Complex numbers Questions and Answers

Let L1 be the line passing through the point P1=(-10, 5, 11) with direction vector →d1= [−2, 3, 2]T, and let L2 be the line passing through the point P2=(-34, 13, -3) with direction vector →d2=[2, -5, 0]T. Find the shortest distance d between these two lines, and find a point Q1 on L1 and a point Q2 on L2 so that d(Q1,Q2) = d. Use the square root symbol 'V' where needed to give an exact value for your answer. d= Q1= Q2= d = 4√33 Q₁=(-4,-4, 5) Q2 = (-24, -12, -3) Above is the answer, however, I am not sure how to get to these solutions.

Financial Markets. The tock and bond markets are not the only financial markets. Give two or three additional examples.

Solve cos^2(x) = 3 sin(x) for all solutions x ∈ [0,2π].

Which of the following explains why f(x) = log4x does not have a y-intercept? Check all that apply. There is no power of 4 that is equal to 0. There is no power of 4 that is equal to 1. Its inverse does not have any x-intercepts. Its inverse does not have any y-intercepts.

Solve for x and check for extranepus roots. (a) √x-1=1 x = (b) √x - 2 = x - 2 X = (c) √x + 6 = x X = (d) √3x + 16 = −8+√4x + 116 x =

2. Show your work. a. Simplify using i: -144 b. Find the absolute value: -1 + 3/ c. Simplify: (1-21)-(-2-i) d. Simplify: (4- i)(2 + 5i) e. Simplify: -2-3i/6i

Newton's Law of Cooling states that for a cooling substance with initial temperature To, the temperature T after t minutes can be modeled 0' by T = (To-T)e+T, where T is the surrounding temperature and r is the cooling rate of the substance. You remove a baked potato from a 400°F oven and place it on the counter in your 67°F kitchen. After 20 minutes, you measure the temperature of the potato to be 128°F. What will the temperature of the potato be after 26 minutes? about 104°F about 69°F about 113°F about 37°F

Write the quotient as a complex number. Show your work. -2i/1 + i

What does the notation Ry-3x+1(DAB) mean? Reflection Rotation Clockwise Counter-clockwise Around the origin to the axis Over the x-axis Over the y-axis Over y-3x+1 180° 90° 270°

Divide and express the result in standard form. 5i/2-7i 5i/2-7i (Simplify your answer. Type your answer in the form a +bi. Use integers or fractions for any numbers in the expression.)

.Find a general solution to y" - 2y + 1y =12.5elt/t² + 1 Use a and b for the constants of integration associated with the homogeneous solution. y =

Perform the indicated multiplication. - 4i(-3+7i)

Given the function h(x)=x²-7x³ +14x² -38x-60 has a zero of 1+3i, find the remaining zeros of the function (using algebra!). Write the function in factored form over the complex number system. Zeros:__________________ Factored:______________

Enter the expression or number that is required to solve the equation. Do not enter any blank spaces in your answers. 2(1 – 5x) = 72 a. Apply the distributive property: Write your response here... b. When the constant term is moved to the right side, the resulting equation is: c. Solve: X = d. Solution set:

The property of equality states that we can add or the same number from each side of an equation and obtain an equivalent equation. The property of equality states that we can or divide each side of an equation by the same nonzero number and obtain an equivalent equation.

Solve the equation. Enter the solution set below. Recall that solution set notation is written in the form {p}, where P is the solution of the equation. (For example, if 2 is a solution, the solution set is {2}.) -4 = 38 + 6x

Question 36 (1 point) At a sandwich shop, 42% of customers buy a drink with their sandwich. Only 28% of customers buy a drink and chips with their sandwich. What is the probability that a customer who buys a drink also buys chips? a)70% b)about 66.7% c)14% d)1.5%

Andy and Cheyenne are planning to have their wedding and reception at a local venue. The venue charges a rental fee of $2030. The menu they have selected costs $36.75 per person. a. If they have $7,500 saved for their reception, what is the maximum number of guests that can attend the reception without going over budget? b. If, in addition to the meal, the couple wants to provide a beer and wine selection at the reception, there is an additional charge of $19.50 per person. In this case, what is the maximum number of guests that can attend the reception without going over budget?

If a linear equation is an identity, what is its solution set? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer.

Let f(x) = - 3x + 7. Find each of the following: f(a) = 2f(a) = f(2a) = f(a + 2) = f(a) + f(2)=

Perform the indicated operation. (4 + 2i)(4-2i)

Write the equation of the line in standard form. slope = 3; (-1, 4) Select one: a. 3x=y-7 b. x-3y = -7 c. 3x-y = -7 d. y = 3x +7

Darnell invested a total of $52,000 in two accounts. The first account earned 13% after one year. However, the second account suffered a 5% loss in the same time. At the end of one year, the total amount of money gained was $2,620. LA at 13% at 5%

Graph the function f(x)=4/ x+2 -1 State the domain and the range (2)

Subtract and simplify. (13+5i)-(4+3i) (13+5i)-(4+3i) = (Simplify your answer. Type your answer in the form a + bi.)

