Sequences & Series Questions and Answers

Use the exponential decay model A Ae to solve the following A tranquilizer is used in the short term relief of symptoms of anxiety Its half life in the bloodstream is 32 hours How long will it take for the tranquilizer to decay to 8 of the original dosage COXIE

2 25 et P3 have the inner product given by evaluation at 7 1 1 and 7 Let po t 2 p t 4t and q t Notice that these polynomials form an orthogonal set with this inner product Find the best approximation to p t t by polynomials in Span P 24 he best approximation to p t t3 by polynomials in Span Po P q is

Once you have completed the above problems and below Complete the Lesson Reflection above by circling your current understan 1 Write an explicit rule in function notation for the arithmetic sequen A student loan needs to be paid off beginning the first year after graduation Beginning at Year 1 there is 52 000 remaining to be paid The graduate makes regular payments of 8 000 each year The graph shows the sequence A home cook needs to boil 1 liter of water on the stove Water boils at 100 C 3 38 Time minutes Temperature C What is the common difference of the sequence represented 46 5 54 lirit rule for the sequence

2 A fly starts out 2 meters from a lightbulb flies closer to the light then farther away 2 meters again At this point the fly goes toward the bulb again but hits the bulb and then finally flies away A Find a function it may be piecewise that gives the distance of the bug from the light as a function of time There is more than one solution here you have lots of freedom with what your function can be but it must satisfy the situational requirements given Demonstrate that your function DOES satisfy the situational requirements

Obtain all elements in Z1s relatively prime with 18

Baue HW Write an explicit rule in function notation for the arithmetic sequence 1 Month Total withdraws When you are finished check the s Tickets Total Cost 1 164 1 75 2 148 4 5 116 100 f n 164 169 16 3 132 2 100 3 125 2 4 150 3 200 5 175 4 260 5 300

Simplify to an expression of the form a sin 8 6 sin 6 cos

If Tanisha has 100 to invest at 8 per annum compounded semiannually how long will it be before she has 200 the compounding is continuous how long will it be Compounding semiannually it will be about 8 84 years before Tanisha has 200 Round to two decimal places as needed Compounding continuously it will be about Round to two decimal places as needed years before Tanisha has 200

The table shows the number expressed in millions of citizens who moved in 2004 categorized by where they moved and whether they were an owner or a renter Number of People in a Certain Country Who Moved in 2004 in Millions Moved to Moved to Moved to Same Region 11 7 18 8 Owner Renter P citizen was an owner Round to the nearest hundredth as needed Different Region 2 8 4 4 Find the probability expressed as a decimal rounded to the nearest hundredth that a randomly selected citizen who moved in 2004 was an owner Different Country 0 3 1 0 he probability that a randomly selected person living alone is male is approximately Round to the nearest hundredth as needed The table shows the distribution by age and gender of the 29 2 million people in a country who live alone Use the table to find the probability that a randomly selected person living alone is male Number of People in the Country Living Alone in Millions Ages Ages Ages Ages Ages Ages 15 24 25 34 35 44 45 64 65 74 275 Total Male 0 8 2 2 2 6 4 2 1 1 1 4 12 3 Female 0 7 1 6 1 7 4 9 2 9 5 1 16 9 Total 1 5 3 8 4 3 9 1 14 0 6 5 29 2

11 3 Find the intersection between the planes x 2y z 3 and x 3y 2z 1

5 x y Z 76 70 10 y max x A 14 B 15 C 16 D 17 E

You want to buy a 20 000 car The company is offering a 3 interest rate for 36 months 3 years What will your monthly payments be Round up to the cents place S607 07

Suppose an and bare series with positive terms and are series with positive terms and b is known to be divergent a If a b for all n what can you say about an Why O converges by the Comparison Test n a converges if and only if n an b We cannot say anything about an Oa diverges by the Comparison Test a converges if and only if 2a 2b b If an br for all n what can you say about an Why a converges by the Comparison Test a diverges by the Comparison Test a converges if and only if an O we cannot say anything about an n a converges if and only if an s 4

About how far offshore does the continental shelf on the Atlantic Coast extend a 400 km b 50 km c 200 km d 800 km e 100 km

Higher Order Differentiation In Exercises 23 24 25 and 26 find a r t b r t c r t r t and d r t x r t 23 r t i tj t k

Express the given product as a sum containing only sines or cosines 170 sin sin 170 COS COS

Use the model A Pe or A P 1 2 where A is the future value of P dollars invested at interest rater compounded continuously or 7 times per year for f years If a couple has 100 000 in a retirement account how long will it take the money to grow to 1 000 000 if it grows by 7 5 compounded continuously Round up to the nearest year It will take approximately years

Identify the intervals where the function is changing as requested Increasing 324 Select one O a 2 2 O b 2 0 O c 3 3 O d 3 0

Two ships set sail from the same port The first ship travels 100 kilometers due north and the second ship travels 150 kilometers at a bearing of 45 degrees east of north How far apart are the two ships from each other when they reach their destinations Use the cosine law to determine the distance between them

A 20ft by 28ft swimming pool is filled with water The depth is measured at regular intervals starting at one corner of the pool and the values are recorded below 05 0 05 10 OT 0 Volume 4 2 W N N N 2 15 2 20 3 744625 14 21 28 7 10 10 10 8 10 5 10 6 7 8 4872 Estimate the volume of water in the pool using the Midpoint Rule with m n 2 ft3

