Heights & Distances Questions and Answers

cose 5 13 Sketch the triangle represented then find the sine tangent ratios

HW 1 Identify the relationship between ZA and ZB lb work Complete problems 1 8 for independent practice b When you are finished check the solutions with your teacher keres Vertical Angles Complementary Angles Supplementary Angles 3 Identify the relationship between ZA and ZB a Vertical Angles Complementary Angles Supplementary Angles 2 Identify the relationship between LA and LB Vertical Angles Complementary Angles Supplementary Angles 4 What is the value of b b b 64

ANGLE ANGLE SIDE In 3 4 find the length of the indicated side d x x y y and use a protractor to measure the indicated angles Mark congruent angles and sides If the triangles are congruent write a triangle congruency statement by AAS 3 A CB FD C B 8 6 4 2 4 6 8 8 6 4 2 0 2 m C m E Congruence Statement 4 6 8 F E m A m F 4 JQ 8 6 4 2 W F FM 8 64 4 2 2 4 02 4 8 m W M Congruence Statement 6 m F R 9 m R m J

10 A function has a vertical asymptote at x 3 and is concave up when x 3 Determine lim f x and explain your reasoning

When the common stock is reacquired at cost higher than issue cost requires a Debit to Loss on Repurchase of Common Shares Option B is correct This done when Par Value method is used Journal Entry for reacquisition of Common Shares in above case will be Credit Account Titles and Explaination Treasury Stock Loss on Repurchase of Common Shares Cash Debit Par Value based on Avg issued price Excess Paid to reacquire over and above par value Total Amount Poid to reacquire shares Explanation is written in Debit and Credit Coloums to understood what values are written Now Also note in the case when shares were initially issued at price higher than par value Then instead of using Loss on Repurchase of Common Shares Account we will use credit balance of Addition Paid in Capital It will be debited instead of Loss on Repurchase of Common Shares Hope you understood the concept if any query feel free to ask in comment section

Stars appear to be white to the naked eye because they emit a mixture of all colors of light However when photographed stars show a range of colors due to their different surface temperatures The coolest stars emit primarily red light while hotter stars emit more blue light This is because hotter stars emit more energy and this energy is released in the form of shorter wavelengths of light such as blue and violet The color of a star can be determined by measuring its spectrum which is the distribution of light that it emits across different wavelengths The wavelength at which the intensity of light reaches a maximum is called the peak wavelength Wien s Law relates the peak wavelength of a star to its surface temperature Surface Temperature 2 98 10 6 K Peak Wavelength nm Where the peak wavelength is measured in nanometers nm and the temperature is measured in Kelvin K For example the Sun has a peak wavelength of about 500 nm Using Wien s Law we can calculate that its surface temperature is about 5800 K The following table shows the relationship between star color and surface temperature Color Red Orange Yellow White Blue Surface Temperature K 3000 3000 5000 5000 6000 6000 7500 7500 Export to Sheets Astronomers use the color of stars to classify them into different types The most common classification scheme is the Morgan Keenan system which divides stars into seven spectral classes denoted by the letters O

10 A function has a vertical asymptote at x 3 and is concave up when x 3 Determine lim f x and explain x 3 your reasoning

3 The measure of two vertical angles are given by the expressions x 3 and 2x 7 Find the value of x What is the measure of each angle

glacier is a mass of ice on land that flows under its own weight due to gravity Which way does a glacier flow Downhill Uphill Depends on the temperature The glacier shown in Cross Section 1 is flowing downhill due to gravity A spike was put in the glacie at the arrow On Cross Section 1 draw an arrow showing the direction that the glacier is moving Imagine the glacier in Cross Section 1 shown is now shrinking due to warming temperatures Which diagram in Cross Section 2 A or B shows where the spike will be found in several years Explain your choice Two students are discussing which way glacier ice moves when a glacier is shrinking Student 1 Glacier ice always flows downhill because of gravity and A shows the ice flowing downhill The glacier shrinks because it melts faster than the glacier is flowing Student 2 I think the ice would flow backwards and carry the spike with it as shown in B Because the glacier is shrinking the ice would flow uphill I With which student do you agree Why rt 2 Glacier budget When a glacier is getting smaller it is often said that it is retreating Explain why this term may cause confusion in understanding how a glacier moves The amount of ice in a glacier is a balance between additions e g snowfall and subtractions e g melting a On Cross Section 3 circle where most material leaves the glacier due to melting b On Cross Section 3 circle where most material is added to the glacier due to snowfall that does not melt in summer

