Sequences & Series Questions and Answers

16 Find the degree leading coefficients and the maximum number of real zeros of the polynomia f x 2 3x6 4x7 6x Also Describe the end behavior long run behavior

12 Solve the following inequality graph the solution set and write the solution set in interva x 3x 18 notation 0 X 2

18 Professor Mishal deposits 10 250 into an account that earns 4 compounded interest How much will the account have at the end of 10 years if it is compounded monthly nt A t P 1 2 How much will the account have at the end of 10 years if it is compounded weekly How much will the account have at the end of 10 years if it is compounded continuously What is the Doubling time A t Pert

Find the formula for an 2 20 f x ab exponential function that passes through the points 0 2000 and

1 The price demand function of a company that manufactures vats a large tank or tub used to hold liquid p x 5x 600 a Find the revenue function R x b The company s fixed monthly cost is 1563 and each unit of vats costs 10 Write the cost function C x where x represents the number of packets of vats produced c Find the profit function P x d How many vats must be produced and sold in order to maximize profit e What is the maximum profit f What price must the company charge in order to W

tax purposes a man uses a method called straight line depreciation to show the loss in value of a copy machine he recently purchased A man assumes that he can use the machine for 7 years The following graph shows the value of the machine over the years What loss in value occurred during the first year Value thousands of dollars Years C

Consider the geometric sequence 7 28 112 448 A common K 12 problem asks students to find a formula a for the nth term beginning with n 1 We wish to prove by induction that an 7 4 1 for each natural number n 1 1 Understand The Question First we must write a recursive definition of the sequence an For the base case a For each k such that ak is defined ak 1 2 The Proof by Induction We proceed by induction on n Note To enter ak type ak

5 Select the correct answer from each drop down menu The asymptote of the function f x 3x 1 2 is y 2 Its y intercept is 0 1 0 2 0 3 0 1 0 1 Reset

A store is having a sale on almonds and jelly beans For 9 pounds of almonds and 7 pounds of jelly beans the total cost is 42 for 3 pounds of almonds and pounds of jelly beans the total cost is 24 Find the cost for each pound of almonds and each pound of jelly beans cost for each pound of almonds cost for each pound of jelly beans Explanation Q Such 200 MG CON

E O SYSTEMS Solving a distance rate time problem using a system of linear Rate of the faster train 1HSdvxh clzpPnLR6L 8 WalASUN5q2zqYYCEOTThlvVguDfOsq A faster than the other If they meet in 6 hour Two trains leave towns 1002 miles apart at the same time and travel toward each other One train travels 17 what is the rate of each train h 05

1 point Solve the recurrence relation an an 3an 1 10an 2 with initial terms a 1 and a 19

Solving a distance rate time problem using a system of Flying against the jetstream a jet travels 2460 miles in 3 hours Flying with the jetstream the same jet travels 6100 miles in 5 hours What is the rate of the jet in still air and what is the rate of the jetstream Rate of the jet in still air Rate of the jetstream mi h mi X Bra 6

Solving a distance rate time problem using a system of A motorboat takes 5 hours to travel 100 kilometers going upstream The return trip takes 2 hours going downstream What is the rate of the boat in still water and what is the rate of the current 9 Rate of the boat in still water 15 H

25 y 20 15 10 5 The scatterplot shows because the values of y x 30 y 20 10 10 20

Solving a decimal word problem using a linear inequality A phone company offers two monthly charge plans In Plan A the customer pays a monthly fee of 32 30 and then an additional 4 cents per minute of use In Plan B the customer pays a monthly fee of 20 and then an additional 7 cents per minute of use For what amounts of monthly phone use will Plan A cost no more than Plan B Use m for the number of minutes of phone use and solve your inequality for m 0 OZO D Brando Oso

Solving a word problem using a system of linear equation One month Isabel rented 7 movies and 9 video games for a total of 73 The next month she rented 5 movies and 3 video games for a total of 29 Find the rental cost for each movie and each video game Rental cost for each movie Rental cost for each video game S D

Find the Taylor series about O for the following function f z sin Log 1 z up to the term in z 4 Kindly use the Composition Rule for solving the problem Thks

