Complex numbers Questions and Answers

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.

Find the numerical value of the area under the standard normal curve that is greater than 1.67.

In the space at the right, graph the circle whose equation is (x + 6)² +(y - 2)² = 36 and fill-in-the-blanks. You may use either algebraic notation or interval notation for the domain and range. _________= North Pole _________= West Pole _________= South Pole _________=East Pole _______________= domain _______________= range

A normal distribution has a mean of 76 and a standard deviation of 4. Determine the z- score for the data value of 88. z=

The point (5,π/4) can also be represented by which of the following polar coordinates ? A. (5,-π/4) B. (-5,5π/4) C. (-5,9π/4) D. (5,3π/4)

A psychology student wishes to investigate differences in political opinions between business majors and political science majors at her college. She randomly selects 100 students from business majors and 100 students from the 180 political science majors. Does this sampling plan result in a simple random sample? Why or why not? a)No, because each individual student does not have an equal chance of being selected. b)No, because each group of 200 students in the sample does not have the same chance of being selected, c)Yes, because each group of 200 students in the sample has the same chance of being selected. d)Yes, because each individual student has the same chance of being selected.

Find the Taylor series of the function f(z) = sinh(3z) at center 2 Find the Laurent expansion of F(z) = 1/(z-2)(z-5) on 2 < |z| <5

Rationalize the denominator and if possible, simplify: (3 + √6) / (9 - √6)

if u =( 8 +i, i, 36-1) v = (1+i, 2, 4i) Find the imaginary part of u.v ? (Round off the answer upto 2 decimal places) ----- I need full answer with explanation --- --

Determine a c and a d function such that c(d(t)) = √(1 - t²).

Find the length of unknown side of the given triangle The side is ___m

The point below is on the terminal side of an angle θ in standard position. Find the exact values of the six trigonometric functions of θ. (-28,45)

Solve for a rounding to the nearest hundredth 45.3^x = 225

Compute the difference quotient f(x+h)-f(x)/h for the function given below. f(x) = 2x2 + 2x - 3 Select the correct answer below: 1. 2x + 2h + 2 2. 4x + 2h +2 3. 4x + 2h-3 4. 4x + 2h - 2 5. 4.0 + 4h-3

1. An ellipse has endpoints of the major axis at (4,1) and (-6,1) and endpoints of the minor axis at (-1,3) and (-1,-1). Write an equation for the ellipse. 2. Find the coordinates of the foci for the ellipse. x^2 + 25y^2 – 8x + 100y +91 = 0

The surface area of a rectangular prism can be found using the formula SA = 2lw + 2wh + 21h. The volume of a rectangular prism can be found using the formula V = lwh. You are packing your fish tank to move, but need to calculate the surface area and volume to choose an appropriate length, width, and height for your package so that it can fit the fish tank you are shipping. Fish Tank Dimensions: 16 in x 8 in x 10 in

The point (5, pi/4) can also be represtend by which of the following polar coordinates? Select ALL that apply. A) (5, -pi/4) B) (-5,5pi/4) C) (-5, 9pi/4) D) (5, 3pi/4) .

Determine whether the given equation is a parabola: x = 7y². O Parabola O Not a parabola If it is a parabola, write the equation in standard form: (y– k)² = 4p(x - h) or (x – h)² = 4p(y – k) Otherwise, leave the rest blank. h= k= p=

Solve the triangle. The Law of Cosines may be needed. (Standard notation for triangle ABC is used throughout. Use a calculator and give your answers as decimals to tenth at the end of the computation. If no such triangle exists, enter 'NONE' in each of the answer blanks.) b= 31.9°, c = 14.7°, C = 27.8° A = B= a=

The point (5, pi/4) can also be represented by which of the following polar coordinates? Select ALL that apply.

An oblique cylinder has a radius of 11 units and a volume of1815π cubic units. What is the height of the cylinder?

Find the solution to the lines x = y +5 and x = 8 + 2y. O (2, -3) O (-2, 3) O (2, 3)

Solve the following y"(t) - 4ty'(t) - 8y(t) = 4 y(0) = 0, y'(0) = 0 Initial value problem.

We will only need one fact: • 4.5 pabs = 5 teeps Now, perform the conversion and give your answer as a decimal number. Do not round your answer. 66.34 pabs²=__teeps²

Sophia's grades have been updated online. Sophia's mom has seen the grades and has started texting her about them. The data is shown in the table. Hours since grades were posted 0 1 2 3 Number of texts 2 6 18 54 Which algebraic expression represents Sophia's mother's attempts to contact her? ○ 3x ○ 2ˣ⁻¹ ○ 2(3)ˣ ○ 2(3)ˣ⁻¹

Let f(x) = ln(x² + 3) and g(x) = √eˣ +1. Find formulas for (a) g(f(x) and (b) g‾¹().

Find the solution of xy" + 5xy' + (4 – 1x)y = 0, x > 0 of the form y₁ = x^r ∑ Cn x^n ( n=0 to ∞ ) where C₀ = 1 Enter r=____________ Cn=__________ , n=1,2,3,............

Determine the equations of the planes that make up the tetrahedron with one vertex at the origin and the other vertices at (5,0,0), (0,-6,0), and (0,0,2). Draw the diagram