For the below problem you will need to reference the Kodak Anthropometry pdf file provided on Canvas Neatly show all work for partial credit 1 A desk is 30 inches tall The desk chair has a seat height of 20 inches For keyboard work it is recommended that resting elbow height be between 1 inch above and 2 inches below the J key on the keyboard Using the Kodak data what percentile range of males and what percentile range of females will fit this workstation Assume that the J key is 0 5 inches above the desk and that a footrest is provided for workers with shorter legs easurement TANDING 1 Forward functional reach a Includes body depth at shoulder b Acromial process to functional pinch c Abdominal extension to functional pinch Abdominal extension depth B Waist height 3 Popliteal height 9 Leg length Tibial height 5 Knuckle height 5 Elbow height Shoulder height B Eye height Stature D Functional overhead reach ATED 1 Thigh clearance height 2 Elbow rest height 3 Midshoulder height 4 Eye height 5 Sitting height normal 5 Functional overhead reach 7 Knee height Males Females 50th 1 1 50th percentile S D percentile S D 32 5 31 2 26 9 24 4 9 1 41 9 41 3 17 9 29 7 43 5 45 1 5 8 9 5 1 9 29 2 2 2 28 1 1 7 24 6 24 5 31 0 34 1 50 6 21 3 17 2 41 4 3 5 0 8 2 1 2 1 1 1 1 6 1 8 2 5 56 6 57 6 64 7 68 7 12 6 69 9 2 6 82 5 3 3 2 4 3 1 24 0 6 1 3 1 2 1 4 15 3 3 1 1 1 0 1 9 23 8 8 2 40 0 38 8 16 5 28 0 40 4 42 2 51 9 56 3 39 6 63 8 64 8 78 4 4 9 9 1 22 8 29 0 32 2 47 2 20 1 16 2 39 6 1 5 27 2 30 7 35 0 1 7 25 7 29 5 34 1 13 22 6 25 6 29 3 2 6 19 1 24 1 29 3 0 8 7 1 8 7 2 0 37 4 40 9 2 2 35 8 39 9 0 9 15 3 17 2 Population Percentiles 50 50 Males Females 5th 50th 95th 1 6 1 4 2 7 38 5 25 9 28 8 38 0 42 0 43 6 54 4 59 7 49 8 55 3 61 6 56 8 62 1 67 8 60 8 66 2 72 0 61 1 67 1 74 3 3 4 74 0 80 5 86 9 2 7 48 4 2 6 2 2 2 4 2 8 0 5 1 2 4 3 7 3 1 0 21 4 1 2 27 4 5 3 9 3 23 6 29 9 10 2 44 7 44 5 19 4 31 9 45 8 48 6 1 6 32 0 34 6 2 6 43 6 48 7 1 0 18 7 20 7 0 7 15 1 16 6 1 7 37 3 40 6 5 11 4 26 1 32 8 37 4 54 8

For the below problem you will need to reference the Kodak Anthropometry pdf file provided on Canvas Neatly show all work for partial credit 1 A desk is 30 inches tall The desk chair has a seat height of 20 inches For keyboard work it is recommended that resting elbow height be between 1 inch above and 2 inches below the J key on the keyboard Using the Kodak data what percentile range of males and what percentile range of females will fit this workstation Assume that the J key is 0 5 inches above the desk and that a footrest is provided for workers with shorter legs easurement TANDING 1 Forward functional reach a Includes body depth at shoulder b Acromial process to functional pinch c Abdominal extension to functional pinch Abdominal extension depth B Waist height 3 Popliteal height 9 Leg length Tibial height 5 Knuckle height 5 Elbow height Shoulder height B Eye height Stature D Functional overhead reach ATED 1 Thigh clearance height 2 Elbow rest height 3 Midshoulder height 4 Eye height 5 Sitting height normal 5 Functional overhead reach 7 Knee height Males Females 50th 1 1 50th percentile S D percentile S D 32 5 31 2 26 9 24 4 9 1 41 9 41 3 17 9 29 7 43 5 45 1 5 8 9 5 1 9 29 2 2 2 28 1 1 7 24 6 24 5 31 0 34 1 50 6 21 3 17 2 41 4 3 5 0 8 2 1 2 1 1 1 1 6 1 8 2 5 56 6 57 6 64 7 68 7 12 6 69 9 2 6 82 5 3 3 2 4 3 1 24 0 6 1 3 1 2 1 4 15 3 3 1 1 1 0 1 9 23 8 8 2 40 0 38 8 16 5 28 0 40 4 42 2 51 9 56 3 39 6 63 8 64 8 78 4 4 9 9 1 22 8 29 0 32 2 47 2 20 1 16 2 39 6 1 5 27 2 30 7 35 0 1 7 25 7 29 5 34 1 13 22 6 25 6 29 3 2 6 19 1 24 1 29 3 0 8 7 1 8 7 2 0 37 4 40 9 2 2 35 8 39 9 0 9 15 3 17 2 Population Percentiles 50 50 Males Females 5th 50th 95th 1 6 1 4 2 7 38 5 25 9 28 8 38 0 42 0 43 6 54 4 59 7 49 8 55 3 61 6 56 8 62 1 67 8 60 8 66 2 72 0 61 1 67 1 74 3 3 4 74 0 80 5 86 9 2 7 48 4 2 6 2 2 2 4 2 8 0 5 1 2 4 3 7 3 1 0 21 4 1 2 27 4 5 3 9 3 23 6 29 9 10 2 44 7 44 5 19 4 31 9 45 8 48 6 1 6 32 0 34 6 2 6 43 6 48 7 1 0 18 7 20 7 0 7 15 1 16 6 1 7 37 3 40 6 5 11 4 26 1 32 8 37 4 54 8

