Heights & Distances Questions and Answers

5 These are 6 Find x and y Y 213 150

Problem 60 Let f x y 4 y to answer the following A Explain why the cross section for the surface z f x y produced by cutting it with planes parallel to x 0 are semicircles of radius 2 B Describe the cross sections of the surface in the planes y 0 y 2 and y 3 C Describe the surface z f x y

4 Find the area of the shaded region The units are in meters A 6 TM

5 Rectangle A is dilated to form rectangle B A 6 e 20 B 30 Target due 10 31 23 39 5 75 What scale factor was used Enter the answer and also provide a 1 sentence explanation that describes how you determined your answer Review the rub you will be evaluated

EXTRA CREDIT The units are in yards Find the area of the shaded region Ashaded Region Tyd

10 The volume of the right rectangular prism is V 270 cm Write a quadratic equation in terms of x Don t solve the equation 2 points x 3

9 A lot for sale in a subdivision has the shape of the quadrilateral shown in the figure Find the area the lot rounded to two decimals 10 points 75 ft 800 40 ft 135f 128 ft

A ball is thrown from an initial height of 4 feet with an initial upward velocity of 40ft s the ball s height in feet after seconds is given by the following Find all t values of for which the ball s height is 26 feet

he what you w ciple Part II 19 Points 1 A e radius of a circle is 5 mm then find the area of the Posttest O 5 square mm O 10 square mm O 15 square mm O 25 square mm Complete

Match the equation with the sentence Susanne was hiking down from Mt Whitney She started at 14 500 ft above sea level and descended 375 ft every 30min Kirk was hiking up to Mt Whitney He started at 7545 ft above sea level and ascended to the top 14500 ft after about 8 5 hours of hiking Using an average pace choose the function that describes his elevation relative to the time in hours Jolie was hiking up to Mt Whitney She started at 7545 ft above sea level and ascended to the top 14500 ft after about 10 hours of hiking Using an average pace choose the function that describes her elevation relative to the time in hours Juan was hiking down from Mt Whitney He started at 14 500 ft above sea level and descended 1400 ft every hour Choose Choose E t 70 3 t 14500 E t 818 81 7545 E t 6961 7545 E t 75 6 t 14500 Choose Pedro loves to try new adventures His most recent adventure was jumping out of an airplane His special watch tells him his altitude He set a timer at the moment he opened

Tutorial Exercise The Cartesian coordinates of a point are given a 7 7 1 Find polar coordinates r 8 of the point where r 0 and 0 0 2 ii Find polar coordinates r 8 of the point where r 0 and 0 0 2 b 5 5 3 i Find polar coordinates r e of the point where r 0 and 0 0 2 ii Find polar coordinates r e of the point where r 0 and 0 0 2

Solve the equations for solutions in the interval 0 360 Use a calculator for Problem 12 give the answer to the nearest hundredth of a degree 9 Sin x 1 3 10 Sec x 2Sec x 0 11 2cos x root 3 0 In degrees just verifying I am doing this correctly Trigonc Sub subj Sear

Use fundamental identities to find the values of the trigonometric functions for the given condition sec 0 6 and tan 0 0 sin 0 cos 0 tan 0 cote sec 0 CSC 0

Question 6 Find the distance between A and B 6 4 2 Points 2 20 Y 18 16 14 12 10 8 6 4 2 0 4 5 O 5 units O 6 units O 7 units 8 units 2 A 4 4 6 8 B 10 12 14 16 18 20 X

Question 10 Points 2 Write the equation of a line that is perpendicular to y 4 5 x 2 and has a y intercept of 1 O y 5 4 x 1 O y 5 4 x 1 O y 4 5x 1 O y 4 5x 1

Find the equation of a line parallel to 2x 3y 9 that passes through the point 1 3 O 2x 3y 11 O 2x 3y 11 O 3x 2y 11 3x 2y 11

