3D Geometry Questions and Answers

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9 59 Locate the centroid 7 y of the composite area

Use a graphing utility to approximate the solutions of the equation in the interval 0 2m Enter your answers as a comma separated list Round your answers to four decimal places 6 5 cos x 21 6 sin x

Because of prevailing winds a tree grew so that it was leaning 3 from the vertical At a point d 40 meters from the tree the angle of elevation to the top of the trees is a 26 see figure Find the heighth of the tree Round your answer to one decimal place h dm

Find all values of 0 in the interval 0 360 that have the given function value 0 sin 8 0 12 Type an integer or a decimal Use a comma to separate answers as needed

A regular hexagon is rotated 360 about its center How many times does the image of the hexagon coincide with the preimage during the rotation O A OB O C O D 1 time 6 times 12 times 3 times

Select the correct answer from each drop down menu AABC has side lengths of 10 units 20 units and 24 units AXYZ is similar to AABC and the length of its longest side is 60 units The perimeter of AXYZ is square units 108 110 135 270 v units If the height of AABC with respect to its longest side being the base is 8 units the area of AXYZ is Reset Next

The diagram shows the lengths of corresponding sides of similar triangles A B C and ABC Which expression gives the perimeter of A B C A B a 4 CA OA 4 4 b c OB 2 a b c OC 4 a b c OD 8 a b c B 8

6 Which of these conditions might be true if polygons ABCD and KLMN are similar O A O B O C O D OE The measures of corresponding angles of ABCD and KLMN are equal but the lengths of corresponding sides of ABCD are half those of KLMN The measures of corresponding angles of ABCD and KLMN are in the ratio 1 2 but the lengths of corresponding sides of ABCD and KLMN are not proportional The lengths of corresponding sides of ABCD and KLMN are equal but the measures of corresponding angles of ABCD and KLMN are not equal The lengths of corresponding sides of ABCD and KLMN are proportional but the measures of corresponding angles of ABCD and KLMN are not equal The measures of corresponding angles of ABCD and KLMN are not proportional but the lengths of corresponding sides of ABCD and KLMN are proportional

Quadrilateral PQRS is dilated by a scale factor of with point R as the center of dilation resulting in the image P Q R S Which statement is true about line segment P S OA OB O C OD P S 8 6 4 2 y 8 6 4 2 2 4 6 0 R Q 2 Segment P S is 4 units long and lies on the same line as segment PS Segment P S is 16 units long and lies on the same line as segment PS Segment P S is 4 units long and lies on a different line than segment PS Segment P S is 16 units long and lies on a different line than segment PS 6 0 X

16 in Fig P5 8 1 20 in r 38 in

Find all solutions of the following equation sec x 4 0 Select the correct answer where k is any integer 5TT 3 TU 3 TL 3 TC 3 TU 3 KIT 2k KI 2k 2 3 2 T 3 2 3 KI 2k KT 4 3 2k 4T 3 5TL 2k 2k 3 ki 5TT 3 k

the perimeter add each side 2 Find the area of a circle 3 Find the volume of the L x W x H

For problems 1 and 2 let z y be a point on the unit circle with the corresponding angle 0 2 7 1 Use the given information to find tan 8 5 points cos 8 0

2 Let 0 6 a Find y 5 points b Sketch the unit circle and on it indicate the point z y as well

Type an equation using n

2x me complementary angle to IS 5 implify your answer Type a fraction with in the numerato

31 Given C is the midpoint of AE BA DE and ZA ZE B A C Prove AABC AEDC JE

27 Given LM JM L K 083 M Prove ALKMAJKM 10

07 11 01 MINEMEN 28 Given ABED A D B A C Prove AABC ADCE E OMAREXHIA

Ccw counterclockwise 1 Translation 5 right and 5 up YA 2 3 2 1 1 3 Reflection Across the line y 1 YA i 3 2 1 5 Translation 5 left YA 5 2 1 11 2 3 4 12 3 3 4 5 4 5 formations 2 Reflection Across Line y x 4 3 5 2 1 A 3 3 2 4 2 1 1 4 Rotation 90 clockwise about the orig YA 5 2 3 4 1 4 3 2 1 1 2 3 5 V 2 3 3 2 1 1 1 4 6 Rotation 180 about the origin YA 5 3 2 1 1 6 2 1 4 1 5 3 4 2 5 3 4 5 Math Aids Com

In the figure above O is the center of the circle and AD 10 If the area of the shaded region is 207 what is the value of a b c d

Given AB LBC ADL DC and BC AD Prove AABC ACDA Step try Statement AB BC AD 1 DC BC AD Type of Statement Reason Given B

empt in Progress For the pair of compounds below determine whether they are identical compounds constitutional isomers or stereoisomers O stereoisomers O constitutional isomers O identical compounds

a Starting with the graph of f x 2 write a function that results from shifting f x down 4 units and reflecting f x about the y axis f x P b Graph function found in Part a Drag the two blue points on graph to the correct points that f x passes through Then use the remaining red point to drag the horizontal asymptote to the correct line Note that all three points are adjusted in increments of 1 4 Y