For the below problem you will need to reference the Kodak Anthropometry pdf file provided on Canvas Neatly show all work for partial credit 1 A desk is 30 inches tall The desk chair has a seat height of 20 inches For keyboard work it is recommended that resting elbow height be between 1 inch above and 2 inches below the J key on the keyboard Using the Kodak data what percentile range of males and what percentile range of females will fit this workstation Assume that the J key is 0 5 inches above the desk and that a footrest is provided for workers with shorter legs easurement TANDING 1 Forward functional reach a Includes body depth at shoulder b Acromial process to functional pinch c Abdominal extension to functional pinch Abdominal extension depth B Waist height 3 Popliteal height 9 Leg length Tibial height 5 Knuckle height 5 Elbow height Shoulder height B Eye height Stature D Functional overhead reach ATED 1 Thigh clearance height 2 Elbow rest height 3 Midshoulder height 4 Eye height 5 Sitting height normal 5 Functional overhead reach 7 Knee height Males Females 50th 1 1 50th percentile S D percentile S D 32 5 31 2 26 9 24 4 9 1 41 9 41 3 17 9 29 7 43 5 45 1 5 8 9 5 1 9 29 2 2 2 28 1 1 7 24 6 24 5 31 0 34 1 50 6 21 3 17 2 41 4 3 5 0 8 2 1 2 1 1 1 1 6 1 8 2 5 56 6 57 6 64 7 68 7 12 6 69 9 2 6 82 5 3 3 2 4 3 1 24 0 6 1 3 1 2 1 4 15 3 3 1 1 1 0 1 9 23 8 8 2 40 0 38 8 16 5 28 0 40 4 42 2 51 9 56 3 39 6 63 8 64 8 78 4 4 9 9 1 22 8 29 0 32 2 47 2 20 1 16 2 39 6 1 5 27 2 30 7 35 0 1 7 25 7 29 5 34 1 13 22 6 25 6 29 3 2 6 19 1 24 1 29 3 0 8 7 1 8 7 2 0 37 4 40 9 2 2 35 8 39 9 0 9 15 3 17 2 Population Percentiles 50 50 Males Females 5th 50th 95th 1 6 1 4 2 7 38 5 25 9 28 8 38 0 42 0 43 6 54 4 59 7 49 8 55 3 61 6 56 8 62 1 67 8 60 8 66 2 72 0 61 1 67 1 74 3 3 4 74 0 80 5 86 9 2 7 48 4 2 6 2 2 2 4 2 8 0 5 1 2 4 3 7 3 1 0 21 4 1 2 27 4 5 3 9 3 23 6 29 9 10 2 44 7 44 5 19 4 31 9 45 8 48 6 1 6 32 0 34 6 2 6 43 6 48 7 1 0 18 7 20 7 0 7 15 1 16 6 1 7 37 3 40 6 5 11 4 26 1 32 8 37 4 54 8

es iable Costs ntribution Margin ed Cost Ome Loss HENNA COMPANY Contribution Margin Income Statement Carvings Units 30 000 17 30 30 000 10 38 Mementos Per Unit Total Per Unit 519 000 17 30 311 400 1 73 207 600 194 240 13 360 Total Total 519 000 1 038 000 51 900 363 300 467 100 674 700 600 790 795 030 133 690 120 330

