Coordinate system Questions and Answers

Find the equation of the hyperbola with vertices (-2, 1) and (6, 1) and foci (-3, 1) and (7, 1). Provide your answer below:

Consider incompressible irrotational flow due to two line vortices, one centred at z = 6 in the complex plane, the other centred at z = 51, both with counter-clockwise circulation T = 2π. (a) Enter the complex potential w of the flow as a function of z=x+iy. w(z) =________ (b) Enter the complex velocity as a function of z. u-iv=________

Graph the function below on a graphing calculator and approximate to the nearest tenth the real zeros of the function. ƒ(x) = x² − 4x − 3 -0.7 0.8 -0.8 1.8 2.4 -0.2

In the figure below, O is the center of the circle. Name a secant of the circle. A. FG B. AO C. HK D. AB

Three ships, A, B, and C, are anchored in the atlantic ocean. The distance from A to B is 36.318 miles, from B to C is 37.674 miles, and from C to A is 11.164 miles. Find the angle measurements of the triangle formed by the three ships. A. m∠A= 17.22942; m∠B = 74.4879; m∠C = 88.28267 B. m∠A= 88.28267; m∠B = 74.4879; m∠C = 17.22942 C. m∠A= 88.28267; m∠B = 17.22942; m∠C = 74.4879 D. m∠A= 74.4879; m∠B = 17.22942; m∠C = 88.28267 Reset Selection

Show that |Re(−2+ z − 3z²+z³)| ≤7 when |z| ≤ 1.

Find the distance between the points (-6, 7) and (0, 8). A. 2.61 B. 7.16 C. 7.8 D. 6.08

Find the midpoint of the segment between the points (1, 1) and (4,-16) A. (-3/2, 17/2) B. (-5,15) C. (5, -15) D. (5/2,-15/2)

What is the image of (5,-2) under the transformation ry = x A. (-2,5) B. (5,2) C. (2,5) D. (-5,2)

Describe the translation. y = (x - 2)² +5 ---> y = (x + 2)² - 3 A.T<-4,8> B.T<4,8> C. T<4,-8> D. T<-4,-8>

Find the coordinates of P so that P partitions the segment AB in the ratio 1:1 if A(-4, 15) and B(10, 11). A. (11, -17) B. (7,-2) C. (3, 13) D. (-4, 14)

Find the point Q along the directed line segement from point R (-3, 3) to point S(6, -3) that divides the segment in the ratio 2:1. A. (3, 0) B. (0, 1) C. (6,-4) D. (3,-1)

Find the distance between the points (0, -4) and (-6, 7). A. 12.53 B. 6.71 C. 45 D. 157

The midpoint of a segment is (2, 1) and one endpoint is (8, 7). Find the coordinates of the other endpoint. A. (-4,-5) B. (-4, 13) C. (14, 13) D. (14,-5)

Find the midpoint of the segment between the points (15, 3) and (2, -14) A. (17,-11) B. (17/2, -11/2) C. (13/2, 17/2) D. (17, 11)

Find the distance between the points (4, 0) and (-3, 4). A. 17 B. √65 C. √17 D. 65

Find the distance between the points (4, -2) and (0, 10). A. 14.25 B. 8.5 C. 8.94

Find the midpoint of the segment between the points (3, 17) and (-14,-8) A. (-11/2, 9/2) B. (17/2, 25/2) C. (-11,9) D. (11,-9)

What is the possible number of common transversal lines of a given 4 pairwise skew lines?

Describe the translation. y= (x – 5)2 + 5 –→y= (x – 0)2 + 0 A. T<5,-5> B. T<-5,-5> C. T<-5,5> D. T<5,5>

Write the equation of the line that is parallel to the line y = -7+ x - 2 through the point (4,-2). A. y=-7/4 x-5 B. y = -7/4 x +5 C. y = 5x - 7/4 D. y= 4/7 x+5

Find the midpoint of the segment between the points (15,-9) and (-2,-18) A. (13, -27) B. (-13,27) C. (13/2, -27/2) D. (17/2, 9/2)

Use the Rational Zero Theorem to find a rational zero of the function f(x) = 2x³ +7x² + 10x +8. Do not include "=" in your answer.

If a translation maps point A(-3,1) to point A'(5,5), the translation is: A. (x+8, y + 4) B. (x+2, y + 4) C. (x+2,y+6) D. (x+8, y + 6)

On the outside, a closed rectangular packing box, made out of cardboard, is 12 inches long, 18 inches wide, and 24 inches high. If the cardboard is 14 inch thick, which of the following is closest to the volume inside the box, in cubic inches? (A) 3,700 (B) 3,900 (C) 4,300 (D) 4,700 (E) 5,200

Use the intercepts to graph the equation. 4x + 5y = 20 Use the graphing tool to graph the line. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line.

Shown on the right is the graph of 7y = 5x + 7. Determine its symmetries (if any). This graph is A). symmetric to the origin. B). symmetric to the x-axis. C). symmetric to the y-axis. D). not symmetric to the x-axis, y-axis, or origin.

For the function y = - 4x + 5, answers parts a. through c. a. Find the slope and y-intercept (if possible) of the graph of the function. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is (Type an integer or a simplified fraction.) B. The slope is undefined. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept is (Type an integer or a simplified fraction.) B. There is no y-intercept.