The function fis defined as f x 7 2x2 4 Find f x 6 Write your answer without parentheses and simplify it as much as possible f x 6 0

E Initial Knowledge Check Boris s cow gives 1 gallons milk each day How much is this in quarts Write your answer as a whole number or a mixed number in simplest form Include the correct unit in your answer 8 08 fl oz c qt gal pt

The graph of a function y f x is shown to the right For this problem we will use it to sketch the graph of y f x 1 Follow the directions below 3 3 2 1 2 3 2 1 3 1 2 2 0 2 y f x 5 2 3 4 a State in words all of the transformations necessary to obtain the graph of y f x 1 from the graph of y f x Use words like shift reflect stretch compress horizontal vertical left right up down 5 b Sketch a graph of y x 1 Five points in the original graph are labeled with ordered pairs label those five transformed points clearly in your new graph You may either draw and label your own axes and sketch it below or on your own paper or you may draw the graph directly on top of the given graph above as long as it is clear what your final graph looks like If

Find an equation of the line L L is perpendicular to y 2x The equation is

A drug is administered intravenously to a patient at the rate of 12 mg h The patient s body eliminates the drug over time so that after t hours the proportion that remains is e 0 25t If the patient currently has 90 mg of the drug in her bloodstream how much of the drug is present 8 hours from now Round your answer to one decimal place mg Show Transcribed Text

Use the given graph of the function f to answer parts a o a Find f 28 and f 12 f 28 f 12 12 12 16 8 1 0 8 8 24 16 8 28 8 24 0 0 4 8 16 8 16 8 8 24 16 0

What is the domain of fg x What is the domain of f g x Difference Quotient Difference Quotient Formula DQ Find the difference quotient given f x 2x 5 Find the difference quotient given f x x 3x 4

8 cm 4 cm 21 cm 3 cm Find the area of the gray region above The figure is not drawn to scale and remember to us 3 14 for all calculations involving Area cm Round answers to 2 decimal place as needed

A thermometer reading 6 C is brought into a room with a constant temperature of 33 C a If the thermometer reads 15 C after 2 minutes what will it read after being in the room for 4 minutes For 9 minutes b Graph the relation between temperature and time Use TRACE to verify that your answers are correct a After 4 minutes the thermometer will read approximately C Round to the nearest hundredth as needed

yd Q Find the diameter of a circle with area of 182 yd Round your answer to the nearest tenth V CAR

Find the perimeter and area of the following composite figure 30 ft 10 ft 7 ft Perimeter Area 7 ft 30 ft 7 ft 7 ft 10 ft feet If needed enter answer to 1 decimal place square feet If needed enter answer to 1 decimal place

Select all polynomials that are in standard form 8x 4 2x 5

Find an equation of the line containing the centers of the two circles whose equations are given below x 7 y 1 9 x 1 y 6 81 www The general form of the equation of the line Simplify your answer

In the contrapositive proof why does n 1 not being divisible by 4 mean that n is not divisible by 4 Consider n 4 for a counterexample 4 1 15 is not divisible by 4 but 42 must be divisible by 4 Using the note above what conclusions about n can you make from n 1 not being divisible by 4 Also why does n 1 not being divisible by 8 mean that n 1 must not be divisible by 4 There are integers that are not divisible by 8 but are divisible by 4 for example 12 Also can you think of any other remainders for n 1 if it is not divisible by 8 other than 1

3 If x is a sequence that the nth term is x ii iii 1 1 Prove that x is increasing sequence Prove that x is bounded sequence Is x convergent sequence 1 2 1 n

The graph of a function g is shown below Use the graph of the function to find its average rate of change from x 0 to x 3 Simplify your answer as much as possible 69

OGRAPHS AND FUNC ENS Writing the equation of a line through two give Find an equation for the line that passes through the points 5 1 and 1 1 0 0 0 2 X

ate problem usin First account Second account 0 Espanc Last year Boris had 10 000 to invest He invested some of it in an account that paid 7 simple interest per year and he invested the rest in an account that paid 5 simple interest per year After one year he received a total of 640 in interest How much did he invest in each account X 15 5 Brandon

