Sequences & Series Questions and Answers

Which methods may be used to solve for two equations at the same time I substitution II translation III elimination IV graphing Select one O a I III and IV only O b none of the above O c I and II only O d I II and III only

nd the present value that will grow to 8000 if the annual interest rate is 2 5 compounded quarterly for 8 yr me present value is Round to the nearest cent as needed

In right ABC with right angle at C let S and T be the trisection points along the hypotenuse AS ST TB Prove that CS CT 5 AB 9 S T B

Solve the compound inequality Write the solution in interval notation 3x 9 and x 4 5

Perform the indicated operations for the given vectors v 7i 8j w 4i 10j Find v w Oi 05 O 13

7 0 38 x 2 9 40 NALYSIS Which solution is incorrect Explain the error A x x 2 0 x 1Xx 2 0 x 1 or x 2 B x x 2 0 x 1Xx 2 0 x 1 or x 2

Problem 5 Is the Function Linear Determine if the functions represented in the tables below are linear If the function is linear give the slope and vertical intercept Then and write the equation a b Average Rate If a function is linear then the average rate of change will be the same between any pair of points If a function is linear then the average rate of change is the slope of the linear function c I A z 110 a r a I a z 1 5 4 42 1 74 2 1 1 27 2 38 3 1 2 12 8 34 5 11 3 7 12 82 8 41 5 2 23 214 10 71 8 10 42 442 11 89 9 02

When the sun s angle of elevation is 31 a building casts a shadow 45 meters long How high is the building

In 2004 a school population was 1001 By 2008 the population had grown to 1697 Assume the population is changing linearly Show your work for each of the following a Find a linear function model for the population of the school as a function of years after 2004 Clearly indicate what your variables represent b Interpret the slope of this linear function Write your answer as a complete sentence c Identify the vertical intercept of this linear function Write it as an ordered pair and interpret its meaning in a complete sentence d Use your model to predict the population of the school in 2016 Show your work

The karyotype pictured shows a n number of chromosomes for a human haploid B 81 K KRB diploid C hu abnorm

An island is located 30 miles N38 23 W of a city A freighter in distress radios its position asN12 29 E of the island and N10 18 W of the city How far is the freighter from the city

Find the linear equation in slope intercept through the point 3 1 and is perpendicular to y 2 8 2 x 2

Arrange the quantities in order from smallest 1 4 KL 1800 L 18 600 dL

11 write the nth term rule an a 1 1 a 10 d n 1 below 15 and d 11 an n 1

Arrange the quantities in order from sma 2 8 dam 0 25 km 260 cm

Determine the geometric by sequence i typing yes or no a 32 128

What does deci mean Type a fraction or a dec 1 dm m Type a fraction or a decima

A spring has a natural length of 20 0 cm If a 28 0 N force is required to keep it stretched to a length of 36 0 cm how much work W is required to stretch it from 20 0 cm to 28 0 cm Round your answer to three decimal places

In the following image the original function black is y x 2 1 0 What is the equation of the shifted graph red y 8

Find the indicated function values for the function f x a f 0 b f 4 c f 3 d f a h e Why must 3 be excluded from the domain off Simplity your answer Simplify your answer c f 3 Simplify your answer d f a h Simplify your answer e Why must 3 be excluded from the domain off a T U b f 4 7x 6 x 3 OA This value of x would make the denominator positive OB This value of x would make the denominator zero OC This value of x would make the numerator and denominator zero On This unl

The moment magnitude scale denoted Mw is a scale that measures the energy released by an earthquake and is now preferred 2 log M 10 7 where Mo is the magnitude of 3 over the Richter scale for medium to large earthquakes The formula Mw the seismic moment or the energy released in dyne centimeters An earthquake in 1964 in Alaska had a moment of 7 5X102 dyn cm Compute the moment magnitude for this earthquake Round your answer to the nearest tenth Source USGS

Find the distance between these two points 5 8 and 3 5 Write your answer in exact form do not use decimal approximations To write a square root such as 15 type in sqrt 15 instead of using rational exponer You are not required to reduce your radicals for this problem

8 Complete the table below Degree 2 712 2 113 3 4 4 5 5 6 Polynomial Functions Degree Even or Odd EVERY Yon Sign of Leading Coefficient I 1 End Behavior using arrow notation

Your manufacturing plant produces air bags and it is known that 60 of them are defective Five air bags are tested Compute the probability distribution of the binomial variable described above and use it to compute the probability that if five air bags are tested at least one will be defective and at least one will not

