3D Geometry Questions and Answers

Step 1 We want to find the exact value of sin From the text the quadrants are numbered counter clockwise from the upper right I II III IV This angle lies in quadrant III III K T sin 27 Step 2 Sketching the angle we draw the triangle formed with the terminal side and the x axis Looking at this triangle we see triangle that it is a 71 632 2 2 To find that value we first have to draw the angle 3 y Likewise the opposite side should be labeled 2A 3 From the text we know that the side lengths are 1 2 3 To label the sides with the proper lengths we note that 2 being the longest side length must be the hypotenuse The smallest angle will be opposite the shortest side Looking at the triangle and taking into account the quadrant so that the sign is correct the adjacent side should be labeled 3 x

Find the x and y intercepts of the graph of the circle If an answer does not exist enter DNE x 10x y 2y 19 0 STEP 1 Consider the equation for the circle x 10x y 2y 19 0 Let y 0 Give the resulting equation below 10x 19 0 STEP 2 Solve your equation from Step 1 for x If one or more solutions exist these values are the x coordinates of the x intercepts of the graph of the circle Enter your answers as a comma separated list x x STEP 3 Consider once again the equation for the circle x 10x 2y 19 0 STEP 4 Solve your equation from Step 3 for y If one or more solutions exist these values are the y coordinates of the y intercepts of the graph of the circle Enter your answers as a comma separated list y 2y 19 0 Now let x 0 Give the resulting equation below STEP 5 Complete the problem by listing the x and y intercepts x intercepts x y smaller x value larger x value y intercept x y 1

K Complete the statement y cos x means that x for 0 syst y cos x means that x for 0sys

A restaurant dining space and hallway is shown in the diagram below This area of the restaurant will have 12 foot ceilings b 1 m Step 1 Calculate the total volume of the dining area and hallway in cubic feet Assume a 6 4 m b 8 4 m and c 12 1 m Use 1 ft 0 3048 m for your conversion Remember to do the conversion for each dimension as we showed in class Round your answer to the nearest hundred not hundredth Volume of the space ft Step 3 The design of the duct work specifies an air speed of 275 ft min Use the formula airflow duct area x air speed MY NOTES Step 2 The design calls for 11 air changes per hour Calculate the total air flow in CFM cubic feet per minute needed to meet the air change requirements for the space Round to the nearest hundred CFM Airflow required CFM to find the duct area needed Round your answer to the nearest tenth duct area sq ft round ASK

Amari Perform the following conversions Marks as indicated 1 A cone shaped fuel tank has the following dimensions D 37 6 in H 42 3 in SHOW YOUR WORK FOR THE FOLLOWING QUESTIONS 7 marks Use the formula for the volume of a cone to determine the A total capacity of the tank r D 2 O Student ID 101313077 Score

Use the diagram below showing the concrete floor of a building At a cost of 30 per cubic foot find the cost of having the floor poured Round your answer to two decimal places 50 ft 25 ft 6 in

Question 7 8 6 4 2 1 2 8 Question 7 Triangle ABC is reflected over the line y 1 to produce triangle A B C 6 4 N C 4 6 8 2 2 Pause A 2 4 1 8 A What will be the coordinates of B 2023 Illuminate Education Inc Q Zoom X

Find the standard form of the equation of the parabola with the given characteristics y 10 V 0 0 2 2 2 2

Question 2 A triangle with coordinates A 1 1 B 4 2 C 3 5 is translated three units down and five units to the left What are the coordinates of the new triangle A A 2 4 B 1 3 C 0 0 A 4 2 B 1 1 c 2 2 A 4 2 B 7 3 C 6 0 A 4 2 B 1 3 C 2 6 B C D

Florence is a nurse on a children s ward Every hour they take the temperature of the 16 children on the ward Here are the results in C 36 6 36 3 36 9 39 7 36 8 37 3 35 9 38 9 37 3 37 9 37 3 39 9 35 2 38 7 36 5 38 6 Fill in the stem and leaf diagram The working out diagram is not marked The answer box will be marked key 3615 means 36 5 working out diagram any order Stem Leaf 35 36 37 38 39 answer box size order Stem Leaf 35 36 37 38 39 8

