Complex numbers Questions and Answers

The slope of the secant to the curve f x 2 between x 0 and x 1 is a 1 Ob 1 1 20 Oc 2 d O

The possible rational roots of 2x 3 x 2 x 2 are

What is the sum of the following arithmetic series 3d 1 d 10 Write the answer in the space below

What is the sixth term of a geometric sequence in which the first term is 800 and the common ratio is 50 Type the answer in the space below

Which is the nth term of the indicated sequenc a 12 r 1 n 16 a1 01 0 1 O 12 O 12

Which is the sum of the following arithmetic series 2k 5 k 2 07 O 12 O 65 O 72

111 12 2 01 a x a x b to carry out and demonstrate Gauss Elimintion procedure elimination of a21 from the second equation by using superposition and linear principles of linear equations is done by multiplying the second equation by a 1 and the first by a21 Show that the result is then aa x a 2x a b a a x a a x a b a Continue this calculation following the procedure demonstrated in lecture notes Chapter 3 and find the expessions for x2 and x successively in terms of the constants indicated by the members terms in matrix A a 1 a 2 az a Following the procedure elaborated in the Lecture Note Chapter 3 page 66 4 and following ones b If the first and second row of the system of linear equations a a 2 a21 a X are interchanged the equation becomes a2 x a 2x b a x a 2x b Continue following previous procedure and demonstrate verify that you will arrive at the expression ax a22 x b a a a 2 x a b a b find the expessions for x and x successively in terms of the constants indicated by the members terms of matrix A

a Solve x 2x 5 5 b If 63A169025 can be divided by 11 with no remainder find the min value of A

3 Find u v u u and v v for the following a u b u c u d u 3 1 4 v 2 2 4 1 1 4 6 v 2 2 3 2 1 1 2 3 v 1 0 5 1 2 1 1 0 2 v 1 2 2 2 1

1 2 3 4 Y 3 5 8 10 a Find an equation of the least squares line for the data Round your numerical values to one decimal place yw X b Draw a scatter diagram for the data and graph the least squares Ine 15 10 QO 10 10

Find the function rule for g x The function fx x The graph of g x is f x translated to the left 6 units and down 5 units What is the function rule for g x Og x x 6 5 O g x x 3 6 g x x 6 5 Og x x 5 6

Complete the description of the piecewise function graphed below f x 7 6 5 4 3 2 1 1 9 6 5 4 3 2 O 7 2 3 4 5 6 1 2 3 4 5 6 A a if 6 x 2 if 2 x 3 if 3 6

A vehicle purchased for 25 000 depreciates at a constant rate of 7 Determine the approximate value of the vehicle 10 years after purchase Round to the nearest whole dollar

A population numbers 13 000 organisms initially and grows by 11 6 each year Suppose Prepresents population and t the number of years of growth An exponential model for the population can be written in the form P a b where P

1 If g x is the f x x after a vertical compression by a shift right by 3 and a shift down by 1 5 a Write an equation for the function g x b The slope of this line is 1 c The vertical intercept of this line is

Question 1 The electrical current in amperes in a circuit varies directly as the voltage When 12 volts are applied the current is 4 amperes What is the current when 33 volts are applied 5 pts 1 Details a Give the General equation using I for current V for voltage and k for the constant of proportionality b What is constant of proportionality Write as a reduced fraction k c What is the mathematical model The specific formula involving I for current V for voltage and the constant of proportionality d What is the current when 33 volts are applied amperes

The current in an electrical conductor varies inversely as the resistance of the conductor If the current is 26 ampere when the resistance is 520 ohms what is the current when the resistance is 500 ohms Round to 1 decimal place amperes

A phone company charges for service according to the formula C n 24 0 03n where n is the number of minutes talked and C n is the monthly charge in dollars The rate of change in this equation is The initial value in this equation is Select an answer B Minutes Dollars per Minute Minutes per Dollar Dollars

Find the slope of the line that goes through the points 11 3 and 4 15 Slope m Enter your answer as an integer or a reduced fraction in the form

The number of aluminum cans used each year varies directly as the number of people using the cans If 450 people use 108000 cans in one year how many cans are used each year in a city which has a population of 160000 cans

On a bicycle Karina rides for 3 hours and is 14 miles from her house After riding for 8 hours she is 34 miles away What is Karina s rate miles per hour mph

If f x is a linear function f 4 1 and f 1 1 find an equation for f x f x

Write an equation for a line parallel to y 3x 3 and passing through the point 4 7 y

