3D Geometry Questions and Answers

Coordinate Geometry:Question 9 Which of the following is the standard form of the equation of a circle defined by x² + y² + 10x = 0? Select one: O x² + (y + 5)² = 0 O (x - 5)² + y = 25 O (x + 5)² + y² = 25 O x² + y² = 25

Alfred is practicing typing. The first time he tested himself, he could type 45 words per minute. After Npracticing for a week, he could type 48 words per minute. After two weeks he could type 51 words per minute. Based on this pattern,predict how fast Alfred will be able to type after 4 weeks of practice. 61 words per minute 51 words per minute 54 words per minute 57 words per minute

Is the following definition of perpendicular reversible? If yes, write it as a true biconditional.Two lines that intersect at right angles are perpendicular. Yes; if two lines are perpendicular,then they intersect at right angles. Yes; if two lines intersect at right angles, then they are perpendicular. Yes; two lines intersect at right angles if (and only if) they are perpendicular. The statement is not reversible.

What is the converse of thefollowing conditional? If a point is inthe fourth quadrant, then its coordinates are negative. If a point is in the fourth quadrant then its coordinates are negative. O If the coordinates of a point are not negative, then the point is not in the fourth quadrant. O If the coordinates of a point are negative, then the point is in the fourth quadrant. If a point is not in the fourth quadrant, then the coordinates of the point are not negative.

Construct an experimental probability distribution. Use the 8-sided die link or random number generator in google classroom to simulate rolling two 8-sided dice 100 times. X represents the sum of the values found by rolling two 8-sided dice. a. Construct a relative-frequency table. b. Graph the experimental probability distribution.

Draw your own triangle given the indicated measures and solve for the other parts using Sine Law. Write an explanation in each line of your solution. 1. <A = 73°, a = 18, b = 11 2. <A = 26°, < C = 35°,b=13

Type the inverse of the matrix. Use decimals. If no inverse exists type "none". [23] 25

The time-t price of a stock within the Black-Scholes framework is S(t). You are given: (i) The stock pays continuous dividends at an annual rate of 0.02. (ii) The stock's volatility is 0.3. (iii) The continuously compounded risk-free interest rate is 0.06. (iv) S(0)=50 A claim on the stock pays (S(2) - 50)³. Calculate the price of the claim at 0.

Problem21.A circular cylinder is formed by rolling an 8 1/2x11" paper vertically and taping it with no overlap. A second cylinder is formed by rolling an 8-1/2 X11" paper horizontally and taping it with no overlap. What is the ratio of the volume of the 8 1/2 tall cylinder to 11" tall cylinder to the volume of th the 11" tall cylinder? (A) 11/8 (B) 17/11 (C) 3/2 (D) 22/17 (E) 11/17

Identify the geometries (Euclidean, hyperbolic, and/or spherical) in which each statement is true. Given a line and a point, there is a unique line containing the point that is perpendicular to the line. Two lines always intersect in a single point. Given two parallel lines and a transversal, alternate interior angles are necessarily congruent. Given triangles ABC and DEF, if AB = DE, BC = EF, and angle B is congruent to angle E, then triangle ABC is congruent to triangle DEF.

Problem 3. Let ABC be a triangle. Let C' be the midpoint of the side AB. Let A' be a point on the side BC such that CA' = 2A'B. Let B' be a point on the line AC such that CB' = 4CA. Let M be the point of intersection of the line A'B' and the line CC'. Does the point M belong to segment CC? Find the ratio of CM: MC'.

A curb is 4 inches high. The ramp from the sidewalk to the street follows the same guidelines as other ramps (no more than 4.8 degrees, so a 1: 12 ratio of vertical to horizontal). What is the horizontal distance for a ramp with a 4 inch vertical distance? Image not drawn to scale. Flared sides smoothly connect the ramp to the sidewalk. The guidelines say the flared sides must be no more than 5.7 degrees (1 : 10 ratio of vertical to horizontal). What is the horizontal distance for flared sides with a 4 inch vertical distance?