ESSMENT Practice Credit Checkpoint Complete the following Show all your work Road Construction The city of Interlaken has three amazing natural recreational areas a lake a cliff and a mountainous area Currently there are two businesses open in the area Half Moon Kayak Rentals and Chupacabra Campground Two new adventure companies want to open their businesses in this area to attract adventure seeking tourists However the issue is the only road that runs through this area is Lombard Road The city wants to build more roads to make the recreational areas accessible to tourists Construct the roads with a ruler and protractor to meet the city s criteria 2 points Interlaken s Road Criteria A straight road must begin at Chupacabra campground and end at iJump Adventure Company A straight road must begin at Half Moon Kayak Rentals and end at Surge Bike Excursions A straight road must pass by iJump Adventure Co and Surge Bike Excursions but never intersect Lombard Road Name the roads and provide appropriate angle measures of all intersecting roads for construction Chupacabra Campground Lombard Road Half Moon Kayak Rentals Surge Bike Excursions

3 Answer the following for the given figure Lesson 4 2 1 point a Suppose 21 is 105 List all the angles congruent to21 Ejib 739 b Suppose 23 is also 105 Name all angles supplementary to 23 What is their measurement A Converse of Alternate Exterior Angles OB Converse of Corresponding Angles C Converse of Alternate Interior Angles D Converse of Supplementary Angles Liner and lines are parallel Answer the following about the given figure Lesson 4 2 1 point 103 c Which angle pairs are alternate interior angles List all angle pairs d What theorem explains why 24 28 e Which angle pairs are same side interior angles List all angle pairs 4 In the figure mz2 m26 What theorem can be used to prove that line a and line b are parallel Lesson 4 3 1 point 0 b 12 34 87 65

Learning Goal from Lesson 5 1 5 4 I can show that triangles are congruent if and only if their corresponding sides and angles are congruent I can prove the following triangle congruence theorems ASA SAS SSS using properties of rigid motion A B How I Did Circle one 7 State the additional congruency statement s needed to prove AABC AFGH for the given theorem 1 point H I got it I m still learning it G a What is the missing side or angle needed to prove AABC AFGH using the SAS Theorem b What is the missing side or angle needed to prove AABC AFGH using the ASA Theorem

2 1 Your Turn E Reason Bank Choose from the phrases in the reason bank below to complete each proof Vertical angles are congruent Given AB AD and 21 22 Prove A BACA DAC Statements 1 AB AD 2 41 42 3 AC AC 4 A BACA DAC 2 AC CD 2 EC CB 3 AC CD 3 EC CB Given C is the midpoint of AD and BE Prove A ABC A DEC Statements 1 C is the midpoint of AD and BE Reflexive Property of Congruence 5 LACB LDCE ARCA DEC Definition of Bisector Reasons Reasons Given SAS Triangle Congruence Theorem Definition of Congruence B B 4

Your Turn 4 Find CR Given CD is the perpendicular bisector of PR Find the following lengths P S 15 D R

angles are supplementary The first one is done for you Same Side Interior Angles 23 and 26 24 and 2 lifelong Geometry A LEARNIND mz Equation m23 m26 180 m2 Credit 3 1 2 4 3 5 8 7 L4L Geometry A 2020 6 Page 14

A Python program that impements a graph using an adjacency matrix A Python a program that implements a graph using an adjacency list Vertex 0 3 2 1 Vertex 1 2 0 Vertex 2 1 0 Vartay 4

B tan given tan tan 2 3x with 2 p Type an exact answer using radicals as needed Rationalize all denominators

Drag the appropriate labels to their respective targets ions molecules has dissolves in water to give ions molecules or both both NaCl a strong electrolyte HI a weak electrolyte CH3CH OH a nonelectrolyte KNO3 a strong electrolyte glucose a nonelectrolyte H CO3 a weak electrolyte

Review Graph the following equations by hand You must clearly graph or list TWO points on each graph Indicate the asymptote with a dashed line Then list the following information for each graph Domain in interval notation Range in interval notation and the Asymptote VA or HA as an equation y log z 3 87654321 Clear All Draw Domain 84 7 6 5 4 3 2 D 2 4 6 7 84 M 23456 8

Your Turn 1 Determine the measure of the unknown angles A 68 b 3 Find the measure of ZAEC and LBED E 60 I D B 2 40 X 25 Z y

