Geometry Questions

An ellipsoid is a 3D shape whose cross sections are ellipses A whispering gallery is a room with a half ellipsoid ceiling If one person whispers from one focus another person can hear them clearly from the other focus Suppose a whispering gallery has 5 foot walls A cross section of the ceiling can be modeled by the ellipse shown below centered at the origin with a horizontal major axis If the maximum height of the ceiling is 20 ft and the width of the room is 50 ft write the equation of the ellipse 201 50 5

What set of reflections would carry trapezoid ABCD onto itself 1 point A BO T 9 2 C Ox axis y x y axis x axis Ox axis y axis x axis Oy x x axis x axis Oy axis x axis y axis x axis T D 3 2 27

Suppose h x is a linear function and the points points 2 4 and 5 13 lie on the graph of h x Complete the following tasks 1 Calculate the slope of the function using the two points provided 2 Substitute either of the points and the slope into slope intercept form and solve for b 3 Write the slope intercept form of the function

earthquake intensity measured by 1 lo x 10 m lo is reference intensity and M is magnitude An earthquake measuring 6 1 on the Richter scale is 125 times less intense than the second earthquake What would the Richter scale measure be for the second earthquake

Exercise 7 3 2 Find the direction and length of each principal axis of the hyperbola given by the equation below and sketch its graph 7x 48x1x2 7x3 25

lete the information on the unit 63 tartos mont wan Th 33 k 511 G TE 77 le 16pts 27t 312 3 5 57t 44T 51 dongtag wens glad of wolad mergan 23 TE 0 1 311 0 1 ME SACEN T 5TE 72 7 TU This alt 11m 2 T 1 0 3 sjo aroddi arize

earning Activity 28 Jace Find the surface area of following 4 m 18 m 5 m 6 cm 2 cm 8 cm 4 cm 6 cm

A circle of radius 12 units is divided into 8 congruent slices 1 What is the area of each slice 2 What is the arc length of each slice square units T units

Find the volume of this object Use 3 for Volume of a Cylinder V r h 4 ft 9 ft 5 ft 5 ft 5 ft Volume of a Rectangular Prism V lwh V ft

3 the area of each regular polygon Leave your answer in simplest form 2 10 8 8 3 13 12 4 10 6 8 3 11 16

1 A diver jumps from a cliff into the water below The path of the diver is given by the function f x t 4t 12 where f is the height of the diver above water level in metres after t seconds Hassan calculated the following average rates of change in the height of the diver over the following intervals 1 1 1 st 2 AROC 1m s ii 2 st 3 AROC 1m s iii 3 st 4 AROC 3m s Based on these values which of the following statements is FALSE about this situation a The AROC from 3 to 4 seconds is a smaller negative value therefore it implies that the diver is slowing down as it gets closer to the ground b The AROC from 1 to 2 sec is that same as the AROCI for 2 to 3 sec and since the first AROC is positive and the second is negative it implies that a maximum height was reached in the middle at 2 seconds c The diver was at first increasing in height and then decreasing to the AROCS changing from positive values to negative values

point In a basketball drill two players start at the same spot on the court One player runs 6 feet down the court and the other player runs 4 5 feet across the court in a direction perpendicular to the first player What is the distance that one player must pass the ball for it to reach the other 6 5 feet 7 5 feet 4 feet 8 feet Da

Determine an equation for the sinusoidal function given 2 45 0 M 135 180 225 270 315 360 45 J 9 0

Which of the following exponential functions grows at the slowest rate Select one O a y 2 O b y 0 5 O c y e O d y 5

1 point Inverse tangent is used to find a missing angle measure when we are given the opposite side hypotenuse opposite side adjacent side adjacent side hypotenuse same side other side and the

4 What inverse trig function can be used to find the measure of angle A tan 1 Cos 1 12 none sin 1

X 12 Solve for X Y 13 Y Round to the nearest tenth X 30 degrees Y 60 degrees X 67 4 degrees Y 22 6 degrees X 60 degrees Y 30 degrees X 22 6 degrees Y 67 4 degrees

A function is defined by f x 3x where x 0 Find f x Select one O a 3 x 1 O b O d 3x x 1

Solve the following exponential equations 4 4x 16 Select one O a x 4 O b OC O d x 2 X 2 x 4

Find the sum of the infinite Geometric Series 25 5 1 1 12 15 Round to the nearest hundredth if necessary M