19 Part 3 of 3 3 points Variable costs Contribution margin Fixed costs Income Sales Variable cost Contribution margin Fixed costs 3 Assume that the company expects sales of each product to increase to 61 000 units next year with no change in unit selling price Prepare a contribution margin income statement for the next year as shown above with columns for each of the two products Note Round per unit answers to 2 decimal places Ingame logo 487 860 81 310 325 240 731 790 194 240 600 790 131 000 131 000 Units HENNA COMPANY Contribution Margin Income Statement Carvings Per unit 17 30 X Answer is not complete 61 000 61 000 61 000 Total 1 055 300 0 17 30 1 055 300 194 240 861 060 Mementos Per unit IS 17 03 X 17 03 17 30 Total 1 038 830 1 038 830 1 055 300 600 790 454 510 IS Total 2 094 130 1 038 830 2 110 600 795 030 Return to question 1 315 570

Slitherlink is a puzzle presented as a dotted grid surrounding some numbers Groups of four adjacent dots act as corners of a square called a cell Some cells of the grid are filled with numbers To fill in the puzzle you create one continuous non intersecting loop drawn from one dot to an adjacent dot horizontally or vertically Connecting one dot to the next draws a side or border of the cell The goal of the puzzle is for your loop to provide the indicated number of sides borders to numbered cells each cell that has a number in it has that many borders from the loop surrounding its cell For example here is a completed puzzle 1 1 3 2 1 2 2 1 12 2 1 1 131 121 3 3 3 21 1 Now let s try putting these strategies to use in some puzzles Here is a Slitherlink puzzle Solve the puzzle but also describe HOW you solve it ww NHO 2 1 0 1 3

The hungry warrior was all bones Her jaw hung open in a perpetual shout I knew them I loved them I realized instantly that I would be a part of them My love I asked Who are these sisters of mine They wronged me he said How have they wronged you He did not answer but tried to take me from behind I would not oblige I clawed at his face He roared I fought I ended He ripped me from the inside out Indeed he had evolved in his passion He was born anew When I watched him sob over my body it was a confirmation He had not cried over the others To atone for such betrayal he said As if my body was the betrayal Let me say this Do not dare mistake my passion my love for forgiveness it is I who

a 3 Draw the preimage of a triangle with coordinates 7 2 1 U 0 1 and V 3 3 Then use the following coordinate plane to complete the following 1 point each T U V Draw a reflection of the triangle across y x Label the new triangle as AT U V Mark the coordinates below 2 4 2 0 4 2 4 Parallelogram QRST has vertices Q 4 2 R 2 4 S 0 1 and T 2 1 Draw and label the image after a counterclockwise rotation of 270 about the origin 1 point 2 4 2 0 2 4 b Rotate AT U V 90 clockwise Label the new figure as AT U V Mark the coordinates below T U V Transformation Rule Preimage Coordinates x y Image

Given r s Prove m Ms 10 8 6 4 Statements 1 r s d b d b 2 m m b a b C 5 m 6 m 7 m ms 2 O A d 0 b a 10 8 0 6 09 4 2 lo 2 4 6 8 10 4 r c d N 2 0 a 0 60 S 00 8 10 X 3 distance from 0 6 to 0 a equals the distance from c d to c 0 definition of parallel lines 4 application of the distance formula substitution property of equality inverse property of addition substitution property of equality Reasons given application of the slope formula The table and corresponding image show the proof of the relationship between the slopes of two parallel lines What is the missing statem 4

6 M AS A M is the result of translating ASAM If the slope of SS is the the slope of MM is If the length of AA is 6 then the lengths of MM is If the length of AM is 5 then the length of A M is

Role I Service Fact service line id service id I service type id employee id I labor cost I service start date service end date I I total service price I Part Fact I service line id I part id I I part vendor I I unit cost I I part count I I part cost at service Explanations Bike Type and Bike Brand Type 1 SCD is chosen because bike types and brands are unlikely to change If they do change a new record can be inserted

