Functions Questions and Answers

A fence 30 feet tall runs parallel to a tall building at a distance of 6 ft from the building as shown in the diagram L 0 e LADDER We wish to find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building 30 ft First find a formula for the length of the ladder in terms of 0 Hint split the ladder into 2 parts Type theta for 0 L 0 Now find the derivative L 0 Type theta for 0 L A 6 ft Once you find the value of that makes L 0 first derivative test and then substitute this value into the original function to find the length of the 0 verify that it is indeed a minimum using the shortest ladder Give your answer accurate to 3 decimal places

C implete this quiz to finish the assignment for ALG 2 Period 4 due on Apr 2 Which ratio corresponds to cos35 4 2 4 2 7 8 3 0 7 8 35 3 0 4 2 020778

6 4 WP SS Using the appropriate tables determine the change in specific entropy between the specified states in Btu lb R Show the states on a sketch of the T s diagram a water p 10 lbf in saturated vapor p2 500 lbf in T 700 F b ammonia p 140 lbf in T 160 F T 10 F h 590 Btu lb c air as an ideal gas T 80 F p 1 atm T 340 F p 5 atm d oxygen as an ideal gas T T 520 R p 10 atm p

III Question 20 of Vicy Policion

5 9c is the hypotenuse of the right tria a 12 b 5 c

N Y 2 0 Microliters ml How to Convert 8ng mL to NL ML

Problems 4 are based on the following table which shows the stock market performance of 40 industries from five sectors of the U S economy as of noon on September 11 2015 Take S to be the set of all 40 industries represented in the table Increased X Decreased Y Financials F Manufacturing M Unchanged Z Totals 4 1 Totals 24 3 8 Information Technology T Health Care H 4 Utilities U 3 10 6 1 3 4 Test the following pairs of events for independence a Z M 3 40 8 065 14 7 b X U c Does the fact that a selected industry is a manufacturing industry make it more or less likely that its stock market performance increased Solution

Question 13 o I below are body temperatures from five different subjects measured at 8 AN emperature F at 8 AM emperature 97 7 99 4 97 3 97 1 at 12 AM 98 5 99 9 97 6 96 7 97 5 D 97 9 e temperature at 8 AM be the first sample and the temperature at 12 AM be

list all the possible rational Zeros for P x Show Transcribed Text C Use Synthetic division test which rational numbers in Part a are rational zeros for P X make sure you find all rational zeros and Justify your answer by showing all greps final all the irrational zeroes for Pa make sure You Sostify your answer by showing all the steps

8 Given f x x 5 3 find the equation for f x for the part of the function where x 5 Use a graphing calculator to graph x

ework Part II For y f x 2x5 find Ax Ay a Ax 3

omplete the left half of the graph of y f x in the figure for each of the following conditions f x f x f x f x Choose the correct graph below A Choose the correct graph below DA Q W Q M OB O B W Q F O C HHH O C N Q G Q M 6 Ay O D O D Q Q Q O 1 Q Q G

Sketch the region enclosed by the given curves Decide whether to integrate with respect to a or y Then find the area of the region Area y 1 8 H 2 y 1 X x 2

The graph of f x is shown it goes through the point 2 1 I I I ir 10 5 2 1 5 10 1 2 3 4 5 6 7 8 9 10 Provide two different graph transformations that produce the curve y f x f x from the curve y log x as follows 1 The graph can be obtained from the curve y log x by a horizontal translation followed by a vertical translation Give such a pair horizontal translation by vertical translation by then 2 The graph can be obtained from the curve y log x by a horizontal stretch followed by a horizontal translation Give such a pair horizontal stretch by factor then

4x Addition Rule of Probability Suppose in a math class of 22 students 14 are boys and 8 are girls On the final exam 4 boys and 6 girls made an A grade x If a student is chosen at random from the class what is the probability of choosing a girl or an A student x x 4x A 4x B C D 10 11 A 2 11 6 11 x If a student is chosen at random from the class what is the probability of choosing a boy or an A student 3 11 3 11

Find f t by first using a trigonometric identity Write your answer as a function of s cos t f t f t COS

IS a A term with an x in it O A theorem for raising expressions to different powers An algebraic expression with two terms A mathematical sentence Next Worksheet Worksheet

If triangle MNO is congruent to triangle STR what must also be true M N OS OMN RT OLM ZR 040 S OZM S ONO SR Next R

question 2 of 5 The hypotenuse leg theorem is only applicable with which of the following types of triangles O Isosceles triangles Isosceles and right triangles Obtuse triangles O Equilateral triangles Right triangles

If triangle ACB is congruent to triangle YXZ all of the following are true EXCEPT A C BZ ZZ O ZA O CB XZ O AC YX OAB YZ OZB ZZ Next Y

Create a frequency chart of the data below using 2 4 as your first interval 2 4 10 6 3 9 11 12 2 3 7 7 4 What s the frequency for data values 2 4 A 6 C 5 B none of the above D 4

Watch help video Tanisha read 4 books in 5 months If she reads at a constant rate how many books did she read each month Give your answer as a whole number or a FRACTION in simplest form

