Sequences & Series Questions and Answers

The count in a bacteria culture was 300 after 15 minutes and 1800 after 35 minutes Assuming the count grows exponentially What was the initial size of the culture bacteria Find the doubling period Find the population after 105 minutes bacteria When will the population reach 10000 minutes

The Republic of Amador is composed of five states A B C D and E According to the country s constitution the Congress will have 200 seats divided among the five states according to their respective populations State Population in thousands Seats for state A A Seats for state E 1112 B 1118 C 1320 D 1515 E Use Adam s method with d 50 6 to apportion the 200 congressional seats for state A and E 4935

5 Find the domain of the following functions x a f x 1 f x 2

The table shows the relationship between the values of x and y X 2 7 Oy x 3 Oy 10x 3 Oy 2x 1 Ou 2x 1 3 17 4 31 5 49 y Which of the following equations describes the relationship for the values in the table

Find the exact value of the expression sin 265 cos 25 cos 265 sin 25 O A OB O C C 1 2 3 2 53 12 3

Which of the following sets of vectors are Linearly Dependent Select all that apply Any 5 polynomials of degree 4 or less Any 6 vectors in R e e e es 1 0 0 0 1 0 1 4 0

Graph the solution set of the inequality on a number line and then write it in interval notation x152xx 3 What is the graph of the solution Choose the correct graph below OA Oc CELEBR 8 D 7

the solution set the inequality and write it in interval notation x 8sx Choose the graph of the solution set DA Da 11 10 OB 13 10

5 5 Find the find the magnitude and the direction of a The resultant of the system of forces below b The equilibrant for the following system of forces below 20N 150 15N 20N

5 Use the graph of the rational function to complete the following statement As x o f x As x o f x W 10 8 6 19 10 8 6 6 1 2 4 6 LC A Asymptotes are shown as dashed lines The horizontal asymptote is y 3 The vertical asymptotes are x 4 and x 1

What are the domain and range of f x 2x 41 O domain x 2 range 00 domain 00 range f x 0 domain 0 00 range f x 0 O domain x 2 range 00 00

37 5 The point P x y is on the terminal ray of angle e If e is between radians and 2 radians and csce 2 what are the coordinates of P x y OP 21 2 OP 21 2 O P 2 21 OP 2 21

Haruto simplified the value below CSC 19 2 Which statement explains whether Haruto is correct X 3x O Haruto is correct because the angle is coterminal with 4 and the reference angle is 4 O Haruto is correct because the angle is coterminal with X which is also the reference angle 1 1 1 2 1 2 3x O Haruto is not correct because the angle is coterminal with and CSC Haruto is not correct because the angle is coterminal with and CSC

Number 7 Opposite Reciprocal 7 undefined 1

Evaluate the expression when x 4 and y 5 x y LX x X y x y y X Type an integer or a simplified fraction

Use the diagram to find the angle measures of the triangle Recall that the sum of the angle measures of a triangle is 180 x x 4 to 9x X 4

etermine the general term yn Zn in the following cases 2 1 Yn 2 Yn 1 4yn 2 2 Zn 2 2Zn 1 3Zn with z 0 0 z 1 4

1 Compute the following Ab 1 2 4 a 2 3 1 1 2 10 2 b 2 1 0 0 1 2 1 0 21 0 1 2 0012

The height h in feet of a ball suspended from a spring as a function of time t in seconds can be modeled by the 2 sin x 1 2 5 Which of the following equations can also model this situation equation 2 sin Oh 2cos x 5 Ob 2cos 5 Oh 2cos x 5 0 f 2cos 1 1 5 Oh 2cos

Gary is solving for x and he uses these steps 2 2x 1 3x 5 3 1 He checks his answer and knows that 3 cannot ever equal 1 so he writes no What is the correct conclusion about Gary s work There is an answer and it is There is an answer and it is O

The graphs of fand g are given Find a formula for the function g g x f x x 4 2 y 10 8 6 4 2 Orq g 4 6 8 10

estimate the slope of the curve at the designated point

Find all solutions in radians of the given equation on the interval 0 2n 5 Points 3 9 cosx 5sin x 6 cos 7 cos O 1 cos None of these expressions I don t know

Rewrite and simplify g x with the given subsititution 5 Points 8 x x 6 tan 0 assume 0 0 sin 0 cos 0 O sec 0 x 36 x None of these expressions I don t know

1 Evaluate each of the following Place any non integer answer in simplest rational form c 2 1 a 4 1 2 d 2 b x 1 A 0 1 4 1 A 0 1 1 1 log 10 i 256

23 Let u x 1 and v x x 1 1 3 Verify that u and u are inverses of each other

A student sells ice cream bars Her weekly salary is given by S x 0 80x 200 where x is the number of ice cream bars sold Her employer determines the amount withheld for taxes using the function W x 0 10x where x is her weekdy salary Wnite the amount withheld as a function of the number of ice cream bars sold Hint Use composition The amount withheld as a function of the number of ice cream bars sold in WIX Simplify your answer Use integers or decimals for any numbers in the expression COT