The probability that a randomly chosen person in the Netherlands connects to the Internet immediately upon wakingt is approximately 0 25 What is the probability that in a randomly selected sample of nine people four connect to the Internet immediately upon waking HINT See Example 2 Round your answer to four decimal places

You are performing 7 independent Bernoulli trials with p 0 3 and q 0 7 Calculate the probability of the stated outcome Che your answer using technology Round your answer to five decimal places at least three successes P X 3

In the exercise X is a binomial variable with n 6 and p 0 3 Compute the given probability Check your answer using technology HINT See Example 2 Round your answer to five decimal places P X 2

Alien Retirement The probability that a randomly chosen citizen entity of Cygnus is of pension aget is approximately 0 4 Wha is the probability that in a randomly selected sample of five citizen entities all of them are of pension age Round your answer to four decimal places P X 5

Population Age The following chart shows the ages of 250 randomly selected residents of a certain country Frequency 120 100 80 60 X 40 20 75 0 14 7 62 What is the associated random variable 91 15 29 30 64 65 74 The associated random variable is the age of a randomly selected resident of this country O The associated random variable is the 250 randomly selected residents of this country O The associated random variable is the collection of ages all residents of this country O The associated random variable is a randomly selected resident of this country Represent the data as a relative frequency distribution using the rounded midpoints of the given measurement classes 22 22 47 Age 70

Divide using synthetic division 3x x 4 x 1 3x x 4 x 1 Simplify your answer Use integers or fractions for any numbers in the expression Do

Give the probability distribution for the indicated random variable HINT See Example 3 Enter your probabilities as fractions Three fair coins are tossed and X is the square of the number of heads showing 0 9 P X X Draw the corresponding histogram P X X 0 3 0 2 P X X 0 4 UU 0 3 0 2 9 0 1 X 0 3 P X X 0 2 0 1 0 1 1 4 1 4 P X X 0 4 LEL 0 3 0 2 4 9 Calculate P 1 X 9 Enter your probability as a fraction 4 1 9 4 9 K

2010 Income Distribution up to 100 000 The following table shows the distribution of household incomes in 2010 for a sample of 1 000 households in a country with incomes up to 100 000 0 3 0 25 0 2 0 15 0 1 0 05 P 0 3 0 25 a Let X be the rounded midpoint of a bracket in which a household falls Find the relative frequency distribution of X and graph its histogram P 0 2 Income Bracket 0 15 Households 0 1 0 05 0 20 000 40 000 19 999 39 999 59 999 240 290 190 10 000 30 000 50 000 70 000 90 000 60 000 80 000 79 999 99 999 180 tlm tudi 10 000 30 000 50 000 70 000 90 000 10 000 30 000 50 000 70 000 90 000 babilitua P 0 3 0 25 0 2 0 15 0 1 0 05 P 0 3 0 25 0 2 0 15 100 0 1 0 05 10 000 30 000 50 000 70 000 90 000 X X b Shade the area of your histogram corresponding to the probability that a randomly selected household in the sample has a 50 000 What is this

Consider the following X is the value of the larger number when two dice are rolled a Say what an appropriate sample space is c S 1 2 1 3 1 6 2 1 2 3 OS 1 2 3 4 5 6 1 2 3 4 5 6 S 1 1 2 2 3 3 4 4 5 5 6 6 S 1 1 1 2 1 6 2 1 2 2 6 6 Os 2 1 3 2 3 1 4 3 4 2 4 1 5 4 5 3 5 2 5 1 6 5 6 4 6 3 6 2 6 b Complete the following sentence X is the rule that assigns to each outcome the smaller 6 5 List the possible values of X O 2 3 4 O 1 2 3 4 5 O 1 2 3 4 5 6 3 4 5 6 2 3 4 5 6 5 number

5 432 5 4 3 2 11 Oy lnx Oy In x 1 Oy e Oy e 77717 1 2 3 4 5 X

1 8 2 Show that cos z cos x sinh y where x iy Find all zeros and periods of cos z Solution Use trigonometric formulas from page 29 and 30 in CA we have cos z cos x iy cos rcos iy sin r sin iy cos x cosh y i sin x sinh y Now take the modulus squared and use cosh y 1 sinh y cos 2 cos r cosh y sin x sinh y cos r 1 sinh y sin r sinh y cos r cos r sin r sinh y cos r sinhy The identity for cos 22 shows that the only zeros of cos z are the zeros of cos on the real axis because cos z 0 cos x 0 r 1 ma m 0 1 2 Translation by any period A of cos z sends zeros to zeros Thus any period is an integral multiple of and since odd integral multiples are not periods the only periods of cos z are 2an 0 n

