Complex numbers Questions and Answers

Add and simplify the result 8x x 5 x 4 8x X 8 x 5

Watch this video and then answer the following question Click here to watch the video Perform the indicated operation and simplify the result 4 Ov 4 14 9y 18y 14 18v

2 In a class of thirty students 12 complete all of the classwork one day What percentage of the class completes all of the classwork a 4 b 12 c 30 d 40

Which values are possible rational roots of 122 147 z 18 0 according to the rational root theorem Select each correct answer 0

What was the approximate number of mobile cellular subscriptions per 100 people in Zimbabwe in 2003 The display gives the result of performing an exponential regression on a data set where the inputs are years since 2000 and the outputs are the corresponding mobile cellular subscriptions per 100 people in Zimbabwe ExpReg y a b x a 1 067905095 b 1 501755837 2 9525580427 r 9759908005 C 2 6

Simplify the following rational expression 64 K 2 k 7k 8 2 64 k

Simplify the following rational expression 3 x 64 2 3x 7x 20 3 x 64 3 Type your answer in factored form

Simplify each rational expression 2 2w 7w 30 5 2W 2w 7w 30 Simplif you Hor

Analyze the polynomial function f x 2 x 4 x 2 using parts a through e c Determine the zeros of the function and their multiplicity Use this information to determine whether the graph crosses or touches the x axis at each x intercept The zero s off is are Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once The lesser zero is a zero of multiplicity zero of multiplicity so the graph of f so the graph of f the x axis at x the x axis at x The greater zero is a

Evaluate the common log Round to 3 decimal places log 60 O 1 7251 O 1 7782 O 10 7782

Solve 382 1315 0x 2 x 1 1 2 0x 1 7 0 x 1

Find the equation of the line tangent to the circle x 2 y 13 at 4 3

Solve Tr 4 2 3 x 5 1 Then find 1 11

If a 3 b 1 evaluate 3a 7 bl A 1 B 1 C 2 D No solution

Sketch the solution to each system of inequalities y 5x 2 lyz x 2 O O 320 1

roblem 1 Let f x 3x x 2 Complete the following a Find the vertex of f x b Does f x have a maximum or a minimum Justify your answer c State the interval s where f x is increasing d State the interval s where f x is decreasing e Write f x in the form of f x a x h k f Sketch the graph of f x Label the vertex and two additional points on the graph yc include the x and y coordinates of all points and appropriately scale the axes to incl entire graph

f x x 2 2x 2 x 10 9 8 7 6 2 3 H if 0 if if x 1 0 x l 5 domair range

6 f x x 2 fo x 10 9 8 7 6 5 4 3 2 10 if x 1 if x 1 4 8 tr N 10 10 domain range

6 52 11 z 4 For each prompt below if no solution exists enter DNE If there are multiple solutions enter your answer as a comma separated list like 1 3 You may find it helpful to rewrite the numerator or denominator in a different form to elp you complete some of the parts a Determine the vertical intercept of f f 0 6 44 b Determine the zeros or roots off Consider the function f x I DNE 20 W V 1 5 Preview c Determine the vertical asymptote s of f Preview Preview d Determine the horizontal asymptote of f Preview

Which graph represents f x 2x 04321 3 2 3 2 NO 1 0 1 2 3 3 2 1 1 1 AN 2 2 3 3 4 4 X X O O 4 3 2 3 2 1 3 2 1 0 1 2 3 444 3 2 y 1 0 1 Ft 1 2 2 3 3 4 X

What is the degree of the power function represented in the table O 1 O 2 O 3 O4 X 1 0 1 2 2 h x 0 8 2 2 8

What is the result of dividing 7 by x 2 O x 2x 4 15 x 2 1 O x 2x 4 2 2 O x 2x 4 O 15 x 2 x 2x 4 z 2

1 2x 1 y sinx R 2x Drag each graph above to match the function below y cos x 1 y sin 2x Ay 2 1 2 T 2 1 0 1

