Functions Questions and Answers

Express the function below using window and step functions and compute its Laplace transform Ag t Q 10 0 10 Q 2 6 8 Click here to view the table of Laplace transforms Click here to view the table of properties of Laplace transforms Express g t using window and step functions Choose the correct answer below Compute the Laplace transform of g t g Type an expression using s as the variable g t 5t 25 II5 6 t 5t 35 II6 7 t OB 9 t 5t 25 II5 7 t 5t 35 u t 6 C g t u t 5 5t 25 II56 t 5t 35 II67 t u t 7 D g t 5t 5 u t 5 5t 7 u t 7

Question 13 5 points b t C 10 XL tl nin fourier dontsm n a 4 ALL 1 2 jw 2 jw 1 e 1 e 2 ju 1 e e 2 w 2 jw 2 jw X t hesaploxinia d e f 24 04161 0 di er 2 jw 1 e 2 jw 1 22 w e 2 jw 1 e 2 jw 2 jw

By inspection determine the range of this relation Y 36 x A 6 6 B 0 6 C 6 6 D 50 61

Suppose that x is a non zero vector in R What is LIXT 0 1 O 2 02 04 X x

The supply function for a product is given by p q2 340 and the demand is given by p q 450 Find the equilibrium quantity and price in dollars equilibrium quantity equilibrium price

x y Find the zeros Enter your answers as a comma separated list X Use a graphing calculator to graph the function Use the vertex and zeros to determine an appropriate window Be sure to label the maximum or minimum point y 2500 2000 1500 1000 500 y 500 1000 y maximum 20 40 60 80 100 120 140 20 40 60 80 100 120 140 X X 25 20 15 10 5 2 maximum 4 6 8 10 12 14 X y 5 10 15 20 25 2 4 6 8 10 12 14 minimum X

O 20 70 60 50 30 10 40 20 30 10 y t y 50 50 100 100 150 150 200 t 200 40 30 20 O 10 50 100 150 t 200 40 30 20 10 b From the equation identify the maximum point on the graph of y p t Round your answers to two decimal places 50 100 150 t 200

O COUNTING AND PROBABILITY Determining a sample space and outcomes for an event A box has four cards numbered 1 2 3 and 4 Jane will toss a coin once and record the toss as heads H or tails 7 Then she will randomly pick a card from the box and record the number chosen Give the sample space describing all possible outcomes Then give all of the outcomes for the event that the coin toss is heads Use the format H 1 to mean that the coin toss is heads and the number chosen is 1 If there is more than one element in the set separate them with commas Sample space Event that the coin toss is heads DO

QUEST The number of cell phones in North American homes has grown according to the equation s 812 1 21 where n is the number of years since 1992 After 55 years what will be the total number of cell phones

Simplify the following expression 180 90

TEACHER If the supply and demand functions for a commodity are given by p q 10 and q 2p 10 1000 what is the equilibrium price and what is the corresponding number of units supplied and demanied equilibrium price number of units units

5 Find an Euler circuits and or Euler paths for the following graph If your answer is yes please write the circuit and or path 10pts e b Euler circuit Yes No Euler path Yes No

After coming in Kepler 22b you have noticed some negative impact on your health due to the gravity difference In order to keep yourself healthy you decided to exercise everyday and drink a special blue drink from this place that will help keep you healthy You are required to take 1000ml of this drink every 3 hours for 6 days If you take the drink now about half of the drink will be in your body after 3 hours A Make a table of values showing the amount of blue drink remaining in the body after 3 hour period of time B Write the amount of blue drink remaining after each 3 hour period as a sequence wire a recursion ormulator the sequence C Graph the sequence D Describe what happens to the drink in your body over time

6 Graph of y f x is shown Find a precise estimate for the values of f 2 f 3 and f 4 Answer f 2 0 3 f 3 2 f 4 3 6

4 A Given the set A 1 2 3 4 and relations R defined on set A as follows R 1 1 1 2 2 1 2 2 3 3 4 4 i Represent the relation R in a directed graph ii By explaining from the directed graph Is the relation R reflexive Symmetric Asymmetric Transitive Equivalence B Solve the following recurrence relations using an appropriate method for each i Un Un 1 n with Uo 3 ii Un 7Un 1 1 with U 1 iii Un 3Un 1 4Un 2 with Uo 2 and U 3 20 Marks

