3D Geometry Questions and Answers

3 Amazing Diagram Find the area of ACDE A D a 0 C E H ACDE b 02

in the list below determine whether or not each example is a rigid motion If it is a rigid motion identify the type of transformation 6 points Example Flipping a pancake Deflating an air mattress Moving a clock s minute hand nlarging a photo ing a golf ball Rigid motion Yes or No If yes what type of rigid motion

Use n 10 and p 0 7 to complete parts a through d below a Construct a binomial probability distribution with the given parameters P x 0 2001 0 2668 P x 0 0000 0 0001 0 0014 0 009 0 0368 5 0 1029 Round to four decimal places as needed X 0 1 2 3 4 X 6 7 8 9 10 0 2335 0 1211 0 0282 b Compute the mean and standard deviation of the random variable using x Hx 7 00 Round to two decimal places as needed ox Round to two decimal places as needed h Ex P x and ox X P x H

1 Using the picture below which statements are TRUE select 2 choices H D F G and H are coplanar J G D and H are coplanar D G F are collinear G F H are collinear

Find the approximate value of using the trapezoidal rule with four subdivisions Draw a graph to illustrate The estimated value is Give your answer accurate to four decimal places This answer is an x dx 3 under estimate over estimate Explanation of answer above because the function is concave up because the function is concave down because the function is increasing because the function is decreasing

Find the first fundamental form of polar coordinate of xy plane First fundamental form of plane is x noso y rsino x y roso asinos

1 Find the volume of the prism 7 ft 7 ft 240 ft 343 ft 251 ft 232 ft 7 ft

Suppose you invest 3800 in an account with an annual interest rate 6 compounded monthly 0 5 each month At the end of each month you deposit 325 into the account Use this information to complete the table below Round to the nearest cent as needed Month 1 2 3 4 LO 5 Prior Balance 3800 4489 72 Question Help D Video 0 5 Interest on Prior Balance 24 19 Monthly Deposit 325 325 325 325 Ending Balance 3800 4489 72

In India many families use mini solar cookers on their balconies In most instances the sun s rays reflect off the parabolic mirror toward the dish which is placed 32 cm from the center of the cooker The distance from the vertex to the edge of the cooker is 68 cm Use the diagram to help answer the discussion questions them Ergo of Cook 12m 320 Certs of C01 Edge of Co What are the coordinates of the edges of the cooker What is the distance all the way across the cooker from the two points labelled edge of cooker

Find the distance between the skew lines with parametric equations x 3 t y 2 6t z 2t and x 2 2s y 6 15s z 3 6s 351 6814

Match the equation with its graph x 36y2 4922 1 O O MORA

Find the first 3 terms in the expansion of 1 2x 4 Select one a b 1 8x 24x 1 8x 24x c 1 8x 24x Od 1 8x 24x

Use the factored form of the polynomial function below to describe its end behaviors x 2 x 3 x 2 x 1 0

This is a vector wit 8 magnitude

Determine the surface area of the geometric figure 3 2 ft 3 ft 2 4ft 3 2 ft 6 ft

When graphing the polar equation r 6 sin 60 as moves from to radius changes from 0 to 6

The center of an ellipse is located at 0 0 One focus Which equation represents the ellipse is located at 12 0 and one directrix is at x 14 1 12 x 2 13 2 y 2 5 2 1 x 2 13 2 y 2 12 2 1 x 2 14 2 y 2 5 2 1 x 2 14 2 y 2 13 2 1 Mark this and return

Listen What is the preimage of A B A B A

Let f be a differentiable function such that f 8 2 and f 8 5 If g is the function defined by g x f x 3 x what is the value of g 8 59 24 NOT 2 61 24 60

What is the value of the trig ratio sin A sin A B 20 C 21 29 A

Graph the function by setting the x intercept and the asymptotes Provide your answer below 10 2 5 0 10 5 f x 4 0 2 0 X 1 x 1 10

Find the volume of the right cone shown as a decimal rounded to the nearest tenth 26 m 18 m Not drawn to scale 3 2205 4 m 3 980 2 m 3308 1 m 3

Find the volume of the square pyramid shown Round to the nearest tenth if necessary 11 cm Not drawn to scale 3 O 126 cm 907 5 cm 3 55 cm 3 605 cm 15 cm 3 11 cm

s For the shown land L 25m L 75m 0 80 0 55 and Area 1800m Area 900m Find the angle 0 L F Area1 8 Marks E Area2 03 D

The volume of the rectangular pyramid below is 120 units Find the value of x X 9 4