Points 0 of 1 Complete the sentence below The domain of both the sine and cosine functions is and the range is Type your answers in interval notation Type exact answers using as needed

Determine the amplitude of the function y 4 cos x Also choose its graph The amplitude is

Clearly A A a b 1 1 a b 1 H H G G A A H H H H Also 3ab 1 1 1 1 1 4 2006 H H 2a b and 2 1 3 b A A H H H H a b A A H H ab G G 1 3ab a b 3ab 2a a 1 2b a 2a b 2b a 2a b 9ab Let P n 25 1 24 n 5735 For n 1 P 1 625 24 5735 6336 24 x 11 which is divisible by 242 Hence P 1 Is true Let P K be the true where K 2 1 25 1 24 K 5735 24 2 where AEN For n k 1 P K 1 25 2 24 K 5735 25 25 1 24 K 5735 25 24 K 25 5735 5735 24 K 1 25 24 2 24 2K 5735 24 24 25 24 24 2 K 24 5736 25 24 24 K 24 239 24 25 K 230 which is divisible by 24 2 Hence by the method of mathematical Induction result is true vne N

15 8 points Find BOTH f g x and g f x to verify the pair of given functions are inverses f x x 3 and g x x 3

Determine if the vectors are linearly independent 6 12 Select the correct choice below and if necessary fill in the answer box to complete your choice A The vectors are linearly independent because the vector equation x v X V 0 has only the trivial so OB The vectors are not linearly independent because if c and C 1 both not zero then c v

EXTRA CREDIT for SUM 3 Q1 Determine the slope of the line represented by the equation 1 75 15y12x Write the slope of the line that passes through the given points 2 through 3 2 and 0 5 B Write the point slope form of the equation of the line that passes through the given points 3 through 3 1 and 1 1 A y 3 x 1 B y 3 x 1 2 C y 3 2 x 1 D y 1 1 x 3 Write the slope of the line that passes through the given points 4 y 3 x 5 4 7 A y x 7t 1 B y x 7 4 C y x 4 D y x All rights reserved 1 1 1 7 Write the slope intercept form of the equation of the line through the given points 5 through 5 4 and 2 2

Consider the multivariate function f x y z 2x y z subject to x y z 1 and x2 2y 1 Find all the extreme values of f ii Find and classify all the critical points of f x y x3 y3 3x2 6y2 1

Perform the indicated operation 5 6i 5 i 5 6i 5 i Type your answer in the form a bi Use integers or fractions for any numbers in the expression

Question 10 HIA Match each graph with its equation v z 2 y 2 y 1 1 y y 1 H EA 4 4 a b C d 3 2 1 34 3 2 1 34 3 2 1 5 4 3 2 1 5 4 3 2 1 34 E 1 E 2 E 4 5 5 3 In 2 3 2 2 2 7 1 1 2 3 4 a 1 2 3 4 5 23 4 5

The function f is defined as follows f x 2x 2 if x 0 if x 0 a Find the domain of the function b Locate any intercepts c Graph the function d Based on the graph find the range OC d Based on the graph find the range Select the correct choice below and fill in the answer box es to complete your choice OA The range consists exclusively of one or more isolated values It can be described as Use a comma to separate answers as needed B The range has at least one isolated value It can be described as the union of the interval s Use a comma to separate answers as needed www The range does not have any isolated values It can be described by Type your answer in interval notation and the set

Does the sequence converge or diverge Give a reason for your answer 2 1 2 an Select the correct answer below and if necessary fill in the answer box to complete your choice O A an diverges because it is nondecreasing and it has no upper bound O B a converges because it is nondecreasing and has a least upper bound of Simplify your answer Type an exact answer using radicals as needed OC a converges because it is nonincreasing and has a greatest lower bound of Simplify your answer Type an exact answer using radicals as needed O D a diverges because it is nonincreasing and it has no lower bound OE a diverges because it has no upper bound and no lower bound OF a diverges because when n is odd the limit of the sequence is therefore the limit does not exist sequence is and when n is even the limit of the

