Application of derivatives Questions and Answers

the area of the region that is trapped between the curves y 4x and y x HINT Draw a picture

1 0 0 8 0 6 0 4 0 2 Y b Find of 2xre da in two ways i Using the Fundamental Theorem of Calculus ii Numerically using a right Riemann sum with n 5 You can use the graph of 2xe below 0 2 0 4 06 09 C

4 Find the area of the region that is trapped between the curves y 4x and y x HINT Draw a picture

c Simpson s Rule is a method of approximating antiderivatives TRUE FALSE

Question 13 of 20 Step The function f is given by the graph below 10 tat HOA Enable Zoom Pan

b If F x G x then F x G x TRUE FALS

0 5 The sequence is geometric Find a the common ratio b the eighth term c a recursive rule for the nth term and d an explicit rule for the nth term 3 6 12 24

6 The fifth and ninth terms of an arithmetic sequence are 5 and 17 respectively Find the first term and a recursive rule for the nth term

1 Find the first 6 terms and 100th term of the explicitly defined sequence

1 Using Venn Diagrams A and B are events in a sample space S such that P A 0 7 P B 0 4 and P A and B 0 2 a Draw a Venn diagram showing the overlapping sets A and B and fill in the probabilities of the four regions formed b Find the probability that A occurs but 8 does not e Find the probability that neither A nor B occurs d Find the probability that A or B occurs e Are events A and B independent That is does P A B P A

44 Find the cube roots of 1 i Leave the answers in polar form What is one answer A 2 cos 255 i sin 255 2 cos 275 isin 275 C V2 cos 285 i sin 285 D 2 cos 255 i sin 255 B

consider two normal distributions one with mean 6 and standard deviation 12 the other with mean 1 and standard deviation 12 Answer th ollowing statements using true or false The two distributions have the same shape answer b The two distributions are centered at the same place answer

2 If it rains tomorrow the probability is 0 8 that John will practice his piano lesson If it does not rain tomorrow there is only a 0 4 chance that John will practice Suppose that the chance o tomorrow is 60 What is the probability that John will practice his piano lesson Hint It will help to draw a tree diagram 5 There are two pra sleidus pections Wan

9 Use logarithms to evaluate 30 00484 What is the logarithm of the answer A 7 2283 10 B 8 5616 10 C 9 5616 10 D 9 228310

45 Solve for the unknown part of the triangle if it exists If c 74 b 48 and C 74 then what does B A 45 10 B 17 50 C 25 20 D 38 30

46 Solve for the unknown part of the triangle if it exists If c 74 b 48 and C 74 then what does A A 20 18 B 67 30 C 42 45 D 28 15

Suppose the scores of students on a Statistics course are Normally distributed with a mean of 372 and a standard deviation of 70 What percentage of the students scored between 372 and 512 on the exam Give your answer to 3 significant figures percent

32 log10 x 9 log10 x 1 x A 10 B 10 1 C 1 D 1 10

35 Solve the equation for x and y x 2 4i 6 y 3 i A x 8 y 7 B x 6 y 1 C x 4 y 7 D x 4 y 5

37 Change 3 cos 300 i sin 300 to rectangular form A 3 2 31435 31 3 B 3 3 3i 2 C 3 3 3i 2 2 3 D 3i 3 2 2

27 x log4 5 x A 1 2 B 42 C 2 4 D 86

31 Perform the indicated operation leave the answers in the rectangular form a bi 3 91 4 71 A 1 16i B 7 2i C 1 2i D 7 16i

15 Transform from rectangular coordinates to polar coordinates 2 2 A 2 315 B 2 315 C 2 45 D 2 315

4 Solve the triangle for the unknown parts c 61 2 A 38 10 B 74 30 a A 41 0 B 63 9 C 61 2 D 38 5

5 Change the polar coordinates 4 120 to rectangular coordinates A 2 3 2i B 2 2i 3 C 2 3 21 D 2 2 3

11 Evaluate the expression log3 200 A 3 475 B 2 381 C 4 823 D 0 207

1 Find the indicated product Leave the answer in polar form 6 cos 38 i sin 38 x 3 cos 62 i sin 62 A 9 cos 24 i sin 24 B 18 cos 100 i sin 100 C 9 cos 100 i sin 100 D 18 cos 24 i sin 24

Nellie is shopping for a new bicycle She is most interested in color and type of tires Red Green Road bike tires Mountain bike tires 2 4 6 4 What is the probability that a randomly selected bike is green given that the bike has road bike tires Simplify any fractions

15 Show that the limacon y t 1 2 cost cost 1 2 cost sin t is a regular curve such that y t 2 y t for all values of t but th 7 is not a simple closed curve

