Sequences & Series Questions and Answers

The height in feet of a ball thrown by a child is modeled by the quadratic equation 1 12 f x 1 2x 3 where I is the horizontal distance in feet from the point at which the ball is thrown Use f to answer the following questions Round solutions to three decimal places if necessary How high is the ball when it leaves the child s hand feet How far away from the child does the ball reach its maximum height feet What is the maximum height the ball feet How far from the child does the ball strike the ground feet

The flow system shown in the figure is activated at time t 0 Let Qi t denote the amount of solute present in the ith tank at time t Assume that all the flow rates are a constant 10 L min It follows that the volume of solution in each tank remains constant assume this volume to be 1000 L The concentration of solute in the inflow to Tank 1 from a source other than Tank 2 is 0 7 kg L and the concentration of solute in the inflow to Tank 2 from a source other than Tank 1 is 0 kg L Assume each tank is mixed perfectly a Set up a system of first order differential equations that models this situation 1 50 HGGI 1 100 Qi Q 1 100 1 50 2 b If Q 0 30 kg and Q2 0 30 kg find the amount of solute in each tank after t minutes Q t kg Q t kg 7 0

If cos a 0 118 and cos 3 0 546 with both angles terminal rays in Quadrant l find the values of tan a Your answers should be accurate to 4 decimal places

Example Use Theorem 4 to find the horizontal asymptote s for the following functions 8x42x 10 3x 3x x 3x 2x 2 4x 7x x a y b y 10x6 5x 13 1 2x 3x 4 c y

Which of the following power functions is the most dominant in the long run Of x 1000x O g x 3x4 Oh x 99x Om x 101x

3 a Find f 1 b Find f 3 4 c Find x if f x 3 2 d Find the domain of f x e Find the range of f x 2 f x 5

According to a particular test a normal score is 400 It can be shown that anyone with a score x that satisifies the 1 23 has an unusual score Determine the scores that would be considered unusual X 400 inequality 11 What values of x represent an unusual score Select the correct answer below and fill in the answer box es to complete your choice Simplify your answer O A Test scores between and would be considered unusual OB Only test scores less than would be considered unusual OC Test scores less than or greater than would be considered unusual OD Only test scores greater than would be considered unusual

In a pet store the ratio of dogs to cats is 5 4 If there are a total of 27 dogs and cats in the store how many dogs are there

Write the fraction as an equivalent fraction with the given denominator 56 5 11 6 36

Solve for all possible values of x x 6 5 17 Ox 6 Ox 18 Ox 138 Ox 150

Multiply 4 i 1 5 09 19 O 1 19 04 5 01 19i 5 2

01 08 MC Simplify 8j 5j 3 5j 7j 12j 7 O 3j 12j2 15j 10 O 3j 12j 12j 4 O 3j 2j 12j 10 O 3j 2j2 12j 4

5 2x 7 3 28 X X

MATHEMATICS Proposition 3 Let x J 0 y J be two solutions of the initial value problem dx f t x x t xg dt then x t y t for all 1 JOJ Proof Recall that both x and y being solutions of the initial value problem satisfy the integral equations on their domain intervals x 1 x f s x s ds y 1 x f s y s ds Therefore x 1 y 1 ff s x s f s y s ds which implies 10 x 1 y 1 0 S 5 x s s y s 0 SK x s y s for all t2te 40 Applying Gronwalls result with A 0 we get 0 x 1 y 1 0 for all t t This gives the desired equality x t y t for all tJJ Towards the uniqueness of the solution of the initial value problem 3 we consider all the solutions of the initial value problem 3 Let the totality of them be denoted by x J XEA the solutions x being thus indexed by a suitable indexing set A Above we have verified that any two solutions say x and xare equal on the overlap of their domains Therefore we patch together all the solutions to get a maximal solution is the solution defined on the largest open interval It is obtained as follows Let J UJ 2 A clearly Jis an open sub internal of I with XJ and all the solutions x patch up to get a solution x J of the initial value problem 3

