Sequences & Series Questions and Answers

Problem 3 Consider the system x X1 X2 x x u a Using the output y x can you design a controller by input output linearization to globally stabilize the origin b Try y ax bx Determine if the system is input output feedback linearized and any associated internal dynamics are stable

Overall around 50 of people have brown eyes You randomly choose 30 locations in your town and noted the eye color of the first person you saw The first time you did this you saw 25 people with brown eyes The second time yo did this you saw 16 people with brown eyes Which statement below is correct Select all that apply You cannot use a z test to compare proportions since your samples are not random The two samples have proportions that are statistically significantly different at the 90 confidence level The proportions do not have a statistically significant difference at the 90 confidence level You can use a z test to compare proportions since your samples are random

tanA tanB 1 2 cosB cosA 0 7cosAcosB 0 What is A and B angle with detailed step

2 Use the Fourier transform to solve this transport equation for u u x t defined on the whole real line 2ut 3uz u x 0 0 exp x You should be able to write your solution u x t entirely in terms of the variable with no integrals x

1 The expression 81x y6 is equivalent to 18

Find the relationship between the value of parameter p and the number of solutions of the system using Kronecker Capelli theorem x 4y 2z p 3x 5y pz 3 px 3py z p

4 1 2 For the matrix M 0 6 4 0 1 6 a List the eigenvalues in increasing order including any that are repeated For example if they are 1 1 and 0 you would enter 0 1 1 b Enter a basis for the eigenspace that corresponds to the lowest eigenvalue For example if your basis is 1 2 3 3 4 5 you would enter 1 2 3 3 4 5 c Enter a basis for the eigenspace that corresponds to the highest eigenvalue

Consider the region given by 1 x y 28 2x y z 2 x y z 0 a Formulate the problem using slack variables s 0 s 0 and s320 Write down the basic solution obtained by choosing the slack variables as pivots Enter in the form z y z 81 82 83 b Is this a feasible solution True False c Write down the basic solution obtained by choosing z 51 82 as pivots Enter in the form x y z 81 82 83 d Is this a feasible solution O True False e Write down the basic solution obtained by choosing x y z as pivots Enter in the form x y z 81 82 83 1 Is this a feasible solution True False

Suppose that f R R is twice differentiable with f z 0 for all z R Show that for any real number L the equation f x L can have at most two solutions

Use grouping to factor the following cubic polynomial Factor the polynomial completely if possible x 3x 10x 30

3 2 1 T a Find the domain of h x 2 Let f x g x 2 and h x ln x 2 b Find the domain of fog x

Simplify the expression 3 7 175 0

Determine the intervals on which the function is a increasing b decreasing c constant a The function is increasing on the interval s 5 2 Use a comma to separate answers as needed Type your answer in interval notation b The function is decreasing on the interval s Use a comma to separate answers as needed Type your answer in interval notation 2 2

10 Solve for x 2x 6 x 11 Solve for x 5x 8 1 6

2 Solve for x 15 12 x 9 33 6 x 12 5x 5x 150 3 Factor completely b

6 A professor is interested in whether giving a practice exam has an impact on the performance of students on their final exam The professor has a class of 60 students Describe a method that the professor could properly divide his students to perform his her class

el solve the problem given below Click here to watch the video Determine the intervals on which the function is increasing decreasing and constant www List the interval s on which the function is increasing Type your answer in interval notation Use a comma to separate answers as needed 12 ky 16 19 TAH

4 4cos 8 2 J A S 3 5 C 3 5 4 9 3 JT do B 3 5 4 3 200 1 D X 200 9 3 5T 3 bi doas

Graph the function f x 1 4x for x 0 x 2 for x 0 Choose the correct graph below O A Ay 10 O B 10 Ay O C 10 Q Points 0 of 1 O D HHHH N LINE A HTIN d

Given f 1 5x k and x 2 is a factor of f x then what is the value of k

Graph the following function Check your result using a graphing calculator f x x 2 for x 4 1 O A 5 for 4 x 5 for x 25 Choose the correct graph below Q OB H HIMI THE A of 19 H O C S O D

5 A student is conducting a survey to find out people s favorite pet The student asks every 4th person that walk into Pet s Mart on a Sunday afternoon

Combine and simplify each of the following Note that each pair of fractions already has a commot denominator a 3x 7 x 2 2x 3 x 2 b 5x 2 4x 12 3x 8 4x 12 c 6x 8x x 25 4x 2x x 25