Find the point at which the line f x O pts 3 4x19 intersects the line g x 3x 9

a or 1 Write each power of 1 i in the form a bi where a and b is zero you can ignore that part of the number For example 0 3i can simply be expressed as 3i a 1 i b 1 i c 1 i d 1 i e 1 i 4 f 1 i 5 g 1 i 6 h 1 i 7 i 1 i 8 0 sigmaxs 10 CAP 2 Compare and contrast the powers of 1 i with the powers of i What is the same What is different

gral 5 2 5 2 x 5 x y f x y z dzdydx is rewritten in spherical coordinates as b rb b3 CDD g p q 0 dpd de then a 2 a3 b b b3

Find the exact value of the real number y 2 y arcsin 5

For each quadratic relation state the coordinates of the vertex and the direction of opening x intercepts the relation has a y x 3 2 b y Then determine how many x 2 4 c y 2 x 4 5 d y 2 x 3 1 e y x 5 Skip

Which of the following describes the translation of y x to y x 7 2

38 A builder is hired to increase the size of a square patio by adding 2 feet along its width and 3 feet along its length The new area of the patio will be 110 square feet What are the new dimensions of the patio

Spring An object suspended from a spring is oscillating up and down The distance from the nigh point to the low point is 30 cm and the object takes 4 seconds to complete 5 cycles For he first few cycles the distance from the mean position d t centimetres with respect to the ime t seconds is modelled by a sine function Sketch a graph of this function for two cycles Write an equation that describes the distance of the object from its mean position as a function of time

Part 2 Find a polynomial function of least degree having only real coefficients with zeros as given 1 7 2i and 7 2i 2 2 and 1 i

CIT rerential 2 4y y e sin b cost 8y 1by e 2 5 e 4

differential 2 4y y sin b cost y 8y 1 by e 5 e 4

2 You are given that U 100 3 And IU 100 20 a What is the order of 3 b Find all the generators of U 100 c Find all subgroups of U 100

Write an equation of a polynomial of degree 6 with 2 imaginary roots one distinct root at negative sqrt of 3 and tangent to the x axis at x 2

Identify all real and non real zeros of the function f x x 5x 3x 15

5 Compute the transfer function of the system 1 x2 U x2 3x12x2 u y x1 x2

Simplify assuming that M N and Kare n x n invertible matrices MK T NMT 1 1 5KTN 1 1

Study the following scenario Stanley has a job that pays 45 000 a year that requires he work 45 hours a week How much money is Stanley paid per week O 3700 O 450 937 50

In a certain year Congress began debating a new health care bill A poll of 1000 Americans at the time indicated that 422 opposed the bill 280 favored the bi and 298 were not sure Based on these results assume you ask a randomly selected American this question Express your answers as exact decimals Part 0 2 Part 1 of 2 a What is the probability that a randomly selected American was in favor of the bill The probability that a randomly selected American was in favor of the bill was Part 1 2 Part 2 of 2 b What is the probability that a randomly selected American was not in support of the bill mbr selected American was not in support of the bill was X

How many different ID cards can be made if there are three digits on a card and no digit can be used more than once What if digits can be repeated Part 1 of 2 There are Part 2 of 2 different ID cards that can be made if no digit can be used more than once X

In my Tae Kwon Do class there a black belt four red belts one blue belt two green belts and four yellow belts If the sensei selects a student at random to lead the warm up find the probability as a reduced fraction that the person is Part 0 3 Part 1 of 3 a Either a green belt or a yellow belt The probability that the student is either a green belt or a yellow belt is DO

How many ways are there to select three math help websites from a list that contains twelve different websites There are ways to select the three math help websites X S

24 Show how you can determine an equation for the logarithmic function graphed below

Mr Frank and a few other teachers played in an 18 hole golf tournament The scores are listed below 88 92 58 126 68 74 84 92 104 Find the range and mode O Range 74 and Mode 88 O Range 45 and Mode 98 Range 104 and Mode 92 Range 68 and Mode 92

VI Solid or Broken 6 5 4 Yes or No 3 2 6 5 4 3 N W 2 1 1 2 3 4 5 6 y axis 1 2 3 4 5 6 x axis

Solve the system of equations by graphing 1 y x 4 3 9 7 A Solve the system of equations using substitution x 2y 6 2x 3y 8 Check anoller203 18ena Jin 8 y x 2 ni sullaupent 2y 3x 2 elve jo Galing berubnd nev 5 S 6 3x y 1 x 2y 5 Check

Solve the system of equations by graphing 1 y 3x 4 9 7 1 y x 1 Solve the system of equations using substitution x 2y 6 3x y 1 x 2y 5 2x 3y 8 Check enolisi p3 1Benin 8 y x 2 couleupent be 2y 3x 2 10 010 TYSV Check

O about 400 about 500 about 450 For the scatterplot shown below what y value would you expect to be paired with x 9 200 700 6 00 500 400 300 200 100 5 6 7 8 9 10 11 12 13 14 15 16 age