Find the average value of the function f x 6 sin x on the given intervals a Average value on 0 2 help numbers b Average value on 0 c Average value on 0 2

Find the curl of the vector field F 6 F x yzi xyzj xyz k curl F Oi Oj Ok

Find zw Leave your answer in polar form z 6 cos K cos isin 6 7k 9 X w 9 cos isin zw cos isin Reduce any fractions Describe the angle using radians between 0 and

10 Find the area enclosed by these two curves y x 2 y x

Use the following 3 5 9 12 110 The mean is 8 The standard deviation is 3 87 Round to the nearest hundredth as needed b Multiply each number in the distribution by 3 and compute the mean and the standard deviation of this new distribution The mean is 24 The standard deviation 11 61 Round to the nearest hundredth as needed c Multiply each number in the original distribution by 9 and compute the mean and the standard deviation of this ne distribution The mean is

ere are 85 students in a college mathematics class Five students are chosen to work on a project together How many different groups of five students SS

Five doctors are selected at random from a hospital employing 27 doctors to fill out a questionnaire is this a permutation or com Select one a permutation Ob combination A44 club of 16 members is choosing a committee of three made up of a president secretary and treasurer is this a permutation of Select one a permutation Ob combination

Determine whether the series is convergent or divergent 1 3 32 64 2 3 4 O convergent O divergent 1 8 3 16 If it is convergent find its sum If the quantity diverges enter DIVERGES DIVERGES

K A ball is thrown upward and outward from a height of 5 feet The height of the ball f x in feet can be modeled by f x 0 3x 1 7x 5 where x is the ball s horizontal distance in feet from where it was thrown Use this model to solve parts a through c a What is the maximum height of the ball and how far from where it was thrown does this occur The maximum height is feet which occurs feet from the point of release Round to the nearest tenth as needed b How far does the ball travel horizontally before hitting the ground feet Round to the nearest tenth as needed c Graph the function that O A A 25 20 15 10 5 0 0 5 10152025 Horizontal Distance models the ball s parabolic path Choose the correct graph below OU OB 25 20 154 10 5 of 0 5 10152025 Horizontal Distance Q O C 25 20 15 10 5 4 0 7 0 5 10152025 Horizontal Distance SU O D 14619 25 20 15 10 of 11 0 5 10152025 Horizontal Distanc

What values of w and x make AQRS ACBD Q R 11 X 9w X 7 8x 49 S B 3x 11 6x W 27 D C

Homewor A weight loss clinic guarantees that its new customers will lose at least 5 lb by the end of their first month of participation or the loss of weight of customers at the end of their first month is normally distributed with a mean of 6 6 lb and a standard deviation of 0 81 lb find the percent of customers who will be able to claim a refund Click here to view page 1 of the standard normal distribution table Click here to view page 2 of the standard normal distribution table of customers will be able to claim a refund Round to the nearest tenth as needed

Evaluate the limit using L H pital s Rule if necessary If the limit is infinite enter o or as appropriate If the limit does otherwise exist enter DNE sin 2x lim x 0 sin 3x

What values of w and x make AHIJ AACB H 14W x 2 W 11 X X 37 I C 10x W 44 B 3x 19 A

Complete the congruence statement B CDAB S R

Which angles are corresponding angles N Q T R ZSRO and ZPOM M P S ZSRO and ZNOM

Abdul entered his sister into their town s Smelly Shoe Competition Abdul observed contestants of all ages proudly strutting around wearing different kinds of smelly shoes Under 18 18 or older Tennis shoes High heels 5 2 6 3 What is the probability that a randomly selected contestant is under 18 given that the contestant is wearing tennis shoes Simplify any fractions

After growing tired of squinting while driving Jackson went shopping for a pair of sunglasses He tried on glasses with different frames and lenses Polarized lenses Regular lenses Cat eye frames Browline frames 3 5 3 8 What is the probability that a randomly selected pair of sunglasses has browline frames given that the pair of sunglasses has polarized lenses Simplify any fractions

Watch the video and then complete parts a through g below Click here to watch the video Use the frequency distribution to the right to complete parts a through g b What is the mode of the data set 15 Type a whole number c How can the mode of any frequency distribution be identified X f 10 2 14 15 20 25 NE NU 6652N T OA The highest value in the data column OB The sum of the values in the frequency column OC The highest value in the frequency column OD The value in the data column corresponding to the highest value in the frequency column

the formula for the sum of the first n terms of a geometric sequence to solve this the sum of the first 12 terms of the following geometric sequence 2 6 18 54

What is the sum of the series Round to the nearest whole number 42 7 429 6

Use logarithmic differentiation to find dy dx y x6 x 6 9 1 log x 2 dy dx X