Identify the correct 3 2 9 5 15 3 6 10 6 O O O box and whisker plot of the given data Then identify the interquartile range T 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 IQR 6 5 H 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 IQR 6 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 IQR 5

Use the graph of y f x given above to find a f 2 D D f 3 3 c The domain 35 d The range 33 y f x 3 4

Identify the greatest common factor then factor it out 18m 6 24

y profit in dollars 400 300 200 100 100 200 300 400 10 20 30 A Give the coordinates of the x intercept 40 50 60 70 80 B Interpret the meaning of the x intercept Select an answer C Give the coordinates of the y intercept D Interpret the meaning of the y intercept Select an answer E Determine the slope of the line written as a reduced fraction Hillcou x units G Write the equation of the line in y mx b form 90 100 F Interpret the meaning of the slope For each 2 unit increase in units sold there is a n Select an answer in profit of Make sure your slope is Round your answer to the nearest cent

Evaluate 4 x 7 5x 11 when x 5 OA 45 OB 4 Oc 68 OD 20 OE 20

What is the result of the operation x x x x x x x x 1 mod P x on GF 2 P x x x x x 1 8

oose the correct graph of the dratic function f x x 4x 3 elect one a O b 10 10 5 5 10 LO 5 5 10 10 0 5 5 LO 5 10 10

Samples of size n 60 are randomly selected from the population of numbers 0 through 9 produced by a random number generator and the mean is taken for each sample What is the distribution of the sample means skewed to the right not enough information provided normal approximately skewed to the left N

SOLVE x 3 x 4 0

2 I want to know if Algebra 2 students at OHS study for their test I ask 20 people throughout the day What is the population

KLMNPQRS Find the given side length or angle measure 4 m R K 2 1 cm N 75 2 9 cm L 79 M R O 5 PS S P

The magnitude of the position vector 7 x y zk is A x y z B x y z 2 C x y z D None of these qual AS

1 Let z 3 4i and w a bi where a b e R Without using a calculator a determine and hence b in terms of a such that is real w b determine arg z 7 c determine W BIB 4 marks 3 marks 3 marks

The probability of event A is P A P A 1 8 Find the probability of the complement of event A

From the graph below write the shaded region in inequality notation 6 6 5 4 3 2 1 y 5 4 3 2 1 1 4 5 6 M 2 3 4 5 6 As an example you could enter 2x 3 E theanswerb Do use E your answer Use for and 4

V 6 5 4 3 2 1 16 A 3 2 1 1 2 LAY 4 10 10 The graph above is a graph of what function

Find the general solution of 3 y y 2y Sinx cos2x y p 50 st

The tables represent the functions f x and g x f x x 7 X 15 12 9 6 3 0 f x 3 7 g x 2x 15 X 15 12 9 6 3 0 g x 15 15 Which input value produces the same output value for the two functions x 12 x 9 Ox 6 x 3

This mapping shows a functional relationship Domain Range AL WN 2 3 4 4 0 1 3 When f x 4 what is the value of x O 0 2 O 3 4

3 46 27 A b 6 B b 13 8 18 16 14 12 10 A 14 12 10 8 C b 6 D b 20 B Y 4 6 14 12 10 8 6 4 26 24 22 20 18 16

5 3x 4 A x 10 B x 23 C x 3 D x 17 14 12 10 4 2 0 2 8 4 4 2 0 2 4 6 22 20 18 16 14

4 Which of the following properties would not be used to justify any of the steps below Statements Justification 3n 4 2 n 2 3n 4 7n6n 8 7n 6n 8 6n 12 8 A Subtraction Property of Equality B Multiplication Property of Equality C Distributive Property D Zero Product Property 1 Given 2 3 4 5

Theis similar to a spending plan O envelope system Obudget spreadsheet O tally system

Use the law of cosines to determine the length x in each figure Leave your answers in terms of redicals 4 b 5cm 60 5 cm 120 cm cm 8cm 8cm

Which of the following is a long term financial plan O Saving for retirement O Setting up of an emergency fund O Wiping out credit card debt

T My Activities QUESTION Tell me what you want to do Q TOMSZ Your income is 2 500 and after the tax of 5 you get 2375 Suddenly the government increased the tax rate from 5 to 10 Now you would get only 2250 Which of the following BEST describes the given situation Income risks O Liquidity risks Inflation risks

What does a goal mean OA target set in to achieve O A commitment to the future O An aim for the future