Espa o Isabel bought a desktop computer and a laptop computer Before finance charges the laptop cost 400 less than the desktop She paid for the computers using two different financing plans For the desktop the interest rate was 7 5 pe year and for the laptop it was 8 per year The total finance charges for one year were 371 How much did each computer cost before finance charges Desktop Laptop 4

V Find an equation for the line below

problem with a linear function Monthly cost in dollars Espa ol The monthly cost in dollars of a long distance phone plan is a linear function of the total calling time in minutes The monthly cost for 44 minutes of calls is 16 67 and the monthly cost for 90 minutes is 22 19 What is the monthly cos for 87 minutes of calls Calling time in minutes 3 5 10 X Brandon V OR EB 13 P

Solving a percent mixture problem using a Amount invested in Fund 8 C 15 Espa ol Mary invested her savings in two investment funds The 8000 that she invested in Fund A returned a 3 profit The amount that she invested in Fund B returned a 10 profit How much did she invest in Fund B if both funds together returned a 8 profit X Brandon V B L

Application problem with a linear function Espa ol The monthly cost in dollars of water use is a linear function of the amount of water used in hundreds of cubic feet HCF The cost for using 13 HCF of water is 36 20 and the cost for using 30 HCF is 65 95 What is the cost for using 19 HCF of water Monthly cost in dollars Water usage in HCF 0 X ER

a syste First mechanic hours Second mechanic hours 3 5 Espa ol Two mechanics worked on a car The first mechanic charged 105 per hour and the second mechanic charged 50 per hour The mechanics worked for a combined total of 25 hours and together they charged a total of 2350 How long did each mechanic work 5 Brandon V of 0

Espa ol In the lab Lucy has two solutions that contain alcohol and is mixing them with each other She uses twice as much Solution A as Solution B Solution A is 18 alcohol and Solution B is 12 alcohol How many milliliters of Solution B does she use if the resulting mixture has 192 milliliters of pure alcohol Number of milliliters of Solution B 0 X 2 P

Solving a percent mixture problem using a linear equation Two factory plants are making TV panels Yesterday Plant A produced 5000 panels Three percent of the panels from Plant A and 10 of the panels from Plant B were defective How many panels did Plant B produce if the overall percentage of defective panels from the two plants was 5 Number of panels produced by Plant B 0 X

problem using a linear Number of pounds of type A coffee Espa ol Kira s Coffee Shop makes a blend that is a mixture of two types of coffee Type A coffee costs Kira 5 85 per pound and type B coffee costs 4 05 per pound This month s blend used four times as many pounds of type B coffee as type A for a total cost of 749 70 How many pounds of type A coffee were used X 1 5 S Brandon V B

1172 49 665 T f 1242 T f 49 0 C I need to see the order of operations Thank you

Dalia is making a blanket from a 4 19 scale diagram The area of the diagram is 32 square centimetres How much fabric will she need for her blanket to the nearest whole number

O GRAPHS AND FUNCTIONS Writing the equation of a secant line Given f x x 3 find the equation of the secant line passing through 4 f 4 and 2 f 2 Write your answer in the form y mx b 0 0 0 8 08 X 5

When laboratory rats are exposed to asbestos fibers some of them develop lung tumors The table lists the results of several experiments by different scientists Asbestos Percent of mice Percent of mice exposure that develop fibers mL lung tumors that developi lung tumors 50 400 500 900 1100 5 6 Asbestos exposure fibers mL 1600 1800 2000 3000 41 36 39 49 27 a Find the regression line for the data Use x for asbestos exposure in fibers mL and y for percent of mice with tumors Round your values to four decimal place

Triangle ABC is drawn on a coordinate plane with A 5 4 B 2 6 and C 2 2 A transformation applied to triangle ABC rotates it 90 degrees clockwise about point A What are the coordinates of C the image of point C A 3 1 B 3 11 C 7 7 D 7 3

Find an equation of the line L L is perpendicular to y 2x in the equation Simplify your answer 8 1 2