Application of derivatives Questions and Answers

A science teacher presented a balloon to his class and posed the question If I keep this balloon in the freezer overnight what will occur He followed up with How certain are you of your answer The teacher recorded his students responses Certain Uncertain Shrink 2 5 Expand 1 2 What is the probability that a randomly selected student believes the balloon will expand given that the student was uncertain Simplify any fractions

Find mZF in rhombus DEFG E D U 51 3u 29 F G

Note To type in the sign type For example to enter the Domain 10 x 10 you would type 10 x 10 85 4 3 2 1 Domain written in Interval Notation Range written in Interval Notation 5 fa 3 2 1 2 25 4 5 y N 3 X 5 q Domain written in Set Builder Notation x Range written in Set Builder Notation

hich of the following sequences is divergent elect one a 1 O b n C O d 2n 2 n 1 n 100 O e n

Complete the congruence statement I 29 yd F H 23 yd G S T R 29 yd 23 yd

A sociology teacher asked his students to complete a survey at the beginning of the year One survey question asked Do you consider yourself responsible Another question asked How many siblings do you have Irresponsible Responsible 0 siblings 1 or more siblings 4 3 4 7 What is the probability that a randomly selected student has 1 or more siblings given that the student is irresponsible Simplify any fractions

If GH 4b 81 and GJ b find GJ in parallelogram HIJK K J I GI G H

a Find the inverse function of f f x b Graph fand f 1 on the same set of coordinate axes Select Update Graph to see your response plotted on the screen Select the Submit button to grade your response Update Graph 8 domain of f 7 range of f 6 domain of f 1 5 The graphs of f and f 1 are reflections of each other across the line 4 3 2 1 y 4 2 1 1 2 3 4 5 6 7 L 8 c Describe the relationship between the graphs Enter a mathematical equation in terms of x and y d State the domain and range of f and f 1 Enter your answers using interval notation 1 2 X

Kelly has 300 ft of garden edging he wants to use to make some planters in his back yard He wants to build the gardens in such a manner as to create four equal sized rectangular gardens sharing no sides within the yard What are the dimensions that will produce the maximum enclosed area Round your answer to 1 decimal place Length Number ft Width Number ft

Which rule explains why these triangles are congruent J K SSS G H AAS

Write the expression as a logarithm of a single quantity In x 93 In x 44

What are the corresponding parts of the figures below Select all that apply G 28 cm 17 cm IF TQ H 13 cm 27 cm I ZG ZR Q 27 cm ZIZT T 28 cm 13 cm S 17 cm R HI ST

Which rule explains why these triangles are congruent Q S SSS N AAS P These triangles cannot be

What values of x and y make ARST AGHI R T X y 5x 8 y 8 S H 15 G 5y x

4 17 Matching Pick the letter of the graph that goes with each numerical value listed below for the correlation Correlations 0 767 0 299 0 980 A Total Value thousands of dollars B 6 Acreage Mean IQ 5432 1 0 500 Acreage 400 300 C 100 200 100 95 A 6 90 500 1000 1500 2000 2500 3000 3500 Area square feet 85 80 5 CONFO 500 1000 1500 2000 2500 3000 3500 Area square feet B TT 4 18 Matching Pick the letter of the graph that goes with each numerical value listed below for the correlation Correlations 0 903 0 374 0 777 20 T 30 40 50 60 Mean Age 900 70 B 100 90 80 C Salary thousands of dollars per year Salary thousands of dollars per year 0 87 0 47 0 67 60 50 40 Height inches 70 60 Strike Outs 50 A 74 72 70 68 66 30 20 1985 4 19 Matching Match each of the following correlation corresponding graph 62 60 B 260 240 220 200 180 160 140 120 100 0 2 5 6 1990 1995 2000 2005 2010 Start Year 8 10 12 7 IrishBlazeFighter 4 6 Education years U 8 9 10 11 12 Shoe Size T 2 2 2 4 2 6 2 8 3 0 3 2 3 4 3 6 ERA Source StatCrunch 2011 MLB Pitching Stats accordin

Complete the congruence statement F 74 G 141 80 65 H U H 65 T 141 74 S 80 R 20

Which rule explains why these triangles are congruent G B ASA SAS A F C SSS These triangles cannot be A

What values of v and w make AGHI AYZX H I W 15v 6w G W 15 N V 42

To get to know her students better Ms Olson surveyed her math students to determine what hobbies and school subjects they prefer Athletics The arts Math Literature 6 6 4 4 What is the probability that a randomly selected student prefers the arts given that the student prefers math Simplify any fractions

Complete the congruence statement F 15 ft G 0 25 ft 25 ft E 15 ft D 15 ft P 25 ft 25 ft M 15 f

What values of u and v make AWXY AQRP X Y U 5u 3 16v W 19v 6 R 4u 16

Use the FTC Part 1 to find the derivative of the function F x x et dt

21 22 23 The probability that there will be a thunderstorm in Los Angeles tomorrow is 7 1 and independently the What is the probability that probability that there will be a thunderstorm in San Francisco tomorrow is there will be a storm tomorrow in San Francisco hut not in Los Angeles Write your answer as a fraction Find the logarithm of log 9 without using a calculato If M x a hx c h 2 7 and h 2 5 what is the value of b tm 3

Keypad X AVUNE 0 T 0 x NZQRC a B02 H T O e log In e x d DA V sin cos tan 1 csc sec cot 1 sin cos tan cse 1 sec cot ens in new window f g 9 18