Consider the following 2 2 4 X 0 61 3 2 1 a Plot the given points 0 y 41 22 9 2 1 16 2 17 10 20 30 40 2 6

Use the following matrices 10 2 32 1 40 3 00 A E Z 1 1 2 31 01 2 3 4 0 0 000 000 42 0 13 35 D B 1130 4211 32 1 328 5 0 Which of the matrices A B C D E F G and Z are square Select all that apply A B C D 211 104 510

normal healing of wounds can be modeled by an exponential function If A represents the original area of the wound and if A equals the area of the wound af cribes the area of a wound on the nth day following an injury when no infection is present to retard the healing A A e 0 36n 0 ppose that a wound initially had an area of 100 square millimeters a If healing is taking place how long will it be before the wound is exactly one half its original size days b How long will it be before the wound is exactly 10 of its original size days

Find the following for the function f x 4x 3x 4 b f 4 c f 4 a f 0 e f x f f x 1 g f 4x a f 0 b f 4 c f 4 d f x e f x f f x 1 g f 4x h f x h Simplify your answer Simplify your answer Simplify your answer Simplify your answer Simplify your answer Simplify your answer Simplify your answer Simplify your answer d f x h f x h

Let N be the set of natural numbers and two functions fand g be defined as f g N N such that f n n 1 2 FIN n if n is odd if n is even 2 and g n n 1 Then fog is 2015 20 166945

Determine the intervals of increase and decrease for the given rational function graph 09 H to Increasing 0

Identify any vertical asymptote s and hole s in the graph of the following x 5 f x x x 20 VA Vertical Asymptote HO Hole HO x 5 no VA VA x 5 HO x 4

Q9 Find the general solution of the following nonlinear difference equation Hint apply linearization Yk 2yk kyk 2yk 0

5 Graph the function y 2 cos 3 x 1 2x

Formative Asst 3 The school newspaper is interested in obtaining information about students Look at the table bel Does Not Have a Job 120 100 220 Seniors Freshmen Total Has a Job 480 300 780 b The probability that the student is a freshman and has a job A student is selected at random Determine the following probabilities Use the values from the table to show how you determined your answer a The probability that the student has a job c The probability that the student is a senior or has a job d The probability that a freshman has a job e The probability that a student with a job is a senior Juniors Sophomores Total Here is some more information about students Walks to School 440 360 800 Total Rides to School 110 90 200 600 400 1000 Total 550 450 1000 Are the events Student is a Junior and Student walks to school independent Use conditional Tobabilities to justify your answer 2

Consider the graph of the function f x ln x 4 A B C 2 D 4 2 2 4 0 N Which is a feature of function gif g x f x 4 2 f vertical asymptote of x 4 x intercept at 5 0 horizontal asymptote of y 4 y intercept at 0 4 4 X

The pentagon in the diagram below is formed b five rays 68 140 60 84 What is the degree measure of angle x

Find the maximum revenue for the revenue function R x 353x 0 6x2 Round your answer to the nearest cent R

Evaluate without a calculator 813 4

Write the linear inequality for this graph 10 9 8 7 6 53 10 9 8 7 5 4 30 2 in OR a S 6 7 8 9 12 6 7 8 9 10

Find a function h x mx b whose graph can be obtained by translating the graph of f x 3 2x down 8 units and to the right 3 units

Decide whether the relation defines a function or not and give the domain and range in interval notation x y Function Not Function choose one Domain

c through 4 4 and perpendicular to x 4 i Standard form

Use Desmos or a Graphing Calculator to solve the equation 4 2 11

Let z g x y f 3 cos xy y ey provided that f 3 4 5 f 3 4 2 f 3 4 5 i Find g 0 3 91 ii Find 92 0 3 iii Find the equation of the tangent plane to the surface z f 3 cos xy y ey at the point 0 3

The graph below represents the growth of Jame s giant peach in inches Which expression can be used to represent the size of the peach for any specific week How big is the peach in the fourth week 600 550 500 450 400 350 300 250 200 150 100 50 1 140 Oy 70 0 5 140 inches 0 70 This image cannot be easily described If you need an explanation of this image please ask your teacher for help Oy 2x 70 78 inches O y 70 2 1120 inches 3 560 O y 0 5x 70 72 inches 2 280

The graph below represents the decay in the mass of a sample of Uranium Which expression can be used to represent the mass of the sample for any specific year What is the mass of the Uranium after five years mass in grams 60 40 0 78 1 39 20 2 19 5 3 9 75 of years This image cannot be easily described If you need an explanation of this image please ask your teacher for help O y 0 5x 78 80 5 grams O y 2x 78 88 grams O y 78 2 2496 grams

Enter the equation g x 4 2 and f x 2 How does the graph g x differ from the graph of f x O The graph stretched horizontally by a scale factor of 4 O The graph compressed horizontally by a scale factor of 4 O The graph compressed vertically by a scale factor of 4 O The graph stretched vertically by a scale factor of 4