Write an equation of a line that is parallel to y 2x 1 and passes through the point 4 6 O y 2x 2 Oy 2x 2 Oy 2x 4 Oy 2x 4

The table below shows the distribution of FTC complaints categorized by payment method and the dollar value of all transactions made under each method Method of payment Bank Account Debit Cash Advance B 0 16 C 0 30 Check Credit Cards Internet Money Order Prepaid Cards Telephone Bill Wire Transfer Total Number of complaints Total value of transactions 85 433 040 168 972 138 88 603 695 96 440 695 9 651 081 38 527 17 332 12 917 46 736 5 734 8 707 119 100 1 028 106 472 356 553 55 898 113 80 860 327 870 511 500 705 082 1 087 434 682 If an FTC complaint is chosen at random which of the following is closest to the probability that the complaint is related to the payment method whose transactions accounted for the highest dollar value A 0 05

14 An observer in the top of a lighthouse determines that the angles of depression to two sailboats directly in line with the lighthouse are 3 5 and 5 75 If the observer is 125 feet above sea level find the distance between the two boats Show your main steps 5 points y 3 5 X 5 75 125 f 25 f

32 10 X Solve for x Round to the nearest tenth

In Exercises 5 to 22 find the missing lengths Give your answers in both simplest radical form and as approximations correct to two decimal places X N Exercises 5 8 7 Given Find Right AXYZ with XZ YZ and XY 10V 2 Y7 and Y7

Find the surface area obtained by rotating 1 x 2 1 x 1 about the x axis

The accompanying data gives the results of a survey on the number of hours spent online per week on a certain social networking website Determine if the mean number of hours spent online per week is the same for males as it is for females Assume that the population variances are unequal Click the icon to view the social media survey data Is there sufficient evidence at the 0 05 level of significance that the mean number of hours spent online per week is the same for males as it is for females Determine the null hypothesis Ho and the alternative hypothesis H Let females be population 1 and males be population 2 Ho H Type integers or decimals Do not round b 2 Female 3 Female 4 Female 5 Female 6 Female 7 Female 8 Female 9 Female 10 Female 11 Female 12 Female 13 Female 14 Female 15 Female 16 Female 17 Female 18 Female 19 Female 20 Female 21 Female 22 23 Gender 4 Male 9 Male 8 Male 5 Male 7 Male 12 Male 1 Male 6 Male 2 Male 5 Male 8 Male 13 3 7 3 8 5 Male 4 Male 6 8 Hours online week 6 14 6 4 6 4 9 3 7 8 6 4 4

2 Write the converse of the statement If it is raining then I will not go to school If I don t go to school then it is raining If I go to school then it is not raining If it is not raining the I will go to school O If it is raining the I will go to school

6 Determine if the following statement is valid or invalid An object is green if and only if it is not blue Valid O Invalid

Identify the hypothesis and the conclusion of the conditional stateme If it is hot then I will go to the beach Hypothesis I will not go to the beach Conclusion it is hot O Hypothesis I will go to the beach Conclusion it is hot O Hypothesis it is hot Conclusion I will go to the beach O Hypothesis Conclusion it is not hot I will go to the beach

A tree casts a shadow 24 ft long At the same time the shadow cast by a vertical 7 ft post is 12 ft long Find the height of the tree The tree s height is ft www

The angle of elevation of a man standing on a road to the top of a building is 60 degrees If the height of the building is 30 feet find the distance between the man and the base of the building O 60 feet O 30 feet O 17 32 feet O 12 98 feet

b 0 A miles a B Two radar stations 6 miles apart are tracking an approaching airplane The angle of elevation from stations A and B to the plane is 61 and 27 respectively Calculate the distance between the airpla and stations A and B respectively Give your answer in miles and to two decimal places miles

State the property or properties used to rewrite each expression log 3x log log 3x

the other things is also equal to the iter 6 Give an algebraic example of this prop Bi Font Family S Symmetric Property Reflexive Property Transitive Property Additive Property er ite