Consider the following compound inequality 12 8 Step 1 of 2 Solve the inequality and express your answer in interval notation Use decimal form for numerical valu Answer 2 Points 9 4 26 8

3 dy y dx y cos n X

Question 5 10 points Graph the solution set of each system of inequalities a x y 4 x y 5 4x y 4 y X b x 2y 2 5 y 3 x x 0 y 0 y

Problem 1 vector addition In the following Figure 1 write the vector b as a linear combination of the vectors u and v Th 2v 2v 7 Figure 1 vector addition

Show that the function f z x x x 2 y 2 y yx 2 y 2 i is analytic in any open set not containing 0 0 Also compute f z

Click here to watch the video Solve the equation for x where x is restricted to the given interva xinh y 4 csc 4x for x in T 0 U 0

13 2 4 6 8 42 44 46 A 24 B 20 D 23 E 24 C 2

man has 460 000 invested in three rental properties One property earns 7 5 per year on the investment the second ears 8 and the third earms 9 The total annual earnings from the roperties is 38 650 and the amount invested at 9 equals the sum of the first two investments Let x equal the investment at 7 5 y equal the investment at 8 and z represent the investme Complete parts a through d below a Write an equation that represents the sum of the three investments Type an equation Do not include the symbol in your C

Find the Taylor series for f x centered at the given value of a Assume that f has a power series expansion Do not show that R x 0 f x sin x a f x 00 R n 0 Find the associated radius of convergence R

Starting at age 50 a woman puts 1600 at the end of each quarter into a retirement account that pays 7 interest compounded quarterly When she reaches age 60 she withdraws the entire amount and places it in a mutual fund account that pays 9 compounded monthly From then on she deposits 300 in the same mutual fund at the end of each month How much is in the account when she reaches age 65 When the woman reaches age 65 there is in the account Round the final answer to the nearest dollar as needed Round all intermediate values to the nearest cent as needed

3 The number of guppies in an aquarium is modelled by the function N t 8 1 0 17 where t is measured in months a Describe what each part of the equation represents 3 marks

To measure a stone face carved on the side of a mountain two sightings 800 feet from the base of the mountain are taken If the angle of elevation to the bottom of the face is 29 and the angle of elevation to the top is 32 what is the height of the stone face The height of the stone face is feet Round to two decimal places as needed

Find the work performed when the given force F is applied to an object whose resulting motion is represented by the displacement vector d Assume the force is in pounds and the displacement is measured in feet F 7i 19j d 4i 45j C Fed the work performed when the given force Facoled to an object whose malting ooties is represented by the displacement vertar d Actume the force is pounds and the disple F 7 1944 AOK TOUR TEACHER

Find the least positive value of 0 0 cot 60 9 1 tan 50 3

Le artidentity to write the expression as a single trigonometnic function value or as a single number sin 38 3 D sin 38 3 wer Type an exact answer using radicals as needed Do not include the degree symbol in your answer

Problem 1 Consider an angle that measures 21 radians a Convert the radian measure to degree measure b Sketch the angle in standard position c Give a negative coterminal angle

Given the equation 2x 3y 6 a second equation that forms a system with no solution is 2x 3y 6 Ox y 3 O4x 6y 6 O4x 6y 12

4 Solve sin 2x cos x 0 x 2 giving exact solutions

at a b c EZ 2 2 20 64 galatasa A 15 yoB 14 ga sat galata a b c ga sat galata y s sat D 12os sat E 1 C 23

5 Which expression is equivalent to 18x 32y O 18 x 32y O2 9x 16y O 18 x y O2 9x 32y

Graph the domain of the following function f x y y x x y 4

Explain whether the following steps to solve a logarithmic equation are true or false Justify your reasoning log 3 log3 27 log3 81 4

1 Suppose that d days from now the number of ants in a colony is give by N 27 2 a How many ants are there initially b How many are there after 8 days c What is the doubling period

On square paper or square grid paper draw rectangles with a perimeter of 48 units Take the following values for the length of the block 1 unit 2 units 3 units and 4 units Find the area in each case and complete the following table 4 1 Length 1 unit 2 units 3 units 4 units Width Perimeter 48 48 48 48 Area MIP2601 102 0 2 8 Do you think a rectangle with a perimeter of 48 units as well as an area of 48 square units exits Explain your answer 4

The population of mosquitoes starts with a nest of 3100 in the forest and grows exponentially at a rate of 17 per m This can be modeled by the equation A 3100 1 17 Estimate the number of mosquitoes in the forest after 1 year 12 months Round to the nearest whole number and do not round until the final calculation Provide your answer below mosquitoes

Catherine is creating a triangular banner for her school s football team She wants the height of the banner to be 4 times as tall as the width of the base of the triangle If she wants the total area of the banner to be 8 feet squared 8 ft how wide should the base of the triangle be in feet The area A of a triangle is A x base x height Provide your answer below

A teacher took a sample of final exam scores from all the final exams given that semester What is the average test score 100 76 95 94 88 72 Provide your answer below

Find the cardinal number of the set C x x EN 30 x 56 anda is divisible by 6 where N denotes the set of all natural numbers

How many teaspoons are in a pint Recall that 1 pt 2 cup 1 cup 16 tbsp and 1 tbsp 3 tsp Provide your answer below

QUESTION 2 1 POINT Let A 1 2 3 4 6 7 8 9 11 12 15 and B 3 5 6 7 10 11 12 13 14 Find An B Provide your answer below