Complex numbers Questions and Answers

For the function given below, (a) use the product-to-sum formulas to express the product as a sum, and (b) use the method of adding y-coordinates to grach the function on (a) G(x)= (b) Choose the correct graph below G(x) = cos(4x) cos(2x)

Which of the following is an equation of a line that is parallel to 3x+7y=10 ?

Write an equation of the line parallel to 4x-7y=11 and contains the point (-28, 5).

Solve the polynomial equation in the complex numbers. 12x⁴ +32x³ - x²-7x-1=0

Suppose that the characteristic polynomial of a matrix A is (λ-8)^4 (λ- 9)². Then the determinant of A is nonzero.

Given the function f(x) = 4x+20 / x²-4x-12 (A) Find the domain in interval notation. (B) For which value(s) of x does f(x) = 0? (C) For which value(s) of x does f(x) = - 16 / 7 ?

Let f(x)= √x Write a formula for a function g whose graph is obtained from the graph of f(x) after the following sequence of transformations: (1) shift left 2 units; (2) shift down 4 units; (3) scale vertically by a factor of 2. NOTE: The order you apply the transformations is important and should be done in the order given. It may help to draw the graph after each step, and then determine a formula for the function at the end. g(x)=

For the following exercises, graph the function and its reflection about the y-axis on the same axes, and give the y-intercept. f(x) = (-2/3 ) (1.25)^3x

Which function is decreasing on the same interval as the function graphed here? A g(s) = 3x²- 12x + 18 B. k) = -2x² - 8x +5 C h(s) = 2x² +8x +3 D. j(s) = -x² +4x - 4

Let F-(xy, yz², zx³), and S be the part of the surface z = xy² (1-x-y)³ lying above the triangle with vertices (0,0), (1.0), (0,1) on the xy-plane, with upward orientation. Compute ff Curl F-ds.

Using laws of logs, the expression log₅ 6 + 3 log₅ 3 - 1/2log₅ 81 can be written as a single log in the form log₅ a. The value of "a" is

Function h gives the height of a tennis ball, in feet, t seconds after it is tossed straight up in the air he equation h(t) = -16t² + 12t +10 defines function h. Write and solve an equation to find when the ball hits the ground. Show your reasoning.

The scores and their percent of the final grade for a statistics student are given. What is the student's weighted mean score? Score Percent of final grade Homework 84 20 Quiz 83 5 Quiz 95 5 Project 95 35 Final Exam 91 35 The student's weighted mean score is ______.

Divide. 6+i/2-4i Write your answer as a complex number in standard form.

Let F₂(t) denote the field of rational functions in t over F₂. (a) Prove that F₂(³√t)/F₂(t) is not Galois. (b) Prove that F4(³√t)/F4(t) is Galois. (c) For which values of n is F₂n(³√t)/F₂n (t) Galois? Justify your answer.

Divide 3i/-3-5i Write your answer as a complex number in standard form.

Suppose we want to choose 2 colors, without replacement, from the 5 colors red, blue, green, purple, and yellow. (a) How many ways can this be done, if the order of the choices matters? (b) How many ways can this be done, if the order of the choices does not matter?

solve the point a and b, by the bisection method x⁵ +11x⁴ +33x³ – 11x² +33x³ - 11x² - 154x -120 x⁵- 11x⁴ +33x³ + 11x² - 154x-120

Verify that the set {(1,1,-2), (1,0, -1), (0,0,1)} is a basis for R³ Use Gram-Schmidt process to obtain an orthonormal basis. Write the vector (3,2,1) as a linear combination of the vectors of this basis

Find all complex solutions to the given equations; 1) x^3 + 8i=0 2) x^2 + i=0

The Nutty Professor sells cashews for $6.80 per pound and Brazil nuts for $4.90 per pound. How much of each type should be used to make a 31 pound mixture that sells for $5.70 per pound? Round answers to the nearest pound.

Rationalizing Denominators of Radical Expressions 1/√75z=√3z/15z

Find the Fourier cosine series of the function f(x) = (M + 1)x² + M, defined over the interval (0,7). Explain briefly the solution steps in your own words.

Multiply (20-4 i)(5+ i) (20-4 i)(5+ i) = ?(Simplify your answer. Type your answer in the form a + bi.)

