2 5 1

Question 15 of 24 Find the unknown side lengths in the pair of similar triangles shown to the right X This test 24 point s possible This question 1 point s possible 15 AA 3 Simplify your answer Type an integer or a fraction 1 X 3 Question 15 of 24 Find the unknown side lengths in the pair of similar triangles shown to the right This test 24 point s possible This question 1 point s possible 15 44

Solve the right triangle B a Round to the nearest tenth as needed Round to the nearest tenth as needed ba A 16 30 b

17 A hill is 525 meters long with a vertical drop of 162 meters Find the angle of depression from the top of the hill to the bottom 525

You just bought a new Sony 55 3D television set for 2300 The TV s value decreases at a rate of 250 per year Construct a linear function model to represent the value of the TV over time in years Clearly indicate what your variables represent and show your work

1 Kim has 8 dollars less than twice Ricky Ifter Ricky has dollars how much money do they have together 80 Kim 8 Rick X A 3x 8 B 3 8x C 3x 8 0 8 3x 8