What is the slope of the line y 2 2 x 3 Choose 1 answer B 1 1 2 O 1 Google Classroom

on the right are four functions each using one of the function representations we ve learned about in this lesson se functions f x g x h x and p t to answer the questions on the left Evaluate f 5 f 5 H Determine z when f x 1 g 57 Determine z when g x 37 h 8 Evaluate g 57 2 Determine when h x 27 p 18 Evaluate h 8 Evaluate p 18 Determine t when p t 13 15 t p t 4 3 2 S f x 3 du 1 2 3 y 2 on 4 X g x 2 15 2 7 10 37 19 23 33 18 37 60 42 57 57 58 76 52 80 1 13 15 18 19 25 28 45 60 85 89 100 94 18 13 75 93 90 48 h x 24x 3 112 17

interval 3 3 X d Interval 2 2 2 12 X f x 3 0 2 3 1 4 0 3 1 0 2 3 5 20 0 LO 5 12 2 4 5 6 12 10

Divide using synthetic division 4 2 2z 3z 35z 27z 22 Z 3 2 2z 3z 35z 27z 22

Write the point slope form of the equation of the line through the given point with the given slope 8 through 2 1 slope 1 A y 2 x 1 B y 2 x 1 C y 1 x 2 D y 1 x 2 9 9 through 5 5 slope A y 5 x 5 B y 5 x 5 C y 5 x 5 D y 5 x 5

Any leftover acetylcholine still floating around in the synaptic cleft will either diffus away or get degraded by an enzyme called acetylcholase acetylcholinase acetylcholinesterase

Solve A 27 m B C D 117 13 m 9 m m m 3 3 243

1 REVIEW SUM 1 Q2 Find the slope of each line GIVEN a graph or an equation 2 2 3 25 5y 8 x Find the slope of the line through each pair of points 5 12 7 19 15 6 Find the slope of each line 5 7 y x 2 3 V 4 4 x 3 3y 6 10 2 7 16

n k 1 2 k 3 i 2 j 0 3i j k

s stepped onto an escalator moving at a constant rate The table below shows his distance from the first floor after different Time seconds 6 9 Distance centimeters 980 890 swer the following questions 12 15 800 710 a Choose the statement that best describes how the time and his distance from the first floor are related Then give the value requested O As time increases his distance from the first floor decreases At what rate is his distance from the first floor decreasing centimeters per second As time increases his distance from the first floor increases At what rate is his distance from the first floor increasing centimeters per second b What was Boris s distance from the first floor when he stepped onto the escalator centimeters 8 08 X

Use the distributive law to find the product 5a 1 ai 1

Click here to watch the video Divide the polynomial by the monomial Check the answer by showing that the product of the divisor and the quotient is the dividend 4 33x 39x 6x 3x 2 33x39x 6x 3x Simplify your answer

From the function s graph identify and interpret its maximum O The function s maximum is 2 385 000 at x 5 This implies the company s maximum annual revenues from selling the cookers will be 2 300 000 This happens if the company raises the unit price by 5 00 five times O The function s maximum is 2 250 000 at x 5 This implies the company s maximum annual revenues from selling the cookers will be 2 250 000 This happens if the company raises the unit price by 5 00 making the unit price 55 dollars O The function s maximum is 2 250 000 at x 5 This implies the company s maximum annual revenues from selling the cookers will be 2 250 000 This happens if the company raises the unit price by 5 00 five times making the unit price 50 25 75 dollars The function s maximum is 2 250 000 at x 5 This implies the company s maximum annual revenues from selling the cookers will be 2 250 000 This happens if the company makes the unit price 5 00 Harry runs a firework business and needs to calculate how high fireworks fly He fires a firework into the air on a hill 100 feet ab level The height of the firework s trajectory can be modeled by the polynomial function in the following graph 160 140 120 100 80 60 40 201 y g 0 2 0 4 0 6 0 8 10 12 14 16 18 20 22 24 2 6 2 8 3 0 32 34 3 6 3 8 4 0 4 2 4 4 4 6 4 8 mat

Use the unit circle along with the definitions of the circular functions to find the exact values for 3 2 the given functions when s Select the correct choice below and fill in any answer boxes in your choice A O A sin Part 2 of 3 3 1 2 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression B The solution is undefined Select the correct choice below and fill in any answer boxes in your choice COS sin O 32 3r 1 32 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression OB The solution is undefined Points 0 of 1 COS 3r 2 n tan 3x 2