Using what you know about angles and translations find all of the angle measures in the image below 21 135 22 23 24 25 26 Explain how you found the measure of 28 27 28 5 6 7 8 3

x t 8 10 cos 27 100 7 20cos 2 250 a Using Euler s relation the signal x t defined above can be expressed as a sum of complex exponential signals using the finite Fourier synthesis summation 3 37 Determine values for fo N and all the complex amplitudes a It is not necessary to evaluate any integrals to obtain a b Is the signal x t periodic If so what is the fundamental period c Plot the spectrum of this signal versus f in Hz P 3 20 A real signal x t has the two sided spectrum shown in Fig P 3 20 The frequency axis has its of rads 90 0 4 90 Figure P 3 20

The diagram shows a triangular prism CD 7 cm AD 10 cm Angle FDC 30 A E 10 cm B Calculate the size of angle AFC Give your answer correct to 1 decimal place D 30 7 cm C

Q4 a Find the ratio of areas and volumes of the two spheres O 2a 2 marks D b Two similar cones have heights in the ratio 3 5 If the total surface area of the larger cone is 75 cm find the total surface area of the smaller one 3 marks

Hint Since AB is perpendicular to BC the slope of AB x the slope of BC 1 O A p q 7 B p q 7 O O C g p 7 O D 9 p 7 B 90 O

Jsing the information provided on the graph draw the line the line that is perpendicular to line segment AB and passes through point P Drawing Tools Select Point Line Click on a tool to begin drawing Reset 10 8 6 4 B 2 A 10 6 2 4 6 8 Delete 2 4 Undo 6 8 a 10 A

D A 2 1 6 4 2 2 4 6 8 0 O B G CO

2 Direct labour per unit Variable overhead perunit 16 3 lost per unit of finished goods Total cont product lost per unit Number of units in fineshed Total cost of finished goods invertory Total product cost per unit Number of units in sold goods Total cost of sold goods 31 31 4 350 134 850 16000 496 000

9 1 Find the measure of x 9 pts for a non trig solution 2 pts for a trig solution A 20 60 to E 30 50 B

20 f com 8 1914 the plans 56 tof 1 PAGE CUS 2642 Tax F

7 D E and F are midpoints If AB 14 find EF A D B E F C Cross off the value of the last digit of your answer

In 8 use the figure to label the given angles then find the indicated angle s Drawing is not to scale 8 Ifm AEB 38 m CEB 67 m CED 42 Then m BED and m AED A B D

2 of 2 ES eBook Print eferences Required information Direct labor hours DLH Machine hours MH Purchase orders PO 35 500 4 000 150 3 Compute product cost per unit for Pup tents and for Pop up tents 4 For each product compute the gross profit per unit selling price per unit minus the product cost per unit Complete this question by entering your answers in the tabs below Activity 17 500 6 000 350 Required 1 Required 2 Required 3 Required 4 Compute an activity rate for each activity using activity based costing Note Round Activity Rate to 2 decimal places Assembly Electricity Materials purchasing Budgeted Cost Budgeted Activity Usage Activity Rate

9 If m BED 15x 47 and mBD 9x 1 find mZCBD 5x3 B D

B 93 E 161

1 m YZV Value or measure Assume tha 144 V Z X 114

5 m EFG 121 H D 39

Finan X Finan X unchUrl https 253A 252F 252Fir Body Con Dre Saved Learning to Read f W Wiki leaving Sewing incorrect for the work you have completed so far It does not indicate He 318 000 84 000 166 000 Sewing Sales on credit 1 275 000 520 000 1 700 000 rect head rates as a percent of direct labor eaving 85 160 5 350 000 Return t S 10 11 of 17 Next Answer is complete but not entirely correct your answers in the tabs below A With 2 W P tries dated June 30 to record a goods transferred from weaving to sewing b goods transferred from sewing sale of finished goods and d cost of goods sold cost of goods sold Hint Compute the total production costs in each department and then subtract the ending the amount transferred out of each department the a cost of products transferred from weaving to sewing b cost of products transferred from sewing to finished

X 17x 20 59 W Y

G 68 H 31 K 115 m GHJ m GIJ

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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