Measurement Seated elbow position Calculations Percentile 9 5 inches Males Males 50th percentile 0 3 inches 7 5 inches 10th percentile Standard Deviation 9 1 inches Females 50th percentile 0 2 inches Males Minimum resting elbow height 9 5 inches 2 inches 7 5 inches Maximum resting elbow height 9 5 inches 1 inch 10 5 inches Females Export t Minimum resting elbow height 9 1 inches 2 inches 7 1 inches Maximum resting elbow height 9 1 inches 1 inch 10 1 inches Percentile range

Read Explore and complete the following adapted from Lesson 3 2 Show all your work Two geometric figures are congruent if and only if they have the same size shape and angle measures In geometry the symbol can be used two indicate the two figures are congruent A landscape architect uses a grid to design the landscape around a mall Use tracing paper to confirm that the landscape elements are congruent A Trace planter ABCD Describe a transformation you can use to move the tracing paper so that planter ABCD is mapped onto planter EFGH What does this confirm about the planters B Trace pools JKLM and NPQR Fold the paper so that pool JKLM is mapped onto pool NPQR Describe the transformation What does this confirm about the pools CDetermine whether the lawns are congruent Is there a rigid transformation that maps ALMN to ADEF What does this confirm about the lawns Reflect 1 How do the sizes of the pairs of figures help determine if they are congruent D C M M N A B H G K Q E E R L N D

Your Turn The figures shown are congruent Find a sequence of rigid motions that maps one figure to the other Give coordinate notation for the transformations you use Then check your answer 1 JKLM WXYZ Step 1 Look at the graph and or table for similarities and differences 8 M 81y Figure 1 0 W 4 X Step 4 Check your answer L K 8 Step 2 Look at coordinate notation rules that could map Figure CDE onto JKL Select two Step 3 Write the coordinate notation for the transformations you use Describe the rule in words x y A Rotation B Reflection C Translation OD The figures are not congruent 1st Transformation 2nd Transformation Did the two rigid motions map one figure onto to another Why or why not Figure 2

X Determine the value of x 5x 16 2x 3 3x 4 B

Determine the values of x and y X y 8y 6 34 6y 12 x

75 5

3 Complected and transfered at 745 000 100 745 000 100 40 Exeling work in process 183000 100 18 3000 1928000 Total units 928000 745000 452 00 790200

Select the correct choice that completes the sentence below The domain of y arcsin x equals the of y sin x function domain inverse range

Given 2 similar triangles Delta ABCand Delta KJI AB 7 9 cm AC 3 8 cm BC 4 8 cm and JK 5 7 cm Construct a diagram of the triangles and determine the lengths of the unknown sides

a moving truck uses a 13 ramp to unload When the ramp is fully extended the distance between the base of the ramp and the back of the truck is 8 What is the angle of elevation

ve the general solution for the following trigonometric equation without a calculator in grees Type DNE on the larger angle if only one equation is necessary tan 48 29 1 275 Reference Angle B B degrees round to two decimal places where kZ smaller angle where kEZ larger angle

15 Write a program that will find the third one if you are given two out of three from the vertex centroid and midpoint For example the second screen shot shows the vertex when 4 7 and 12 2 are inputted for the centroid and midpoint NORMAL FLOAT AUTO BEAL RADIAN MP MISSING VERTEX 2 CENTROID 3 MIDPOINT NORMAL FLOAT BUTO REAL RADIAN MP GCA B MCC D A 74 B 7 C 12 D 2 12 25 Done

Select all the correct figures Which numbers have line symmetry 2 3 7 8

Which letter has point symmetry A L D

se an identity to simplify the following expression tan 17 1 tan 17 Choose the correct expression equal to OA 1 2 cos 17 OC 1 2 tan 34 tan 17 1 tan 17 below B 1 TIN tan 17 OD sin 34 G

Determine the magnitude and direction of the vertical shift and the phase shift for the function below f x sin x 7 3 Select the correct answer below O O O The vertical shift is left 7n units down and the phase shift is 3 units to the 4 The vertical shift is 7 units up and the phase shift is 3 units to the left 4 7 The vertical shift is 3 units up and the phase shift is right The vertical shift is right 7 The vertical shift is 3 units down and the phase shift is left 4 7n 4 units to the units up and the phase shift is 3 units to the 4 7x O The vertical shift is 3 units down and the phase shift is right 4 units to the units to the 11

