Complex numbers Questions and Answers

Which of the following statements is true? (A) sin z / z2 has a removable singularity at z = 0. (B) The function 1/zsinz2 has a pole of order 3 at z = 0. (C) The function e2/z2 has a simple pole at z = 0. (D) The function 1/z e^1/z has a removable singularity at = -0. (E) For function f(z) = 1/z^3(1-z)^3, we have Reso f(z) = 0.

Given this table about Tuberculosis (TB), which is a disease that affects the lungs. Most Americans are tested for TB when they are young, and when they will be working with youth. What would the expression P(haveTB | Test positive) represent? People Tested for TB Have TB Does not have TB Total Test Positive 198 98 Test Negative 2 9702 9704 total 9800 Select one: a. Joint Relative Frequency b. Marginal Relative Frequency c Conditional Relative Frequency d. None of these

1. Below is a graph of the height of a passenger car on a Ferris wheel. a. How does this function differ from other types of functions you have studied such as linear, polynomial, and exponential functions? b. What is the domain of this Ferris wheel height function? What is the range? 2. Find a definition of periodic function and then rewrite it in your own words. 3. What other situations might be modeled by a periodic function?

Solve for the exact solutions in the interval [0, 2π). If it has no solutions, respond with DNE. 8 sec² (x/2) = 4

Sketch a graph of the function f(x) = 5 sin (1/2 x )

For y = 2 sin 5x, its amplitude is its period is

Let ø:G -> H be an isomorphism, show that 1.ø-¹: H->G is an isomorphism 2. if K≤ H, then ø-¹(K) ≤ G

P(Z)= Z⁴ +(2-7i) Z⁸+ (-14-14i) z² + (-28+8i)Z+16i please factorise the above equation.

Expand log₃ (1/x²y3ᶻ) completely. Keep variables in the order that given in the original term. I.e. For log(), present the answer as log a-log 3-log b, but not log 3-log b + loga.

A hockey coach wanted to know the relationship between the number of shots his team takes during a game and the number of goals they score.. Shots 11 20 24 28 27 33 17 38 Goals 1 2 0 3 2 3 1 4 a) Write the linear regression function with values to the nearest TENTH. b) Extrapolate how many shots would be required to score 5 goals. Round answer to nearest shot

Evaluate J by means of Simpson's rule with n = 2m = 20 and h=0.05: J = ¹∫₀e^(-x²)dx Note that this integral cannot be evaluated by elementary calculus, but leads to the error function.

Starting at point A, a ship sails 20 miles on a bearing of 200°, then turns and sails 40 miles on a bearing of 300°. Find the distance of the ship from point A.

Let f(x) and g(r) be defined as follows: f: (4,0)→ R. f(x) = ln(x-4) 9: R R. g(x)=x²-5 Calculate the following compositions and determine the range and domain of each of them. Please note that drawing a graph of the composed function is not sufficient working to show your answer for the domain and range. (a) (fog)(x) (b) (gof)(x)

Use the graph below to answer the following questions. Be careful with the input and output variables. Not everything is x or y! What is the minimal degree that the function q could have? The zero at w = 1 would have multiplicity Write an equation using function notation, as in f(x), with the smallest possible degree for the function graphed above.

Find the equation for the line that passes through the points (8, -5) and (-9, -1). Give answer in point-slope form. You do not need to simplify. ________

Complete the following table. Remember that 180° = π radians. Angle (degrees) 30⁰ 36° 45° Angle (radians) π/6 Angle (radians) Based on this, if x is an angle measurement in degrees, then the corresponding angle measure in radians is ___________ radians.

The reference angle of 215 degrees is ______ degrees. The reference angle of 320 degrees is _____ degrees. The reference angle of -132 degrees is _____ degrees.

American General offers a 10-year annuity with a guaranteed rate of 4.95% compounded annually. How much should you pay for one of these annuities if you want to receive payments of $1900 annually over the 10 year period? How much should a customer pay for this annuity?

You need to build a trough for your farm that is in the shape of a trapezoidal prism. It needs to hold 100 liters of water. What are its dimensions (base 1, base 2, height, and depth)? You would also like to paint it, so you need to find its surface area. How much paint should you buy?

Without using a calculator, compute the sine, cosine, and tangent of 5π/3 by using the reference angle. (Type sqrt(2) for √2 and sqrt(3) for √3.) What is the reference angle? In what quadrant is this angle?

The reference angle of433° is The reference angle of -257° is The reference angle of 208° is

For f(x) = a*sin(bx), use: Amplitude = |a|; Period T =2.π/|b| ;Section Width =T/4 Without graphing the function y = - 7 sin(9x), determine its amplitude, period, and section width (distance between critical points). Leave answers in exact form; type pi for π. amplitude =? period=? section width=?

Factor the following polynomial using the formula for the sum of two cubes. z³+343 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. z³ + 343 = __________(Factor completely.) B. The polynomial is prime.

Kevin and Randy Muise have a jar containing 67 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $12.95. How many of each type of coin do they have? The jar contains ____ quarters. The jar contains ____ nickels.

Write in radical form. Do not simplify. 14x¹/⁴ = ________

Asume that the binary operation ab=a +6-540 is defined on 7 Which statement is NOT correct? is assosiative is the identity element of (Z,*) Every element of Z has an inverse (25) dosed

Find z, z₂, and z1//z2if z₁ = 6( cos 100+ i sin 100) and z₂ = 10 (cos 280+ i sin 280"). Write your answers in standard polar form with the argument in degrees.