Sketch an odd function with a positive leading coefficient having all of the following features: .Zeroes at x = 3, x = 1, and x = -1 y-intercept at 3 2 turning points

Complete the square and then use the shifting technique to graph the function. f(x)=x²-2x-1

A baseball team plays in a stadium that holds 52000 spectators. With the ticket price at $10 the average attendance has been 22000. When the price dropped to $7, the average attendance rose to 26000. Assume that attendance is nearly related to ticket price. What ticket price would maximize reve?

Sketch a graph of the function f(x) = -3 sin(4x).

Find the result of the parallel transport of a vector throughout: a) the equator of the sphere. b) the horizontal circles of the cylinder x^2+ y^2 = 1, z = z0. c) the vertical lines of the cylinder x^2 + y^2 = 1, x0 = xO, y = y0. d) the horizontal circles of the cone x^2 + y^2 = z^2, z = z0. e) the horizontal circles of the sphere x^2 + y^2 + z^2 = 1, z = z0 NOT DEFINITION. PARALLEL TRANSPORT OF VECTOR

Write the canonical equations of the straight line passing through the point M₁(2,0, -3) and parallel; a) to the vector a = (2, -3,5); b) to the straight line( x-1)/5 = (y+2)/2 =( z+1)/-1; c) to the axis Ox; d) to the axis Oy; e) to the axis Oz.

Use Taylor's Theorem to obtain an upper bound for the error of the approximation. Then calculate the value of the error. (Round your answers to three significant figures.) sinh(0.7) ≈ 0.7 + (0.7)³/3! R₃ ≤ ____ R₃ = _____

The following is a list of P/E ratios (current stock price divided by company's earnings per share) for 19 companies. 57, 53, 50, 46, 42, 35, 31, 56, 52, 49, 45, 55, 55, 51, 51, 48, 48, 48, 44 Draw the histogram for these data using an initial class boundary of 30.5 and a class width of 6. Note that you can add or remove classes from the figure. Label each class with its endpoints.

Instructions: Work the following two situations and upload the documents with your processes. Situation 1: Explain the characteristics that determine whether a function is invertible. Present an algebraic example and a graphical example that justifies your argument. Situation 2: Find the inverse for the function f(x) = 3/x-1 and present the Domain and Range sets for both f(x) and f^-1(x).

1) Find the number of sides of a polygon if the sum of the measures of the interior angles is: (a) 1,800 (b) 2,700 (c) 540 (d) 2,160 2) Find the measure of the remaining angle of each of the following figures, given the measures of the other interior angles. (a) Quadrilateral: 42,75, and 118 (b) Pentagon: 116, 138, 94,88 (c) Hexagon: 95,154,80, 145, 76

(13) Find the number of sides in a polygon if the sum of the measures of the interior angles is 4 times as great as the sum of the measures of the exterior angles. (14) Find the number of sides in a regular polygon if: (a) The measure of an interior angle is 3 times the measure of an exterior angle. (b) The measure of an interior angle equals the measure of an exterior angle. (c) The measure of an interior angle exceeds 6 times the measure of an exterior angle by 12.

A tank in the shape of a hemisphere has a radius of 3 feet. If the liquid that fills the tank has a density of 88.2 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?

Given that P(B) = 0.50 and P(A and B) = 0.20, what must the P(AB) = ? a)0.1 b)0.2 c)0.4 d)0.5

Nine people are entered in a race. If there are no ties, in how many ways can the first two places come out? a) 40 b) 5 c) 72 d) 144

Without looking at a chart: θ= 30° in a right triangle. If the hypotenuse of the triangle is 4 units long, what does sin equal?

A company makes a table for $15 and sells it for $19. What is the percentage of markup?

A bag contains six red marbles, seven green marbles, eight blue marbles, and five yellow marbles. If a marble is selected at random, determine the probability that the marble is either green or blue. The probability that the marble is either green or blue is ___________

A teacher has a bag of marbles. There are 6 red, 6 blue, 8 green, 7 purple, and 8 yellow marbles in the bag. As the students enter the classroom, they draw a marble and keep it. If the first student in the room draws a yellow, and the second draws a purple, what is the probability that the third student will draw a blue? 1) 25% 2) 33% 3)18% 4) 22%

Trapezoid ABCD has an area of 400 in^2. If the height of the trapezoid is 16 in and one of the bases measures 18 in, find the length of the other base.

The standard equation of a circle with center (-4, 3) and radius 7 is a (x-4)² + (x+3)² = 7 b (x + 4) + (y - 3) = 7 c (x-4)² + (x+3)² = d (x+4)² + (y-3)² = 49

One of the letters from the word RECKLESSNESS is chosen at random. a. What is P(S)? Explain your reasoning. b. What is P(vowel)? Explain your reasoning. a. P(S) is_____ since there are 12 letters in the word and_____ of the letters are S. b. P(vowel) is______ since there are 12 letters in the word and _____of them are a vowel.

Use the given equation of the circle to identify the center and radius. (x - 14)² + (y - 9)² = 25 (A) Center: (14,-9) Radius: 25 (B) Center: (14,9) Radius: 5 (C) Center. (-14, -9) Radius: 5 (D) Center: (-14,-10) Radius: 5