Locate and interpret the function s maximum O The function s maximum is 2 2 at x 6 2 It implies the stock s price hit the maximum of 2 20 at 2 12 p m O The function s maximum is 8 at x 7 1 It implies the stock s price hit the maximum of 8 00 at 3 06 p m O The function s maximum is 7 2 at x 8 It implies the stock s price hit the maximum of 7 20 at 4 00 p m O The function s maximum is 6 2 at x 2 2 It implies the stock s price hit the maximum of 6 20 at 10 12 a m Johan is observing some suspicious activities on a web server The following graph shows the web server s CPU usage in the past 10 minutes TCPU Usage in Percent

f 2 2 62 5 Does the parabola defined by fopen upward or downward O Downward O Upward Determine the vertex in z y form of the parabola defined by f Is the vertex the maximum or minimum value of f O Minimum O Maximum Determine the y intercept in x y form of the parabola defined by f Determine the x intercept s in x y form of the parabola defined by f If multiple x intercepts exist enter the solutions using a comma separated list If no z intercepts exist enter DNE

11x 4 X 1 www The solution is Type your answer in interval notation Use integers or fractions for any numbers in the expression Type an exact answer

x x 8 16 Determine the vertex of the parabola in x y form Determine the y intercept of the parabola in x y form Determine the x intercept s of the parabola in x y form If mulitple intercepts points using a comma separated list If no x intercepts exist enter DNE

d the exact value COS Type an integer or a fraction Type an exact answ

Question 1 3 2 1 Find the exact length of the arc intercepted by the given central angle in the figure to the right The length of the intercepted arc is Type an exact answer in terms of Use integers or fractions for any numbers in the expression Points 0 of 1 2x 12 3

How many solutions does the following system have 2x 3y 1 1 3x 2y 1 1 1 point O infinitely many solutions O two solutions

Question 11 Use the distributive law to find the product z 5z 4z

y f x Ay K 3 OA 1 5 29 y g x OB 0 20 OC 25 O D

Use the figure shown to the right and the given values to find sin 0 b and c 0 45 a 7 sin 0 0 b Type an integer or decimal rounded to three decimal places as needed

The value of sin 30 is not Why is this true Choose the correct answer below A Since the value of sin 30 is B Since the value of sin 30 is 3 2 1 2 1 the value of sin 30 is not the value of sin 30 is not 1 2 1 2 is 12 Oc In the expression sin 30 30 means 30 radians the value of sin 30 is 2 OD Since the value of sin 30 is 0 9880 the value of sin 30 is not while the value of sin 30 is

onvert the following degree measure to radians 60 Question 8 3 1 17 Points 0 of 1 60 radians Simplify your answer Type an exact answer using a

Use elimination to determine whether the followin system has no solution or infinitely many soluti 25x 20y 70 20x16y 2 Choose the correct answer below OA There are infinitely many solutions B There is no solution

6 Shayna completes of a project in of an hour How many hours will it take her to complete the entire project

At a parking lot the attendant can wait on 50 people per hour If people arrive randomly at an average rate of x cars per hour the average number of cars N waiting to exit the lot is given by the equation below where x 50 Complete parts a and b x N x 3000 60x a Approximate x when N x 7 X Round to the nearest whole number as needed

Graph y f x Use division factoring or transformations as an aid Show all asymptotes and holes 2x 11x 15 2x 9x 10 f x Choose the correct graph below O A Ay O B Ay SOU MIXE O C Ay O Points 0 of 1 D

Solve the equation x 12 X 4 X Type an integer or a simplified fraction Use a comma to separate answers as nee

The graphing calculator screen below displays the percentage of an adult brain y for a child at age x where 1sxs11 LnReg Use this information with numbers rounded to the nearest whole number to find the percentage of an adult size brain a child has at age 6 Round to the nearest whole number as needed 85 82 84 y a blnx a 29 23236624 b 30 26661497 83

The function P x 0 45x 87 models the relationship between the number of pretzels x that a certain vendor sells and the profit the vendor makes Find and interpret P 900 Profit Made on Pretzel Sales 1000 900 800 700 600 500 400 Profit dollars 300 200 100 500 600 700 800 900 1000 Number of Pretzels Sold 813 813 is the profit the vendor makes from selling 900 pretzels 405 900 is the profit the vendor makes from selling 405 pretzels 900 900 is the profit thovendor makes from selling 900 pretzels

A sofa regularly sells for 690 The sale price is 552 00 Find the percent decrease of the sale price from the regular price

cm Find the area of the figure 6 cm 1 L 16 cm A cm Area of a rectangle lw 1 length w width bh Area of a triangle 2 b base h height USE A

Multiply 2 16 1 25 2 16 1 25 Simplify your answer Type your answer in the form a bi Type an exact answer using radicals