The average weight of a male child's brain is 970 grams at age 1 and 1270 grams at age 3. (a) Assuming that the relationship between brain weight y grams and age t years is linear, write a linear model for the data? (b) What is the slope? What does it tell you about brain weight? The weight of a male human brain is decreasing by m grams/year. A human male's brain reaches a maximum weight at age 3. At birth, a human brain weighs 970 grams. A human male's brain weight is constant for his entire lifespan. The weight of a male human brain is increasing by m grams/year. (c) Use your model to estimate the average brain weight at age 2. (d) Use your school's library, the Internet, or some other reference source to find the actual average brain weight at age 2

Identify the equation of the surface. z=x²/4-y²/9 x²/4+y²/9+z²/4=1 z=x²/4+y²/9 x²/4+y²/9-z²/4=1 x²/4+y²/9=1

If a function has a horizontal asymptote, it cannot have a vertical asymptote. a) False b) True

A new car is purchased for $47, 000 and over time its value depreciates by one half every 3.5 years. Write a function showing the value of the car after t years, where the annual decay rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of decay per year, to the nearest hundredth of a percent. Function: f(t)=? Growth ___% increase per year

Complete the table of values for the following function and then plot the points to graph the function by hand. f(x)=1/2x²

Sketch graphs of each of the following: (a) the polar equation r = 1 + 2sin(3θ) (b) the curve determined by the parametric equations { x = t³/² + 1 } { y = √t }, t > 0

The function f(x) = x² +1/x³-4 has; a) A Vertical Asymptote b) A Horizontal Asymptote c) An Oblique Asymptote d) Both a and b e) Both a and c f) None of the above

Write in the form a + bi, where a, b ∈ R. {(2 - i)(4 - 3i)²}/(3 + 2i)

Using Euler's equation {e^i(x+y) = e^(ix) * e^(iy) prove (1) sin x + sin y = 2sin{(x + y)/2} * cos{(x - y)/2} (2) sin x cos y = {sin(x + y) + sin( x - y)} / 2 (3) cos x cos y = {cos(x + y) - cos(x - y)} / 2

Find all of the solutions of 2 sin²(x) - 3 sin(x) - 2 = 0 between - π and π a) x = π/6 and 5π/6 b) x = π/6 and -5π/6 c) x =-π/6 and 5π/6 d) x =− π/6 and – 5π/6

For the curve f(x) = -2(3)ˣ +3, the range of the function is: a) R: {yly <3, y ≤ R} b) R: {yly> 3, y ≤ R} c) R: {yly ≤ 3, y ≤ R} d) R: {yly> 3, y ≤ R}

8500 dollars is placed in an account with an annual nearest year, how long will it take for the account interest rate of 7%. To the 59700 value to reach dollars?

Which quadrant would an angle of 14π/3 rads have its terminal arm, if rotated from standard position? a) Quadrant III b) Quadrant IV c) Quadrant II d) Quadrant I

Multiply. (7 +3i)(-4-3i) = (Simplify your answer. Type your answer in the form a + bi.)

1. Factor the polynomial f(x)=x^4 +2x^3-2x^2 -6x -3 into factors of the form(x-c). (b). Find any x-intercepts of the function y =f(x). (c). Use a graphing calculator to sketch f(x) =x 4 + 2x 3 - 2x 2 - 6x - 3. Determine the coordinates of the minimum value of f(x).

Find the angle between v and w. v = -2i+ 5j, w = 3i+9j The angle between v and w is ____º. (Do not round until the final answer. Then round to the nearest tenth as needed.) Plot the complex number. Then write the complex number in polar form. Express the argument in degrees. -11-11i Plot the complex number on the complex plane to the right. Write the complex number z=-11-11i in polar form. Select the correct choice below and fill in the answer box(es) within your choice. (Type an exact answer, using radicals as needed.)

The maximum height of water near a tidal power station in New Brunswick is 6.4 metres at 4:30 am and the minimum height is 3.6 m, 6.2 hours later. What is the depth of the water at 6:45 pm? a) 5.8 m b) 5.6 m c) 6.8 m d) 2.8 m

The price of a video game system dropped by 18%. What is the current price if it used to be $140?

Find the percent change to the nearest percent: 200 students to 456 students.

Prove that, for every positive integer n, there exist two regular polygons with the property that the ratio of the measure of an interior angle of one of the polygons to the measure of an interior angle of the other equals n+1/n

z2=8.6exp(3.245i) Convert z into Cartesian coordinate Pls use matlab to solve it and provide screenshots

Let A € Cnxn be a matrix with the spectrum A(A) = {a, b, c, d, e} (if you prefer a concrete example let A(A) = {1,3+i, 3-i, 1/2+2i, 1/2-2i}). Each eigenvalue occurs with an algebraic multiplicity of roughly n/5. Explain why in general we can expect GMRES to converge in 5 steps.

The cities of Abnarca and Bonipto have populations that are growing exponentially. In 1980, Abnarca had a population of 26,000 people. In 1990, its population was 31,000. Bonipto had a population of 34,000 in 1980. The population of Bonipto doubles every 55 years. (Round your answers to the nearest whole number.) (a) How long does it take the population of Abnarca to double? (b) How long will it take for Abnarca's population to equal that of Bonipto?