Find the sum S 6 K 1 Select one O a 728 O b 364 OC 364 O d 346 3 k 1

Solve the following exponential equation 9 2x 1 27 x 0 Select one O a 1 O b 1 O C 2 d 2

Solve the following equation x log 1 2 16 Select one O a 4 O b 2 O C 2 O d 4

Choose the graph of In x 1 Select one O a O b O C 10 10 10 20 10 0 10 20 10 0 10 20 10 0 10 10 10 20 20 20

onvert the following to the exponential form 2 log 5 25 Select one O a 30 1 O b 52 25 O c 53 125 O d 35 243

olve the following equation e 3x 9 elect one O a 0 459 O b 0 327 OC 0 237 O d 0 732

The function f x 3 demonstrates Simplify the following log 2 x 8 log2x4 Select one O a log2x linear degression linear growth exponential decay quadratic increase exponential growth logarithmic growth

mplify the following log 2 x log 2 x 4 elect one a log x b c d 4 log2x 8 log 2x 2log 2x

the following graph of a function modeling damped harmonic motion Find the equation for the function pictured in terms of y and 1 Assume that a factor of e provides the desired damping effect and that the graph has no vertical or horizontal shifts 4 2 2 Enable Zoom Pan t

y 2 x find the value of y elect one a 1 4x b 4x C 22x d 24x

onvert the following to logarithm form 4 16 lect one a log 42 16 b log 2 16 4 O c log 4 16 2 O d log 16 4 2

Find a 8 of a geometric sequence if the first few terms of the sequence are given by 1 3 9 27 Select one O a 2 187 O b 7 880 OC 1 934 O d 3 405

What operation s would you perform on the longer leg across from the 60 degree angle of a 30 60 90 triangle to get the length of the hypotenuse Divide by 2 multiply by 2 Multiply by 2 Divide by 3 multiply by 2 Divide by 2

1 point The sine of 72 degrees is 0 95 What s the cosine of 18 degrees 1 0 95 0 8 0 05

8 1 point B 48 b C a 3 2 a 3 3 46 If c 6 solve for a a 3 a 6

Step 1 of 2 Identify the shape of the more basic function that has been shifted reflected stretched or compressed Answer 3 Points MM MM Keyboard X

Determine in which of the four quadrants angle is located given Answer 5 Points csc 0 0 and cos 0 0

Note I means perpendicular A Given AC LBD and C is the midpoint of BD Prove A ABC ADC B C right angles 3 4 Statements AC LBD C is the midpoint of BD ZBCA and LDCA are D AC AC A ABC A ADC Reasons 1 2 Definition of perpendicular All right angles are Definition of Bisect 5 6 Which choice belongs in space number 3 LABC LADC A BCAA DCA OZBCARGA

What is the volume of the square pyramid cm Round to the nearest tenth as needed C

17 1 point B 1 Which construction is shown Rhombus Copy an Angle Perpendicular Bisector Perpendicular Through a Point C

Which of the following can only be used after you prove triangles are congruent Alternate Interior Angles CPCTC Substitution Reflexive

1 point Which of the following can be used in this picture with no additional information needed Vertical Angles CPCTC Substitution Alternate Interior Angles

6 1 point A B C E Which angle is congruent to angle B Angle E Angle D Angle F Angle C

6 5 ft Surface Area 13 ft 5 ft

6 1 point Given DF ER DH EG and DF ER Prove H is the midpoint of FG Statements DF EH DH EG 1 LDFHLEHG and LDHF LEGH ADFHAEHG Reasons Given Given 2 3 FH HG 4 H is the midpoint of FG 5 Which statement belongs in space number 3 AAS The triangles are not congruent HL ASA

8 1 point Which construction could this be Inscribed Equilateral Triangle Inscribed Star Inscribed Octagon Inscribed Square

Verify each identity 1 tan x tan x 4 COS X cos 2x sin xcsc x

13 Given the formula A r find the area A of a circle whose radius is 0 00000607 in O3 32929 x 10 in 9 70 O 3 721 x 10 in 9 3 51649 x 10 9 in 3 68449 x 10 1 in

Which of the following types of angles are congruent Corresponding Complementary Supplementary Linear Pair

Which of the following can be used when two triangles share an angle Substitution Reflexive Alternate Interior Angles Vertical Angles