6 A Give the graphical representation of the following deterministic finite state automata with its transition function K 90 91 92 E 0 1 90 A 9 Transition function Present State 70 71 72 Next State for Input 0 90 92 72 Start symbol S P S AB Aa Bb B b Next State for Input I B Give the languages and their natures descriptions generated by the following grammars i N S A B a b ii N S A B a b Start symbol S P SAB AaAla BbBlb 9 9

population and the land area of a particular country for selected years from 1800 through 2000 Use the information to find the population density of a certain country for the year 1900 to the nearest tenth expressed in people per square kilometer Click here to view the bar graph The population density in 1900 was approximately Round to the nearest tenth as needed Bar Graph and Data pulation millions 350 300 250 200 150 1 in 10 1 yd 1 m 1 acre Resident Population and Land Area Population Land Area 40 35 3 0 25 lan OU 6 5 cm 0 09 m 08m2 2 6 km 0 4 hectare ha abs to suog A

3 A For a function f IR R defined by f x x 4 find the following using images and inverse images given that A 1 1 2 and B 5 4 12 23 60 i f B NA ii f A uf B B Show if the expression f x x 4 defined in A above has an inverse by first finding out if it is bijective Write its inverse if it has 10 Marks

evaluate the left Riemann sum with n 6 taking the sample points to be left endpoints Round your answer to six decimal places 3 f x 3 cos x 0 x 4 What does the Riemann sum represent The Riemann sum represents the net area of the rectangles with respect to the x axis Illustrate with a diagram y 3 0 3 3jp 5A 8 15 3 4 y 3 0 3 k 100 R 8 714 3A 8 KIN 2 5 8 3r y 3 0 3 1 8 I 4 3 A 8 5 pr 8 y 3 O 3 4 3jpr 8

Find the Riemann sum for f x 3x 1 6 x 4 with five equal subintervals taking the sample points to be right endpoints Explain with the aid of a diagram what the Riemann sum represents 11 Need Help SESE 9 7 5 3 53 9 11 13 17 191 11 9 7 5 3 5 9 11 13 15 17 19 The Riemann sum represents the net area of the rectangles with respect to the x axis 6 O 4 2 y 11 9 7 5 3 3 5 9 11 13 15 17 191 114 9 7 5 3 S 7 y 9 11 13 15 17 19 2

7 Determine if the equation below is an example of exponential growth or decay 719 0 81x exponential growth O exponential decay O This is not an exponential equation This equation is exponential but shows neither growth nor decay

0 11 In 2000 a sample of a radioactive substance had a mass of 900 milligrams Since then the sample has decayed by 2 8 each year Lett be the number of years since 2000 Let y be the mass of the substance in milligrams Write an exponential function showing the relationship between y and f 0 8 08 DO 0 0 0 0 11 1 12

a Kelko is at a charity fundraiser and has a chance of receiving a gift The odds in favor of receiving a gift are a gift 10 X 0 S b A child has a box of candy which might have a toy inside The probability of the box having a toy is What are the odds against the box having a 13 toy X DID 060 15 Find the probability of Kelko receiving S

Given the graph of Gas Remaining vs Distance Traveled shown below determine a ay mx b form equation b the meaning of the slope m in the context of the situation including units c the number of miles that can be traveled with 10 gallons of gas remaining Gas Remaining L 20 O 50 100 150 250 300 350 400 450 500 550 600 Distance Traveled km

Linda is filling a tank The graph shows the amount of water in liters in the tank versus time in minutes 800 720 640 560 480 Amount 400 of water liters 320 240 160 80 0 6 Time minutes 8 9 a Choose the statement that best describes how the time and amount of water are related Then fill in the blank O As time increases the amount of water in the tank decreases At what rate is the amount of water decreasing liters per minute liters per minute O As time increases the amount of water in the tank increases At what rate is the amount of water increasing 10

The assets in billions of dollars for a financial firm can be approximated by the function A x 317e 051x where x 7 corresponds to the year 2007 Find the assets in each of the following years a 2013 b 2016 c 2019 a Which of the following describes how to find the assets in 2013 using the given information Select the correct choice below and fill in the answer box to complete your choice Type an integer or a decimal OA To find the assets in 2013 find the intersection point of the graphs y 317e 051x and y the y coordinate OB To find the assets in 2013 substitute for x and evaluate to find A x In 2013 the assets are about billion Type an integer or decimal rounded to the nearest tenth as needed b Which of the following describes how to find the assets in 2016 using the given information Select the correct choice below and fill in the answer box to complete your choice Type an integer or a decimal OA To find the assets in 2016 substitute for x and evaluate to find A x OB To find the assets in 2016 find the intersection point of the graphs y 317e 051x and y the y coordinate In 2016 the assets are about billion Type an integer or decimal rounded to the nearest tenth as needed The assets in 2013 are represented by for x and evaluate to find A x OB To find the assets in 2019 find the intersection point of the graphs y 317e 051x and y the y coordinate c Which of the following describes how to find the assets in 2019 using the given information Select the correct choice below and fill in the answer box to complete your choice Type an integer or a decimal O A To find the assets in 2019 substitute In 2019 the assets are about billion Type an integer or decimal rounded to the nearest tenth as needed The assets in 2016 are represented by The assets in 2019 are represented by