0 NUMMMM 1 2 5 2 1 0 0 Ay 1 T 10 47 5 2 y sin x X n 5 Q G 5 3 2 1 0 0 Ay I 0 1 2 3 2 Drag each graph above to match the function below y sin x n x X T 5 1 0 0 V 6 5 15 5 y cos x GLOB T 5 y cos x 5 3 2 1 0 0 2 0 6 11x 5 Q

4 y x 5 y x 5 PART A Graph the functions Q

2 5 pts Two cables are attached to a tower to stabilize it In the figure the cable on the left is 150 ft long and forms an angle of elevation of 58 The cable on the right forms an angle of elevation of 29 How long is that cable marked with an x Show your work Round to 1 decimal Use correct units 150 ft 58 Tower X 29

Roll the Die C X Let s implement your randomization plan Roll the die below and assign treatments to each of the nine cows shown in the picture below by marking or circling each cow eyes marking place a circle around the cow crosses marking place an X over the cow no marking underline the cow Below is the randomization plan you proposed on the previous screen You can go back and make changes to your plan if you need To use a 6 sided die to randomly assign each cow in a herd of 50 cows to one of three treatments artificial eyespots cross marked or unmarked you can follow these steps 1 Label the die Assign two faces e g 1 and 2 for the artificial eyespots treatment Assign two faces e g 3 and 4 for the cross marked treatment Assign two faces e g 5 and 6 for the unmarked treatment 2 Roll the die for each cow in the herd By following this labeling

A pyramid was built about 2590 BC Its original height was 518 feet 11 inches but due to loss of its topmost stones it is now shorter Find the current height of the pyramid using the information given in the figure on the right The current height of the pyramid is feet CHCEC 38 8 45 52 the final newer Thed to two decimal places as needed

7 Graph the equations below to form the figure Label the coordinates of the vertices 10 3 y 4 2 3 y 2 x 1 y 1 x 4 x 5y 10 10 4 points a How many sets of parallel sides does the figure have Show calculations to justify your answer 4 points b How many right angles does the figure have Show calculations to justify your answer 1 point c Does the figure have 4 congruent sides Show calculations to justify your answer d What is the most precise name for this figure 4 points 2 points

Q i ii A iii iv D 6cm 8cm B Q4 The diagram above shows the net of a right rectangular pyramid in which ABCD is base and 0 0 03 04 are brought together to form the vertex O When the solid is formed ABCD is the base AB 8cm AD 6cm and BO 13cm a Draw a sketch of the pyramid b Calculate the C height of the pyramid volume of the pyramid area of triangle AOB inclination of the triangle BOC to the hoge ABCD

33 Given K N JK MN KL NO K K N J LM Prove AJKLAMNO DEL F 0

24 Given ZJELM JK MN and K N K 0 Prove AJKL AMNO L N M

Use the figure to solve triangle ABC Round lengths of sides to the nearest tenth and angle measures to the nearest degree A Round to the nearest degree as needed Round to the nearest degree as needed B C O Round to the nearest degree as needed Find the measures of the unknown sides of triangle ABC O b a Round the final answer to the nearest tenth as needed Round all intermediate values to the nearest thousandth as needed 17 36 4 21 2 27 B a 13 7

9 Using Figure 9 13 below a Draw isobars at 4 mb intervals e g 1004 mb 1008 mb 1012 mb 11 b Label the low pressure center with an L c Draw the warm and cold fronts L49 38 124 31 O 41126 33 O 128 34 22 36 124 28 38 110 41103 30 L48 4 40 088 42 109 36 20 48 126 38 38 448 026 50 52 128 45 096 43 4569 R 40 66 59 d Label a maritime tropical mT and continental polar air mass CP e Outline the area where cloud cover exceeds 75 f Shade the areas receiving precipitation 61 075 57 60 040 48 63 153 61 Figure 9 13 45 114 66 24 60 ras 57 39 084 39 024 61044 57029 54 66 53 70 40 591 39 154 39 4332 41 46 124 43 54 097 43 45 099 66 111 55 71 72 69171 64 61 60 9 149 45 163 8 4 1 11

4 Find all points on the curve r 2 2 cos 0 where the tangent line is vertical List the points in polar form

Find the exact value of each expression it it is defined If an answer is undefined enter UNDEFINED a tan 0 b tan sqrt 3 c tan sqrt 3 3

A cell phone tower is anchored by two cables on each side for support The cables stretch from the top of the tower to the ground with each being equidistant from the base of the tower The angle of depression from the top of the tower to the point in which the cable reaches the ground is 23 If the tower is 140 feet tall find the ground distance between the cables