2 Consider the complex numbers below in polar form 7 cos 77 Z i sin Z2 Z Z2 1 12 Cos 0 0 sin 0 0 cos 01 02 sin 0 0 3 cos 72 72 i sin 2 a Find the product z z Write your answer in rectangular form a bi form a hi

22 9 18 PM 0 Let f be a function defined by f x k 1 f 8 a k 1 0 b k 1 0 c k 1 0 d k 1 0 k 1 1 k3k 1 9kk 1 k3k 1 k59k 1 kgk 1 9kk 1 kgk 1 9kk 1 k8k 1 k59k f None of the above 1 x 5 9kk4 Print Test k on its interval of convergence Find

The half life Step 2 of 3 Answer How to ente

Let f x y x e y and a I x y 8 Find the first order approximation x y of f x y at a

You deposit 5000 in an account earning 3 interest compounded monthly How much will you have in the account in 10 years

Quest Jose hopes to earn 700 compounds semi annua

Exponential Function Evaluation Given the function f x 330 1 3 evaluate each of the following Note Round your answers to two decimal places as needed A Evaluate f 10 f 10 B Evaluate f 5 f 5 C Evaluate f 0 f 0 D Evaluate f 5 f 5 E Evaluate f 10 f 10

1 nts 00 23 31 eferences When do the effects of warranty obligations affect the state Multiple Choice O O None of these answer choices are correct When the sale of merchandise is made When the warranty obligation is recognized When there is a settlement of a warranty cla

10 8 9 log a b 8 y x 3 Shift the graph of the function to the 7 3 x 5 6 x 5 25 4 x 3 x 3 Top Ten Mistakes When in doubt 2 x 25 X 1 x 3 AND x 3 units Additional comments about the mistake from Mrs Kiriazes Think of 8 as 1 8 1 64 64 Remember to simplify using the Order of Operations 1 Grouping 2 Exponents 3 Multiplication and Division Left to Right 4 Addition and Subtraction Left to Right Product Property of Logarithms log ab loga logb This is the transformation mistake that I ve tried to warn you about all semester Be sure to shift left when you add inside the input AND shift right when you subtract inside the input When you divide or multiply both sides of an inequality by a negative number STOP and SWAP the direction of the inequality 3x 15 x 5 If you remember this rule you won t make mistakes with the exponent rules x x x x x x x x x x x x r When you see a fractional exponent think Radical The bottom of the fraction is the Root of the radical Just like the bottom of a tree is its roots 253 25 5 If you get confused put a front of the parentheses to remind you to distribute the negative to all of the terms in the parentheses x 1 3 x x 3 x x 3 x 3 You can only cancel factors not terms Factors can be cancelled because anything anything 1 Factors are all multiplied Terms are added or subtracted CAN T be simplified any further x c x e It s the same refrain When in doubt write it out x 3 x 3 x 3 x 6x 9

100 6k Find the bounds for the series 1 k 1 9k 1 O 1 1 O 1 100 k 021 33 O 1 100 3 E1 100 1 2

Given the graph at the right y tanx red graph identify the following for the blue graph and write an equation in the form y Atan Bx D Stretching factor Period Vertical Shift Equations for asymptotes Equation for the blue graph 3m 2 5m 4 TT 37 4 11 2 T1 4 10 9 8 7 6 5 4 3 2 1 0 1 2 43799 4 5 6 7 8 11 4 11 2 3 4

110 6x e A Find the value of 6x e dx 3 Determine whether 6n e is convergent or divergent 72 n 1 Enter CONV if series is convergent DIV if series is divergent

Sn 4n y 3n 271 6 5 4 3 321 123456 2 3 4 7 8 27 371 41 Write an equation for the function graphed above 5

Use the appropriate test to determine convergence or divergence of the following series For any convergent series that are alternating do they converge absolutely or do they converge conditionally Explain how you know For each part your explanation should include i The name of the test you are using to decide about convergence or divergence ii Be sure to explain why any tests you use apply iii Show all the steps and explanation for each test k k k 1 a b 1 k 1 C CM8 IM8 k 4 13

3 Let f x y 3x y 4xy Find 41 2 4 2 2 4 2 f 2 axdy ay ax and dya