A pyramid with three regularly side S ABC know m BSC 60 degree Through BC make a perpendicular line H with AS Height of the pyramid is 2root2 Find the slice of H with the pyramid

As shown in the diagram below the radius of a cone is 2 5 cm and its slant height is 6 5 cm 6 5 2 5 How many cubic centimeters are in the volume of the cone 1 12 5m 3 30 0m 2 13 5 4 37 5m No Work No Credit Please show

Triangle ABC with vertices at A 0 0 B 3 5 and C 0 5 is graphed on the set of axes shown below 0 1 23 m Which figure is formed when ABC is rotated continuously about AC P FG 3

Let s say every one of the eight cubical cells in the picture has a side length of 10 metres If this net of cubical cells is folded up into a tesseract and you start moving through the cubical cells in the direction of the arrow how far have you moved when you return to your starting point Answer

Which figure can have the same cross section as a sphere 1 21 R

In the diagram below congruent figures 1 2 and 3 are drawn F E D B 2 F cu D D E C B 2 a rotation followed by a translation 3 a translation followed by a reflection 4 a translation followed by a mitation is 3 Fr B A Which sequence of transformations maps figure 1 onto figure 2 and then figure 2 onto figure 3 1 a reflection followed by a translation U

A solid metal prism has a rectangular base with sides of 4 inches and 6 inches and a height of 4 inches A hole in the shape of a cylinder with a radius of 1 inch is drilled through the entire length of the rectangular prism 4 in in 4 in 6 in What is the approximate volume of the remaining solid in cubic inches

How can we conclude that a and b are perpendicular if a b 0 Select one a The graph of the vectors are in opposite quadrants b None of these O c If the vectors are perpendicular the magnitude of one of the vectors would be zero so the dot product would be ze d The slopes of the vectors are reciprocals of one another

The Horizontal Line Test If it is possible to draw a horizontal line that touches the graph in at least two places then the function does not have an inverse Parabolic graph with no inverse Same graph with a red horizontal line that touches the graph in two places When the inverse function exists we can sketch a graph by switching the roles of x and y For every point on the graph swap the x and y values Another way of describing this transformation is to reflect the graph over the line

BY USING MATHEMATICA SOFTWARE 1 Given four points 0 1 1 2 2 2 and 3 1 with no order Plot a control polygon connecting four given points to generate the following cubic B zier curve DA a h c d e

At what point do the curves r t t 5 t 35 t and r s 7 s s 2 s intersect x y z Find their angle of intersection 0 correct to the nearest degree 0

Evaluate the flux integral SF ds where F x y z x 1 y 2 3 and C is the outward upward oriented half sphere z 9 x y 0 z 3

Find an equation for a parabola with vertex 1 3 and focus 1 3

Dmitry and Sofie were converting the rectangular equation x y 5y 3 to polar form They each take a different approach for the first step and ask you if they are correct Dmitry x y 5y 3 r 5 sin0 3 You conclude Sofie x y 5y 3 r cos 0 r sin 0 5 rsin 3 correct because you remember that is true

2 Anton will be constructing a segment bisector with a compass and straightedge while Maxim will be constructing an angle bisector with a compass and straightedge Describe the similarities and differences between their construction steps

Find the angle of the sector below if the area of the sector is 36T P 18 Q

3 The volume of a triangular prism is 70 in The base of the prism is a right triangle with one leg whose measure is 5 inches If the height of the prism is 4 inches determine and state the length in inches of the other leg of the triangle

Find the distance from the point to the plane 2 4 1 x 4y 4z 18 The distance is

Determine the graph of the equation 2 2 4 Choose the correct graph of the equation OA O C B O D G 0 y

Determine the graph of the ellipsoid 36x y 2 36 Choose the correct graph of the equation OA OB O C

5x 2z 133 hes Identify the surface by type paraboloid ellipsoid etc Choose the correct graph of the equation below OA O B HID O C

Find the equation for the plane through the point Po 0 5 5 and normal to the vector n 7i 2j k Choose the correct answer below OA 7x 2 y 5 z 5 0 OB 7x 2y z 5 OC 7x 2y z 0 O D x 7 5 y 2 5 z 1 5

14 Which statement below correctly relates BDC and ZBAC B A a ZBDC and ZBAC are complementary ZBDC and ZBAC are supplementary b c ZBDC and ZBAC are congruent d It is impossible to determine a relationship between ZBDC and ZBAC

Find the lateral area of each cone 2 A 20 cm 57 9 cm 10 m 2 m ANS L A bi

17 Which of the following sets of numbers can be the lengths of the sides of a tri A 12 9 4 B 1 2 3 C 5 5 10 D 2 5 18