Calculate the Euler characteristic of the surface M:xy-z=0

Determine the volume of region inside both x² + y² + (z-2)² = 4 and z =√3x² + 3y².

The voltage V. in an electric circuit is measured in millivolts (mV) and is given by the formula V=0.2sin0.1m(t-0.5) +0.3, where t is the time in seconds from the start of an experiment. Use the graph of the function to estimate how many seconds in the 40 second interval starting at t= 0 during which the voltage is below 0.21mV. Select one: a. 14.06 b. 7.03 C 12.97 d. 27.16

If the lengths of the legs of a right triangle are 5 and 7, what is the length of the hypotenuse? A. 2√3 B. 12 C. √35 D. √74

Assume the Cartesian model for Euclidean geometry. Find the images of the points (0,0), (0, 2), and (2, 1) under the following isometries. (a) The glide reflection GAB, where A = (-2,0) and B = (0, 1).

For a regular octagonal prism, suppose that the length of each base edge is 2.5 cm. and the apothem of each base is 3 cm. The altitude of the prism measures 4 cm. Find the total (surface) area and volume of the prism.

Imagine if you will that across the 26 stores assigned the $499.00 price point, an average of 127.4 phones were sold, whereas an average of 119.6 were sold for $519.00. Further, 117.8 were sold at the price point of $549 and 114.3 were sold for the price point of $599.00. Perform the appropriate multiple comparison test at alpha = .05, to see which means are significant from the others, if any. According to your findings which means are pairwise different from each other and why? Show all work

What is Volume? What are some ways knowing the volume of an object will help you in the real world?

Solve sin^2(t) = 8 cos(t) for all solutions 0 <t <2π t= Give your answers accurate to 2 decimal places, as a list separated by commas

Find all solutions z = x + iy of the equation f(x) = ai where a is a strictly positive real number and f:C--> C:2 -->e^iz + e^-iz.

Sketch the following regions in cylindrical coordinates: (a) 1 ≤r ≤ 3,0 ≤ θ ≤ π/2,0 ≤z≤1 (b) r² + z² = 9 (Hint: what is this in Cartesian coordinates?)

If a person obliquely leans on the wall with a protruding part at the bottom as follows and is measured at 180cm, how can I calculate the difference with the height in case there was no protruding part but the person stood straight with the wall to be measured?

An action movie production team needs glass spheres to hold a green liquid that looks like an explosive. If all of the available 3,392.92 cubic inches of the liquid is to be poured into 30 glass spheres, what should the diameter of each sphere be? Assume that each sphere is filled to the top. A). 3 inches B). 4 inches C). 6 inches D).8 inches E). 9 inches

A candle manufacturer sells cylindrical candles in sets of three. Each candle in the set is a different size. The smallest candle has a radius of 0.5 inches and a height of 3 inches. The other two candles are scaled versions of the smallest, with scale factors of 2 and 3. How much wax is needed to create one set of candles? A. 27π cubic inches B. 36π cubic inches C. 53π cubic inches D. 86π cubic inches E. 98π cubic inches

Type the correct answer in the box. The volume of clay used to build a cylindrical pillar with a height of 9 centimeters is 324πt cubic centimeters. The area of the base of the pillar is ______ π Square centimeters.

A satellite launch rocket has a cylindrical fuel tank. The fuel tank can hold V cubic meters of fuel. If the tank measures d meters across, what is the height of the tank in meters? A)2V/πd² B)4V/d² C)V/πd² D)4V/πd² E)8V/πd²

A cylindrical can has a radius of 7 inches and is 3 inches tall. Find the volume of the can. Volume =_________

The volume of a sphere with radius r is given by the formula V = 4/3πr³. Find the volume of a sphere with diameter 30 inches is __cubic inches. Use 3.14 or the π key on your calculator. Round your answer to the nearest tenth if necessary.