2 Tell whether the transformation appears to be an isometry Explain your answer

9 Determine the number of lines of symmetry for each figure a b c

11 Find an equation of the sphere that passes through the point 4 3 1 and has center 3 8 1

5 Describe and sketch the surface in R represented by the equation x y 2 hu

5 Describe and sketch the surface in R represented by the equation x y 2

Select the correct answer from each drop down menu Consider the figure formed by AAEB and ADCB sharing a common vertex B A The figure E has point symmetry does not have point symmetry D because rotating it 180 about point B maps AAEB onto ADCB The figure because point E is the same distance but in the opposite direction from point B as point C and point A is direction from point B as point D

2 Tiana and Ronald like to run as part of their exercise routines on the weekend They each go on runs from their house Tiana s house is located at point T and Ronald s house is located at point R on the coordinate plane shown LI V 20 12 R 10 12 14 1 On Saturday Tiana runs 3 miles north then 4 miles east and then back to her house via the shortest route Ronald runs 3 miles west then 4 miles south and then back to his house via the shortest route Draw the routes on the coordinate plane Demonstrate that the two triangles formed by their routes are congruent Include a triangle congruence statement Then determine a series of transformations that maps one triangle onto the other

29 C 1 sino A r 3 sing intersection ts 12 n

In Exercises 7 and 8 sketch a diagram of the description 7 RS bisecting KL at point R In Exercises 9 14 use the diagram to determine whether you can assume the statement 9 Planes A and B intersect at EF 10 Points C and D are collinear 11 HJ and ID are perpendicular 12 GD is a bisector of EF at point D 8 AB in plane U intersecting CD at point E and point C not on plane U 13 IHHG 14 ZHJD and ZHDJ are complementary angles C IG D B

For an FCC structure select all reflections that can appear in the XRD pattern O 100 O 110 O 111 O 200 O 210 O 220 O 211 221

A surfer is riding a 7 foot wave The angle of depression from the surfer to the shoreline is 10 What is the distance from the surfer to the shoreline

12 A fire hydrant sits 72 feet from the base of a 125 foot tall building the fire hydrant to the top of the building

4 Name the figure below and solve for x 5x 139 92 wn angle measures for the quadrilateral in the diagram 9 1 71 3x 1260 2 180 7 1 2 5 n The polygon is a pentagon 2x 5 Name the figure below and solve for x 5x x 8 n Ya 75 5 8 25 Explain the Error Find and explain what this student did incorrectly when solving the following problem What type of polygon would have an interior angle sum of 1260

5 After performing the translation described below what will be the coordinate of point M translation x y x 7 y 1 Ay Moy thew enoudes on wollo sit30 das S ANDRETT 6 After performing the translation described below what will be the coordinate of point R translation x y x 5 y 1 Ay Che R

28 Find the measure of angle A A x 34 x 64

2 Givens AVD 3x 17 DVC Sx 3 Prove m4BVC 77 Statements Reasons

Complete the equation for the line perpendicular to g x 6x 5 and passing through the point 9 2 help equations Y

A parcel delivery service has contracted you to design a closed box with a square base that has a volume of 11 000 cubic inches Complete parts a d a Express the surface area of the box as a function of x X

Graph the function by setting the x intercept and the asymptotes Provide your answer below 10 2 0 5 10 3 0 f x P 4 10

N 7 Figure 1 Map of 300 mb winds at 12Z 10 MAR 2011 1 Look at the accompanying Figure 1 With a pencil shade a small oval around each station where wind speeds are 60 knots or greater such as San Francisco Then shade the area between adjacent shaded stations where the wind speeds are also presumed to be 60 knots of more Next draw lines along the northern and the southern boundaries to highlight the shaded area limits of the 60 knot or greater region Finally draw a heavy smooth curved arrow through the core of the shaded highest wind speeds Add an arrow head to show wind direction 2 The large arrow you drew on your map approximates the location of the existing polar front jet stream across the United States Now imagine that you are in a gondola attached to a helium filled balloon that is located over central Washington State Assuming your balloon stays at the 300 millibar level and travels with the air flow draw your path as you travel across the country Through what state or states are you likely to leave the United States

D C b G A F Refer to the figure index the following vectors and planes Vector AB AE and BD Plane AFEC FBCD and BFGE E B

50 Think back to August 6 1945 The United States has just dropped an atomic weapon on the city of Hiroshima killing tens of thousands of Japanese and devastating the infrastructure A Keynesian at that time might conclude that there is a silver lining in the destruction as economic prosperity will result Evaluate the logic of this claim in a few sentences

5 How many lines of symmetry do the flags below from various countries have Justify your answer Cuba 9x9 bigh nort thighh wold exostane ort suk Switzerland Jamaica assiq

6 Identify the transformation below Then describe its scale factor C 9 12 30 15