Find the derivative f x 6 5x 9 f x

Based on the above snippet of a function definition what should the length of any input to the function be 0 1

Osin 1 x 360 120 2 8 Determine the period of the function y 60 sin K

point at least 3 heads Answer Answer s submitted Six coins are tossed Find the probability

The general form of sinesoidal curre is YASin B n DO where A period Given y 60 sin 360 120 comparing and we get fo A

DENU From the list below choose a function that is not one to one but is onto Op R R p x x6 R xER x 0 Og Z Z g n x 10 O f Z Z f n 2n Oh R R h x x R xER x 0

Sketch the graph of the function f Z Z defined by the formula f n 2n 3 on paper digitize it and then upload i here Please notice that the graph must be done manually No computer graphs will be accepted

15 1 point The decay of 200 particles of a particular radioactive substance is given by y 200 0 93 where x is the number of days and y is the number of particles remaining It costs the laboratory 1 50 per day to store eac particle What is the cost of storing the particles on the fourth day 225 b 100 81 d 150

8 1 point Which graph represents the function y a 2 20 10 10 20 20 10 10 20 H 2 2 4 4 x C d 3 4 2 2 20 10 10 20 20 10 10 20 2 2 4 4

7 1 point Which function describes exponential growth a f x 180 0 95 C b f x 13 7 f x 18 9 10 d f x 24 6

12 1 point A bacterial colony with an initial population of 50 doubles every 5 h Which of the following equations models the exponential growth for time 1 in hours C A 50 2 a b A 50 d 50 A 50 2

14 1 point A 300 g sample of thorium 234 has a half life of 24 days The mass of thorium in grams that remains 7 after t days can be modelled by M t 122 5 g b 150 g 300 What mass will remain after 31 days 177 5 g d 193 75 g

9 1 point Which equation best represents this graph a y 4 2 b 1 C y 2 4 d y 4 2

Consider the following differential equation dy dx Y 2 x 1 which option that correctly describes how the solution can or cannot be found a Neither the integrating factor method nor the separation of variables met b Either the integrating factor method or the separation of variables metho c The integrating factor method only d The separation of variables method only

The time it takes in hours to travel from bridge A to bridge B can be approximated by T v toll plazas a Find and interpret T 65 b Find and interpret T 65 a T 65 2 35 Round to two decimal places as needed If a person drives 65 mph excluding stops the travel time will be 2 35 hours Round to two decimal places as needed b Find T v T v 120 0 5v where v is the average velocity in mph while driving excluding periods when stop

Find the indicated derivative 8 5t 7 dt y 8 5t 7 9

Find the derivative of the function y 2 6x 4 6 dy dx Tyne an expression using

se the quotient rule to find the derivative of the function dy y 5 X 7 7

You and Bimo are playing a game that is popular here For this game you are required to throw a blue diamond as high as you can Players of this game must stand on a special box to throw the diamond When calculated with your height the starting point becomes 7 33 meters with a velocity of 27 meters Bimo on the other hand has a starting point of 3 2 meters with a velocity of 17 meters 1 write an equation for both you and Bimo 2 What is the maximum height the ball reaches before it falls back down to the ground 3 How long does it take for the ball to reach its maximum height 4 When does the ball hit the ground 5 Draw a graph and state the similarities and differences between your and Bomo s throw 6 Determine the number of zeros 7 I Are there any points of intersection between your and Bimo s throw

4 In this question you may take for granted that d 1 dx a Compute b Calculate loga dx r log x x Hence compute Vx 0 logadr

10 5 10 5 5 10 Submit Skip you cannot come back 5 10 X Step 1 If the line slopes upward toward the right the slope is Select B If the line slopes downward toward the right the slope is Select B The slope of a Select line is 0 because Ay 0 The slope of a Select line is undefined because Ax 0

Match the story with the The water gushed out more and more slowly Choose the graph below that best illustrates the story OA GOD O C

The hazardous liquid oozed more and more slowly Choose the grach below that best illustrates the story OB OC O P

Determine a regular singular point XO of the differential equation x 2y x 2 2x y 2y 0 x 0 and first derive the recurrence relation and then find th series solution corresponding to the minimum root of th indicial equation