Determine the type of the second-order surface and find the coordinates of its center (if it exists): 3x² + y² + 4z² - 2xy - 6xz+4yz + 4x - 2y - 6z= -=-1

A gumball has a radius that is 32 mm. The radius of the gumball's spherical hollow core is 28 mm. What is the volume of the gumball if you do not include its hollow core? Answer: ______x mm³

A regular right square pyramid has a lateral surface area of 161 m² and a total surface area of 235 m². Determine the length of the edges of its base, its slant height, its height and the length of its lateral edges. Express your answer to 3 sig figs. 1). Length of edges of the base =_____METRES 2). Slant height =____METRES 3). Height =____METRES 4). Length of the lateral edges =____METRES

Problem 18. Let P = (0,1/2), Q=(1/2,0) and R = (-1/2,0). 1. Compute the perimeter of the hyperbolic triangle △PQR. 2. Compute the angles ∠PQR, ∠QRP and ∠QPR.

Calculate the volume of a cylinder that is 5 cm tall with a radius of 4.3 cm. Round to the nearest tenth of a cubic cm Enter the number portion only.

Out of 100 emails, 60 are spam and 48 of those contain the word buy. Of the remaining 40 emails that are not spam, only 4 emails contain the word buy. Given that an email is spam, what is the probability that it contains the word buy? A 0.80 B. 0.87 C. 0.92 D. 0.97

Amy has a box containing 6 white. 4 red, and 8 black marbles. She picks a marble randomly. It is red. The second time, she picks a white marble. In the third attempt. Amy picks a white marble again. Amy has not replaced the marbles she picked. The probability that the fourth marble Amy picks is black is______ If Amy picks a black marble in the fourth attempt, the probability that in the fifth attempt she will pick a red or a black marble is_____

Select the correct answer. A company that manufactures smartphones makes 70% of the phones with a touch screen and 55% of the phones with HD movie capability. 30% of the phones have both a touch screen and HD movie capability. What is the probability that a smartphone chosen at random has either a touch screen or HD movie capability? A.19 /20 B. 47/50 C.13/20 D. 43/50 E. 17/20

Find the shortest distance from the point P to the plane and find the point Q on the plane closest to P if P(2, 3, 0) and the plane has an equation 5x+y+z=1.

In the accompanying diagram of circle O, AOED is a diameter, PD is a tangent, PBA is a secant, chords BD and BEC are drawn, m∠DAB = 43, and m∠DEC = 72. Find: m∠BDP, mAB, mAC, m∠P, m∠CBD

The given plane intersects the following paraboloid in an ellipse. Find the points on the ellipse that are nearest to and farthest from the origin. x + y + 2z = 2; z = x² + y² ) (nearest point) ) (farthest point)

Which of the following statements is false? A. A square is a regular quadrilateral. B. The diagonals of a rectangle are perpendicular. C. Opposite sides of a parallelogram are congruent. D. A rectangle is an equiangular quadrilateral.

In AABC, |OG| = 2, |GA| = 3 and |A'O = 4. What is R? (As usual, O is the circumcenter, G is the centroid, A' is the midpoint of BC, and R is the circumradius.)

Use spherical coordinates. Evaluate ∫∫∫Ex y² dv, where E is the solid hemisphere x² + y² + z² ≤ 4, y ≥ 0.

Use cylindrical or spherical coordinates, whichever seems more appropriate. Find the volume of the smaller wedge cut from a sphere of radius a by two planes that intersect along a diameter at an angle of π/3

Use cylindrical coordinates. Evaluate ∫∫∫E (x - y) dV, where E is the solid that lies between the cylinders x² + y² = 1 and x^2 + y^2 = 16, above the xy-plane, and below the plane z = y + 4.

Out of all points in the top half of the unit ball, what is the average distance from the origon?

A stone pyramid in Egypt has a square base that measures 146 m on each side. The height is 94 m. What is the volume of the pyramid? m³

A cylindrical soup can has a radius of 1.3 in. and is 5 in. tall. Find the volume of the can. Round your answer to the nearest tenth if necessary.

A cone-shaped pile of sawdust has a base diameter of 36 feet, and is 14 feet tall. Find the volume of the pile. Round your answer to the nearest tenth if necessary.