Determine if Set of Points is a Function Apr 17 9 53 22 AM Watch help video Which set of ordered pairs represents a function 2 0 5 5 1 3 2 0 O 3 9 3 9 3 5 5 0 O 4 6 1 3 1 1 2 9 O 3 2 3 9 7 6 3 3

Watch help video It cost Adam 5 04 to send 84 text messages How much does it cost to send one text

Through ten games of basketball this season Christopher has made 4 out of 8 of his free throws Which word or phrase describes the probability that Christopher will hit his next free throw O likely O an equal chance or 50 50 O certain

Area of a Circle in terms of pi Apr 17 9 39 09 AM Watch help video The diameter of a circle is 16 in Find its area in terms of Answer A 256 in

Abigail buys a ticket for a raffle with several prizes The probability that she wins a prize is 100 Which word or phrase describes the probability that Abigail will win a prize an equal chance or 50 50 O unlikely O impossible

created question Points 0 of 1 opulation of a town t years after the beginning of the year 2000 is given by 6179 0 026t year 2009 ID YOUR ANSWER TO THE NEAREST PERSON Find the AVERAGE population of the town from the beginning of the year 2 verage population was

Sine Graphs Determine which of the below is a possible phase shift of the following Sine graph O K N 2 O O 2 O X 4

express linnits as bo Iim CX Ax c 844 5 f x dx 1 im E 178 3 v dr

Ol or Clid Eli a A 0 Data set 10 KX G 24 Print B 20 4 8 0 0 6 11 10 6 13 Done ESE C 20 0 7 20 M 10 I X OD 20 0 compute the x and y Sav 10 E

ace RIGONOMETRIC FUNCTIONS ving a right triangle right triangle r answers to the nearest tenth

A TV was discounted by 45 and sold for 580 Whic of the following is the closest to the original value of the TV A 260 B 320 C 1055 D 1 290

C FUNCTIONS etry to find angles of elevation or depression in orrect

3 P LLL Show that if f and f are both analytic on a domain D then f is constant Solution A Kumjian Let D be a domain and let f be a complex valued function such that both f and fare analytic on D Then both Ref f f and Im f f f must also be analytic on D Since Ref and Im f are also both real valued it follows by the theorem on page 50 that both are constant Hence f Ref ilm f is constant

3 Show that if f and f are both analytic on a domain D then f is constant

0 6 Q2 0 7 Total 13 The table shows the number of shots taken by each golfer at the 9th hole of a course one morning Complete the cumulative frequency column no of shots 2 3 4 5 6 7 8 no of golfers f 1 9 14 5 2 0 1 cum freq 1 Find the median lower quartile upper quartile interquartile range shots 2 shots 1 shots 1 shots 1 Ma

triangular pyramid is formed from three right Use the information given in the figure to find th of applicable round your answer to the nearest The lengths on the figure are not drawn accurat K L N 41 85

Suppose that 6 machines can complete a certain task in 6 days If there are 9 machines how many days would it take for them to finish the same task days 27

Use substitution x 3y 18 to solve the system 3x 5y 34 x 0 00 8

Here is a Venn diagram showing the sets A and B as well as the universal set U The numbers shown are elements of these sets U 5 6 1 3 B a An B 0 0 b A c AUB 2 4 7 Find the sets below Write each answer in roster form or as X 0 0

Omar is sitting in a movie theater 5 meters from and the angle of depression from his line of sigh

TRIGONOMETRIC IDENTITIES AN Finding solutions in an inter all solutions of the equation in sin 0 1 0 your answer in radians in terr re is more than one solution s

e the method of this section to solve the linear programming problem Minimize C 2x 3y 6z subject to x 2y Z 11 x 2y 2z 10 3z 12 2x 4y x 0 y 0 z 20 e minimum is C at x y z

The graph with the equation y sin x sin 7x cos x cos 7x 0 2 by 2 2 1 viewing rectangle a Describe the graph using another equation b Verify that the two equations are equal a Write another equation of the given graph Type an equation using x as the variable is shown in a e Q 57

3 Find all zeros and periods of cosh z and sinh z

Divide using synthetic division 16 16 Simplify your answer Do not factor

Which of the following is the complete list of possible zeros of the given function OA OB f x x x 4x 3x 15 O C 15 1 13 5 13 3 515 1 13 15 15 3399 5 1 5 H 1 3 3 O D The function has no rational zeros H 59

Determine whether the function is a polynomial function If it is identify the degree g x 6x x 1 Choose the correct choice below and if necessary fill in the answer box to complete your choice OA It is a polynomial The degree of the polynomial is OB It is not a polynomial

In a recent study 25 males used a new weight loss supplement and 20 of them experienced weight loss after two weeks In the same study 50 females used the same supplement and 44 of them experienced weight loss after two weeks Fill in the blanks below to make the most reasonable statement possible The new weight loss supplement was less effective on Choose one in the study That is because only of them lost weight after two weeks whereas of the Choose one lost weight after two weeks X