9 For kite ABCD m A m B 20 m C m B 60 Find m B 2 points A D B C

6 A ladder leans against a building that is perpendicular to the ground such that it makes a 74 angle with the ground and its bottom lies 2 75 feet from the base of the building a Determine the height that the ladder reaches up the wall to the nearest tenth of a foot b How long is the ladder Round to the nearest foot 74 2 75 ft boooooo HH

Assume lies in quadrant 3 and the terminal side of 0 is perpendicular to the li y 19 x 6 Part 1 Determine sin e Part 2 Determine sec 8 sin 8 sec 8 X

Given the rotation of AABC shown below determine the counter clockwise angle of rotation that occurred about point D Show all relevant lines and measurements you made to determine your answer A A C B C

5 In the diagram below MNPQ is a parallelogram whose diagonals are perpendicular Prove MNPQ is a rhombus M Q R N P

A rope is used to support a flag pole The rope is attached to the top of the 42 ft pole and attached to the ground 15 1 ft from the base of the pole How long is the rope Select one a 140 6 ft O b 44 6 ft OC 49 6 ft d 33 6 ft

How far from the base of a building must the bottom of a 15 foot ladder sit for it to make a 52 angle with the ground Round to the nearest tenth of a foot 15 ft bo

5 A person sights a boat from 235 feet above sea level as shown If the angle of depression from the man to the boat is 21 then determine the boat s distance to the edge of the cliff to the nearest ten feet 235 ft 21

A long wire is attached to the top of a 175 foot tall electrical transmission tower If the wire needs an angle of 65 with the ground then how long must it be Round your answer to the nearest foot feet 65 make 175 feet person sights a boat from 235 feet above sea level as shown If the angle of depression from the man to boat is 21 then determine the boat s distance to the edge of the cliff to the nearest ten feet

Verify the identity Simplify at each step 9 cos x 9 sin x 9 cos 2x x 9 cos x 9 sin x 9 cos x sin x 9 cast 1 sin x

of the following statements is false one Every chord is part of a secant Every diameter is part of a secant Every diameter is a chord Every chord is a diameter the standard equation of the circle in the graph one 012 o 212 19

Sketch the graphs of each equation Find all points of intersection of the pair of graphs x y 8 y x 4 Graph x y 8 Choose the correct graph below OA OB 15 O C G O D

Select the simplification that accurately explains the following statement oot 4 2 2 1 4

Define a function f that represents a bucket s height d above the water in feet in terms of the angle of rotation measured in radians from the 3 o clock position Then use your function to find a bucket s height above the water when the angle of rotation is 4 radians from the 3 o clock position

In the figure below KN and KL are tangent to the circle centered at O The segment NL passes through the center of the circle Given that KN 5 1 and NL 2 4 find NM N M 0 L NM X

use the relationship given in the right triangle and the inverse sine cosine and tangent functions to write 0 as a function of x in three different ways It is necessary to rationalize the denominator 1 2 25 6 5

AB is a vertical tower of p units high D and Care in the same horizontal plane as B the foot of the tower The angle of elevation of A from D is x BDC y and DCB 0 The distance between D and C is k units D x Y R k B 6 1 1 Express p in terms of DB and x 6 1 2 Hence prove that p e C ksinetanx sinycose cosysine 6 2 Find BC to the nearest meter if x 51 7 y 62 5 p 80 m and k 95 m 2 5 4 11

8 From the observation deck of a lighthouse 70 meters above sea level the lighthouse keeper can see a fishing boat The angle of elevation from the boat to the lighthouse is 25 What is the horizontal distance to the nearest meter from the base of the lighthouse to the fishing boat A 32 m B 77 m C 150 m D 165 m 70 m 6 Hint the slant height is 9 4 01 Find the surface area of the solid to the right x 25

The points scored on a test for a sample of 40 students are summarized in the following table Number of students Score for each student 7 15 points 14 4 90 80 70 60 Find the mean points scored Round your answer to the nearest tenth