O Macmillan Learning Use the quadratic formula and the factor theorem to factor the quadratic polynomial The factors may involve complex numbers x 2x 17 Express numbers in exact form Use symbolic notation and fractions where needed x 2x 17

11 11 y2 x 5 12 12 y 2

Determine the leading coefficient of the quadratic function y Give an exact answer Use symbolic notation and fractions where needed leading coefficient Determine whether the graph of the given quadratic function is concave up or concave down The graph is concave down x 9x concave up

2 5 5 y2 8x 4 A B M C D 3 4 6 B 012 37 3 A B 5 D 6 A 7 zoom in

Macmillan Learning Find the vertex of the parabola y x 4x 10 Give your answer in the form Express numbers in exact form Use symbolic notation and fractions where needed vertex Indicate whether the vertex corresponds to a maximum or a minimum minimum maximum

Macmillan Learning Write the polynomial P x with zeros x 2 and x 6 and with leading coefficient 3 in factored form Express numbers in exact form Use symbolic notation and fractions where needed P x

Consider the rational function below 4x 4 12x 2x a Find the horizontal asymptote Enter None if appropriate y b Find the slant asymptote Enter None if appropriate

Consider the rational function below f x Domain 3x 9 x 9 a Find the domain Enter your answer in interval notation b Find the vertical asymptote s Separate answers with commas Enter None appropriate

Divide using synthetic division 4 x 27x 67 x 5

Bonus 3 Show that f x h f x h for f x 3x 1 5x 4 is equal to 7 5r 4 5 x h 4

1 Algebra Prep 2023 Kia Software LLC ATT right re Graphing Linear Inequalities Sketch the graph of each linear inequality 4x 3y 6 A B D 2 2 y 2 A B C D D X ZOOL

Multiply 2i 4 5i 2i 4 5i Simplify your answer Type your answer in the form a bi

or or y 200 50 e y 200 50 Therefore 40 e 1 50 40 ERT 40 loge Here the equation 4 gives the time t at which the salt in tank is y kg Step 4 Since e 40 is always positive from 3 we conclude that y 200 at all times Thus the minimum amount of salt content in the tank is 200 kg publishe 3 Also from 4 we conclude that t 0 if and only if 0 y 200 50 i e if and only if 200 y 250 i e the amount of salt content in the tank after the start of inflow and outflow of the brine is between 200 kg and 250 kg Rationalised 2023 24 4 Limitations of Mathematical Modelling Till today many mathematical models have been developed and applied successfully to understand and get an insight into thousands of situations Some of the subjects like mathematical physics mathematical economics operations research bio mathematics etc are almost synonymous with mathematical modelling But there are still a large number of situations which are yet to be modelled The reason behind this is that either the situation are found to be very complex or the mathematical models formed are mathematically intractable MATHEMATICAL MODELLING 207 The development of the powerful computers and super computers has enabled us to mathematically model a large number of situations even complex situations Due to these fast and advanced computers it has been possible to prepare more realistic models which can obtain better agreements with observations However we do not have good guidelines for choosing various parameters variables and also for estimating the values of these parameters variables used in a mathematical model Infact we can prepare reasonably accurate models to fit any data by choosing five or six parameters variables We require a minimal number of parameters variables to be able to estimate them accurately Mathematical modelling of large or complex situations has its own special problems These type of situations usually occur in the study of world models of environment oceanography pollution control etc Mathematical modellers from all disciplines mathematics computer science physics engineering social sciences are involved in meeting these challenges with courage

Divide 12 7i 6i 12 7i 6i Simplify your answer Type your answer in the form a bi Use integers or fractions for

Perform the indicated operation 3 2i 3 i 3 2i 3 i Type your answer in the form a bi Use integers or fractions for any numbers in the exp

Find the product 3 8i 3 8i 3 8i 3 8 Simplify your answer Type your answer in the form a bi