Keypad 1 x AVUNES O 2 a B02 HA log in e 11 DO NZQRC D 8 2023 Hawkes Learning CO apA V 0 0 0 20 BAAR 3 4 opens in new window 888 f x x x and g x 3x 4 f g 4 MacBook Pro

Use the graph to the right to write an equation of the line The equation is Type your answer in point slope form Use integers or simplified fractions for any numbers in the equation 6

For the graph to the right indicate if a correlation exists between the quantities on the horizontal and vertical axis If so indicate if the correlation is a strong positive correlation a strong negative correlation a weak positive correlation a weak negative correlation or no correlation Choose the correct answer below O A Strong positive correlation OB Weak positive correlation OC Strong negative correlation D Weak negative correlation E No correlation

One angle of a triangle is three times as large as another The measure of the third angle is 50 more than that of the smallest angle Find the measure of each angle The measure of the smallest angle is The measure of the second largest angle is The measure of the largest angle is

Determine the measure of x MAX Type a whole number 102 99 X

Consider the function f x x 3x on the closed interval 3 x 2 a Find where the global maximum and global minimum occur b What are the global maximum and global minimum values from part a

Ough e Determine the total number of observations Determine the width of each class Determine the midpoint of the second class Determine the modal class or classes Determine the class limits of the next class if an ditional class were to be added The total number of observations is 10 17 18 25 26 33 34 41 42 49 50 57

5 Use the method of variation of parameters to find the general solution of the following system 2 1 x 2 x X X 1 3t

a Suppose g is a differentiable If f x 2g x ln g x x function with g 1 2 and g 1 1 find f 1 Express your answer as a single number

Consider the recurrence relation a 3a IL 2 with base condition a 2 n 1 0 a Use iteration to obtain an explicit formula closed form for the nth term in this sequence b Prove using induction that this formula satisfies the recurrence relation

900 A marketing group determines that the demand equation for a barstool can be modeled by p where p is 0 4 the price in dollars and q is the number of barstools The cost for manufacturing and shipping is 100 per stool A Find the Revenue Cost and Profit functions

e average cost of a turntable is given by C x 140 000x 30 0 02x dollars per turntable Week oduction is currently 3 000 and is increasing at a rate of 120 turntables per week What is the average cost of producing 3000 boats 3 How is the average cost changing per week Is it increasing or decreasing dx Hint Find dC dt when x 3 000 and 120 dt

emaker of a candy that comes in colors gives the portion of each color as shown A candy is ected at random from each of two bags Find the bability that the two candies have the following or s Color Proportion Brown 0 2 Red 0 1 Yellow 0 2 Green 0 2 Orange 0 3 hat is the probability that one candy is yellow and the other is red

20 15 10 5 y 20 15 10 0 10 15 20 5 10 15 20 Show Transcribed Text X

Find the Fourier series of f on the given interval f x e X f x 2 C Give the number to which the Fourier series converges at a point of discontinuity of f If f is continuous on the given interval enter CC

Sketch a possible graph of a function f x that satisfies the following conditions f x 0 on 1 f x 0 on 1 f x 0 on 2 and 2 00 f x 0 on 2 2 lim f x 2 8118 lim f x 0

d the minimum and maximum values of z 7x 6y if possible for the following set of con 3x 4y z 12 x 4y 28 x 20 y 20 lect the correct choice below and if necessary fill in the answer box to complete your choir A The minimum value is Round to the nearest tenth as needed B There is no minimum value

Question 4 7 2 7 Part 1 of 2 e the following linear programming problem imize z 10x 12y ject to 3x 8ys 24 10x y 24 x20 y20 maximum value is

L 2 Kaity has 2000 linear feet of fence and wants to enclose a rectangular field with it for her farm animals The field will border a straight river and she needs no fence along the river What is the largest area she can enclose P 21 2 A W W 2l 20 2 000 000 2l u 31

Picos co 5 Consider the function f x x 3x2 on the closed interval 3 x 2 a Find where the global maximum and global minimum occur f x x 3x2 2 1 f x 3x 6x f 3 3 3 6 3 f 3 27 18 9 with f x not test endpoints a 3 2 6 2 2 12 12 24 why f 0 x f x x 3x 439 3 3 posible locations of extrema from here 247 how do you find posi q b What are the global maximum and global minimum values from part a Global maximum is

Points DETAILS PREVIOUS ANSWERS Find the interest rate needed for an investment of 4 000 to grow to an amount of 4 400 in 5 months if interest is compounded monthly Round your answer to the nearest hundredth or a pel point 0 83 X

Find the derivative of the function f x In 4x f x 1 4x X

00 Calculate the sum of the series a whose partial sums are given S 6 3 0 6 n n 1

Online Video Viewers As broadband Internet grows more popular video services such as YouTube will continue to expand The number of online video viewers in millions is projected to grow from 2008 through 2013 according to the rule N t 135e0 067t 1 t 6 where t 1 corresponds to 2008 Round your answers to one decimal place a How many online video viewers were there in 2011 176 5 million b How fast was the number of online video viewers changing in 2011 million per year 1 Enter a number

Find the derivative of the function x ex 3 f x

Listen Determine the volume of the solid obtained by rotating the region bounded by the given curves about the specified line y ln x y 1 y 3 x 0 about the y axis e6 e O e6 e 2 none 2