Complex numbers Questions and Answers

Given the point P(1.0,-1) and the plane with equation 5x+4y+z6 enter the coordinates of a point Q that lies on the plane, below, Q=( You have not attempted this yet Write down a vector u that is parallel to a normal vector to the plane. Please enter a row vector of form [A, B, C), i e. use the list syntax. You have not attempted this yet Find the exact value of the shortest distance d from the point P to the plane. d= You have not attempted this yet

Suppose is an angle such that cos(θ)=-3/4 a)If 0 <θ < π, then cos(θ/2)=____ and sin(θ/2)=____ b)If π <θ< 2π, then cos(θ/2)=____ and sin(θ/2)=____ c)If 2π < 0 < 3π, then cos(θ/2)=____ and sin(θ/2)=____

The area is bounded by y=eˣ, y=e, and y-axis. Find the centroid of the volume if the area is revolved about the x-axis.

In triangle ABC, m<A = 28 degrees, m<C 132 degrees, and the length of AB = 6. a)Find the measures of the other sides and angles. b)length of AC= c)length of BC=

Simplify √-63 using the imaginary number i. (a.)3√-7 (b.) i√63 (c.)-3√7 (d.)3i√7

Consider the following incomplete-information game. First, nature chooses between one of the following two A and B tables, each with probability 0.5: Then, players 1 and 2 simultaneously choose U or D and L or R, respectively, and obtain payoffs according to the table chosen by nature. (a) Suppose player 2 does not observe nature's move. Does player 1 benefit from information? (b) Suppose player 1 observes nature's move. Does player 2 benefit from information?

An angle has a terminal side which contains the coordinates (-6, -2). What is the value of secant of this angle? In answering the question, please describe by typing in your mathematical steps.

The height of the tip of an airplane propeller above the ground once the airplane reaches full speed can be modelled by a sine function. At full speed, the propeller makes 200 revolutions per second. At t = 0, the tip of the propeller is at its minimum height above the ground. Determine whether the instantaneous rate of change in height at t = 1/300 is a negative value, a positive value, or zero.

Prove that if u and v are linear independent, then u + 3v and 3u - v are independent as well.

Determine if the following relations are functions. Then state the domain and range.

Determine which of the following statements are true and which are false. There exist vectors V, W E R³ with ||v|| = 1, ||w|| = 1, and vxw = (1/3, 1/3, 1/3). Choose 2. If v E R³ then v X v =v². If v, w E R5 then vxw = -(w x V). If V, W E R³ then ||vx w|| = ||wxv||. There exist vectors v, w E R³ with ||v|| = 1, ||w|| = 2, and vxw = (2,2,2). True False

A local club is arranging a charter flight to Hawaii. The cost of the trip is $593 each for 85 passengers, with a refund of $5 per passenger for each passenger in excess of 85. (a.) Find the number of passengers that will maximize the revenue received from the fight. (b.) Find the maximum revenue. The number of passengers that will maximize the revenue received from the fight is [?] (Round to the nearest integer as needed.)

Let Z5 = {0,1,2,3,4}. Find the value of x in each of the following equations in Z5. Show your complete solution. Provide a justification for your answers 1. (3 x 5 x) +5² = 1 2. (3 + 5 x) x 5² = 1

Let z₁ = 3-4i and z₂ = -1-1. Find Z₁ A. -3 + 4i B. 3+4i C. 5 D.-3-4i Given g(x) = (2)²ˣ+¹; find g(-1) A. 2 B. 1 C. -1/2 D. 1/2

True/False: It is possible for six king chickens to be tied with the highest score (highest score means most number of victories). If yes, then demonstrate. If no, explain why not.

Evaluate. (-125)^1/3 Provide your answer below:

A retailer buys 800 USB Flash Drives per year from a distributor. The retailer wants to determine how many drives to order, x, per shipment so that her inventory is exhausted just as the next shipment arrives. The processing fee is $20 per shipment, the yearly storage cost is $2.50x, and each drive costs the retailer $4.80. (a) Express the total yearly cost C as a function of the number x of drives in each shipment. (b) Use a graphing utility to determine the minimum yearly cost and the number of drives per order that yields the minimum cost. (a) C(x)=_____ (Do not factor.)

Find the solution of the exponential equation 6eˣ =18 in terms of logarithms, or correct to four decimal places. X=

Find the exact value of each trigonometric function without a calculator. (Use the Unit Circle) 22. tan(-45) 23. tan 4π/3 24. sin(-2π/3) 25. sin 210

Given 7(d²y)/(dx²) - y +x=0 with the boundary conditions y(0) = 5 and y(21)=8. Solve the above boundary value problem with Central Divided Difference Method with △x = 7

Simplify 1 + cot(t)/1 + tan(t) to a single trig function. a) Use Reciprocal Identities to rewrite the expression to only have sine, cosine or tangent function. b) Times an appropriate trig function to get rid of the complex fraction. c) Cancel the common factor between the numerator and denominator. d) Express the final answer without fraction. 1 + cot(t)/1+tan(t)

Simplify ∛(250x⁴y³). (Assume all variables are positive.)