Given: f(x) = 2x + 1 and g(x) = 3 - x² Find (g o f)(x)

At a particular high school, 27% of the students participate in student council and 56% of the students participate in sports. If 35% of the students participate in either student council or sports, what is the probability that a student participates in BOTH student council and sports? A) 0.21 B) 0.56 C) 0.48 D) 0.15

A team of researchers is monitoring the population of crickets a particular town. They do not know exactly how many crickets are remain but the model they use represents the minimum number of crickets remaining in the town. According to their model, the minimum number of the species remaining, in thousands, multiplies by 10 every month. The researchers determine that right now, the population of crickets is at least 5 thousand. Once the minimum population reaches 1 million, measures an to stop the increase in population. If P represents the actual population of crickets in the town, in thousands, and t represents the time, in months, which of the following's of inequalities can be used to determine the possible number of crickets in the town over time? (A) P ≥ 10(5)ᵗ P ≤ 1,000 (B) P ≥ 5(10)ᵗ P ≤ 1,000t (C) P ≥ 10(5)ᵗ P ≤ 1,000t (D) P ≥ 5(10)ᵗ P ≤ 1,000

Express in radical form, with no exponents. x^(-1/2)

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

Explain how to find the area of the given triangle using SAS.

The volume of water is: v= 40000 (2+cos(8π/X)) where x ≥ 16. Determine the volume when the water is DECREASING at 8m/hour and the depth is 48m.

Calculate ⁵√(-3 + 3i). Give your answer in a + bi form. Round your coefficient to the nearest hundredth, if necessary .

An imaginary number (unit) is a subset of the Real number system. True False

Simplify the following expression. i/(a+bi)

Given the quadratic form {4(x1)²} + {4(x2)²} +{4(x3)²} +{(2x1x2)} + {(2x1x2)} + {(2x2x3)} Give an orthogonal transformation of the quadratic form. (Each question Score 20, Total Score 20)

Simplify the following expression. 1/(a-bi) Write the final answer in standard form a + bi.

Suppose cos A=-9/41 and A is an angle in Quadrant Three. Then cos 2A=____

Divide (-9+i)/(3+7i) Give your answer in the form a + bi.

For the function f(x)=3log[2(x-1)]+4 a) Describe the transformations of the function when compared to the function y = log x b) sketch the graph of the given function and y=logx on the same set of axes. c) State the domain, range and the equation of the asymptote.

Considere las dos rectas l₁ : −20x + 5y = 25, l2 20x + 5y = C. Si se sabe que la distancia entre l₁ y l2 es igual a 4√425, entonces un valor que C puede tomar es:

In 2 minutes, a conveyor belt moves 300 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 18 minutes. If both belts are used, find how long it takes to move the cans to the storage area. The time it takes to move the cans to the storage area using both belts is (Simplify your answer. Type an integer, fraction, or mixed number.)

Simplify: 3i/(1 + 3i) A) 3i + 9/10 B) 3i/4 C) -1 -3i/5 D) 3i/7

1)Lines PQ and RS are perpendicular. Find x. P(1, -2); Q(3, 4); R(x, 6); S(5, 5) X =_____ 2)Determine which, if any, of the three lines PQ, PR, and QR are perpendicular. P(6,-8); Q(2, 8); R(6, 9) a)QR and PR are perpendicular. b)PQ and PR are perpendicular. c)PQ and QR are perpendicular. d)No two lines are perpendicular.

Sketch each of the following angles in standard position on the x-y coordinate plane.Then draw a line (down or up) from the tip of the arrow to the x-axis. Then write in the value of the reference angle into the acute central angle. A. 150° B. -120° C. -336° D. 585°

Use a double integral to find the area of the region inside the circle x² + (y-7)² = 49 and outside the circle x² + y² = 49 in the first quadrant

Let A = be an n x n matrix , where a is a real constant . Find an invertible matrix P such that P^-1 A P is diagonal .

Given the identity [sin(2a)/1 + cos(2a)]=tan(a)/1 prove the identity by following the implied steps and starting with the left side: sin(2a)/1 + cos(2a) 1). Substitute double-angle formulas into the numerator and denominator: 2). Simplify coefficients in the numerator and denominator: 3). Reduce out common factors: 4). Rewrite as the right side of the equation:

x²/25 + (y-2)²/36 = 1 For the following ellipses determine location of its foci. (a) foci at (0, 2 + v11), (0, 2 - v11) (b) foci at (0, 5 + v21), (0, 5 - v21) (c) foci at (0, 3 + v25), (0, 3 - v25) (d) foci at (0, 1 + v36), (0, 1 - v36)

Suppose is an angle such that cos(θ)=-1/3 a)If 0 < 0 < π, then cos(θ/2)=____ b)and sin(θ/2)=____ c)If π <θ< 2π then cos(θ/2)=____ and sin(θ/2=____ d)If 2π <θ< 3π, then cos(θ/2)=____ and sin(θ/2)=____

Describe the transformations which have been applied to f(x)^2 to obtain g(x) = 2 - 2{(1/2)x + 3}^2