Express 9[cos(60°) —isin(60°)] in the form a+ bi

Determine whether each of the following mapping is a homomorphism (justify your answer). If yes, find its kernel. i. Define : Z → R by p(x) = x. (where Z and R are both groups under addition). ii. Let(G,*) be a group under a binary operation and let y: GG be defined by y(m) = m² for all meg.

Using Euler's equation (eixes) eix e¹g) prove (1) sini+sing = 2 Sin (x+y). cos (x-4) sin(x+y)+sin(x-y) (2) Sinx cosy (3) cost cosy = = cos(x+y) - cos(x-y)

Solve the following instance of SAT with the partial enumeration algorithm: (Y₁ VY₂ VY₁) A (Y₁ V-Y₂) A(-Y₁ VY3) A(-Y₁ V-Y₁).

If a linear function has the points (-9,9) and (-1,8) on its graph, what is the rate of change of the function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The rate of change is (Type an integer or a simplified fraction) B. There is no solution

Find the indicated roots. Express answers in trigonometric form. The sixth roots of 729( cos 0+ i sin 0). Choose the sixth roots of 729( cos 0 + i sin 0) below.

11. (Equations with fractions/decimals) In college algebra, you will not only see equations with fractions, but you will also see equations with decimals. Keep in mind that decimals are just an alternative form for fractions. a) Convert each decimal to a fraction: b) Solve each equation. 0.7x + 2 = 1 x + 3 = 0.15x - 2

Which of the following values of x is not in the domain of g(x) = 4x-1/2x+1 ? x=-1/12 (1) x = -1/2 (2) x =-1 (3) x=-1 (4) x = -3

The diagram shows a cable car following a straight path as it climbs up a mountain slope from A to C. The cable car moves along AB for 500 m and then along BC for another 400 m. The angle of elevation of B from A is 13⁰° and BD, the vertical height between B and C, is equal to 120 m. 2 marks 2 marks 2 marks 5 marks

Complete the following simplification. 6 cis(47,000°)/cis(47,000°)= 6 cis_____

Select the correct answer below: f(x)=2-log1/3 (2-1) f(x)=1-log1/3 (x-1) f(x)=2-log1/3 (2+1) f(x)=1-log1/3 (x + 1)

Solve 6*6 = 36*+1. a. X=-4 b. x=4 C. X=6 d. x=-6

-6 + |x² + 2| <= 7y 8 + |x² + 3| <= 5y Determine if (-3,3) is a solution to the system of inequalities above. Select the correct answer below: (A) Yes (B) No

An investment of $76,000 was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from the investments was $5940. The interest from the first investment was 6 times the interest from the second. Find the amounts of the three parts of the investment. (A) The first part of the investment was $____. (B) The second part of the investment was $____. (C) The third part of the investment was $____.

Find f+g, f-g, fg and f/g Determine the domain for each function. f(x)=3x²-25x-18, g(x)=x-9 (f+g)(x) = (Simplify your answer.)

Exponential variable on both sides 5. 5³x = 3x+4

Choose the correct statement. For any angle 8, we have sin (-θ)=sin θ . (So sine is an odd function.) For any angle 8, we have sin (-θ) = sin θ. (So sine is an even function.) Neither of the above answers are true. (So sine is neither an odd nor an even function.)

Solve the equation cotθ = √3 for all values of 0 in the domain 0 ≤θ < 27. Also, draw either a horizontal, vertical or diagonal line that goes through all solutions to the equation. Express your answer both in radians and degrees.

Find the domain of the following function: f(x)=1/ (x-8)(x - 6) Select the correct answer below: a) All real numbers b) All real numbers except 8 and 6 c) All real numbers except - 8 and -6 d) All real numbers except 8 and -6 e) All real numbers except-8 and 6

Plot the complex number. Then write the complex number in polar form 1-3i Plot the complex number.

Find zw. Leave your answer in polar form. z = 3 (cos π/7 + i sin π/7) w=5(cos π/11 + i sin π/11)

If f(z) has an inverse function f-¹(a), could either the graph of for the graph of f-¹ be symmetric with respect to the y-axis? Please, explain your reasoning or use an example to illustrate your answer.

How long will it take for a $2500 investment to grow to $3500 at an annual rate of 7.5%, compounded quarterly? Assume that no withdrawals are made. Do not round any intermediate computations, and round your answer to the nearest hundredth. If necessary, refer to the list of financial formulas.

c) An analyst models the spot interest rate with the following stochastic differential equation: dR = (u - Rt)dt + dB, where u is a positive constant. Using Ito's lemma on the function f(t, Rt) = exp(t) Rt show that: R₁ = μ + exp(-t) (R₁ -μ) +exp(-(t-s)) dBs

Let p be an odd prime number. Which integers a have the property that the inverse of a is congruent to a modulo p? Study the case p =7 and p = 11 first. Reorder the factors in (p-1)! in such a way that all pairs of inverses are written adjacent to one another. Compute (p-1)! modulo p after this reordering. What is (p-1)! mod p.