Find the z-score for which the area to the right is 0.05. Select one: A. 1.73 B. 1.88 C. 1.64 D. 1.44

Let M2x2 be the vector of all real 2 × 2 matrices and A =[-¹₁ 3]. B = [2 }) linear than tor and define a L: M2×2 → M2×2 by L(X) = AXB. Compute the trace and determinant of L. [14M]

Find the parametric equations of a circle with radius of 7.5 where you start at point (0,7.5) at t = 0 and you travel clockwise with a period of 9. Note: t is in radians. x(t) = y(t) =

Find the exact value of each of the following using the special triangles, the unit circle, or both. In each case, state the reference angle and the quadrant in which the angle terminates. No decimal answers.

5. Find the distance between Las Vegas (36° N, 115° W) and Paris, France (49° N, 2° E). Use R 6366 km. =

Simplify the following; 15-(12-2*5)+9

Use the table to determine a solution of the equation. Use synthetic division to verify that this number is a solution of the equation. Then solve the polynomial equation. 35x³-47x² +13x-1=0 X Y₁ = 35x³-47x² + 13x-1 -3 -1408 -2 -495 -1 -96 0 -1 1 0 2 117 3 560 Which solution of the equation can be determined from the table? The solution is

An investor wants to analyze the earnings of a mutual fund account. Seven years ago, the value of the account was $22,000 and it is now worth $27,500 (no additional deposits were made). If the account is compared to a bank account paying interest that is compounded continuously, what interest rate would the bank account have to pay to match the mutual fund accounts earnings?

Suppose that A, B, and C are 5 x 5, 5 x 4, and 4x 6 matrices, respectively. Determine which of the following products are defined. (a) BA. Answer: ________ (b) BC Answer: ________ (c) CB Answer: ________ (d) AB Answer: ________ Note: i) For those defined, enter the size of the resulting matrix (e.g. 3 x 4 with spaces between the numbers and x). ii)For those undefined, enter undefined.

Given p= < 7,2> and < 8, 9>, find p v|and|p |v| p-v|=___ p|-|v|=___

Simplify the following expression. (4+2i)/(1+i)

Simplify the following expression. (1-3√-4) (2+√−9)

Solve the equation by completing the square. 2a² +24a= -78 a= ________ (Simplify your answer. Type an exact answer, using radicals as needed. Express complex numbers in terms of i. Use a comma to separate answers as needed.)

Evaluate the line integral ∫c F.dr. where F(x, y, z) = sin zi + 2 cos yj + 4zzk and C is given by the vector function r(t) = t⁵i-t⁴j+t³k. 0≤t≤1

Simplify. (b.b⁴/ c².c³)⁴

A plane is defined by the equation x = 0. a. What is a normal vector to this plane? b. Explain how you know that this plane passes through the origin. c. Write the coordinates of three points on this plane.

Find the exact value. # 44 cos (165°) a) Write the given angle 165° as a sum of two special angles that are less than π Enter the combination with the smallest angle first. Enter the smaller angle on each possible combination. 165°=________degrees +_______degrees OR 165°=________degrees +_______degrees b) Use the first combination and Sum/Difference Formula to evaluate exactly. cos (165°) =________

NOTE: The picture is NOT drawn to scale. Ancient alien theorists manning two radar stations located b = 71 km apart both detect a UFO located between them. The angle of elevation measured by the first station (A) is α = 86.2° and the angle of elevation measured by the second station (C) is γ = 83.7°. How far is the UFO from station A? distance from A =_______km How high is the UFO above the ground? h =_______km Enter your answer as a number; your answer should be accurate to 2 decimal places.

I= ∫₁ In(Inx)/1+2xcosα+x²dx Malmsten Integral This might be one of the coolest integrals in calculus, it shows the beauty of mathematics I= ∫₁ In(Inx)/1+2xcosα+x²dx where-π<α<n

Set-up the iterated double integral in polar coordinates that gives the volume of the solid enclosed by the hyperboloid z = √1+x²/2+y²/2 and under the plane z = 5.

Find the standard matrix for the linear transformation T: R²->R² that rotates points about the origin π/6 by radians and then dilates points horizontally by a factor of 25/22.

Perform the operation. Write your answer in terms of i. (7+2i) -(6-i)-(3-4i) Provide your answer below:

Aidan received a 70-day promissory note with a simple interest rate at 4.0 % per annum and a maturity value of RM17,670. After he kept the note for 40 days, he then sold it to a bank at a discount rate of 3%. Find the amount of proceeds received by Aidan.

Determine the surface area of the portion of 4x+3y + 5z = 8 that is inside the cylinder x² + y² = 49.

Find the least squares best fit quadratic function y = f(x) = ax²+bx+c to match the given 4 data points: (x, y) ∈ {(0,0), (0, 1), (1, 1), (-1, 2)}

What is the sum of the coordinates of the point obtained by first reflection (8,8) over the line x = 3, and then reflecting that point over the line y = 4? (A) -2 (B) 8 (C) -8 (D) 3 (E) 4

Determine the surface area of the portion of the sphere of radius 4 that is inside the cylinder x²+y²=3.

Suppose that an instructor uses four grades to determine a student's course average: a quiz , an assignment, a mid-trim exam and a final exam. These are weighted as 5%, 15%, 25% and 60%, respectively. If a student's scores are 70%, 80%, 60%, and 90%, respectively, compute the student's course average. a) 73.7 b) 77.1 c) 77.3 d) 83