Complex numbers Questions and Answers

The population of a town January 1, 2012, was 32450. If the population of this town January 1, 2020, was 35418, what would be the average annual rate of increase?

Evaluate the expression (- 4 - 4i)/4i and write the result in the form a + bi.

For positive acute angles A and B, it is known that sin A =35/37 and tan B =7/24. Find the value of sin(A- B) in simplest form.

For the function f(x) = x² + x +4, find and simplify the difference quotient: {f(x+h)-f(x)/(h)}

On December 5th in Champlain, MO the probability of snow is 28%, the probability that the maximum temperature for the day will be above zero is 80%, and the probability that it will both snow and be above zero is 60%. What is the probability that it will snow OR the temperature will be above zero? Show your work.

What is the component form of the vector with an initial point of (-2, 5) and a terminal point of (7,-3)? A.(9,8) B.(9,-8) C.(-9, -8) D.(-9, 8)

Bill has $750 in a regular savings account earning 6(1/4)% annual interest that is compounded continuously. How much will be in the account at the end of 10 years?

A bag of marbles is comprised of 58 red marbles and 79 blue marbles, and the marbles are evenly distributed in the bag. Suppose you take a scoop of 58 marbles from the bag. a. About how many red marbles should be in the scoop? (Hint: the number of red marbles should be how many times as large as the total number of marbles?) b. About how many blue marbles should be in the scoop?

The profit from the production and sale of music players is given by the function P(x) = 400x-0.2x² - 5000, where x is the number of units produced and sold. a. What is P(100)? Interpret this result. b. What is the profit from the production of 1900 units? Write this in functional notation. a. P(100)=

Truck mileage. The equation ŷ = 45.683-0.005211x gives the approximate gas mileage (in miles per gallon) for a light truck that weighs x pounds. The equation is valid for 4000 ≤ x ≤6000. a) How many miles per gallon does the equation predict a light truck weighing 4750 pounds will get? Round to the nearest tenth. b) Why can't the equation be used to find the mileage for a truck weighing 6500 pounds?

1. True of False 2. Explain why? Let u, v and w be nonzero vectors in R³. If u and v are each orthogonal to w, then u and v must be parallel.

Carson invested $100 in a 8-year CD that earns 13% annual interest that is compounded continuously. How much will the CD be worth at the end of the 8-year term? Include a dollar sign in your answer and commas when appropriate. Round to the nearest cent. Provide your answer below:

90 decibels is twice as loud as 80 decibels. Rock concerts are 110-120 decibels.Regular conversation is 60 decibels. How much louder is the 110 db concert than a normal 60 db conversation using this relative logarithmic scale?

1. To concatenate two strings without using any built-in function 2. Check whether two strings are equal or not without using any predefined functions such as strcmp()

Include Small individual graphs of five different curves that include a super (large) positive k value; a positive k value close to O; the k value equal to 0; a negative k value close to 0; a super (large absolute value) negative k value.

Solve the following equation in the complex number system Express solutions in both polar and rectangular form x¹-256i=0 A. 4(cos 22.5° + i sin 22.5°), 4(cos 112.5° + i sin 112), 4(cos 202 5°+ i sin 202 5°), 4(cos 292 5+ i sin 292.5%) B. 4(cos 225+ i sin 22.5°), 4(cos 247 5°+ i sin 247.5"), 4(cos 202.5+ i sin 202 5), 4(cos 337 5° + i sin 337.5") C. 4(cos 67.5°+ i sin 67.5°), 4(cos 157 5°+ i sin 157 5°), 4(cos 247 5° i sin 247 5"), 4(cos 337.5°+ i sin 337 5°) D. 4(cos 67 5+ i sin 67 5°), 4(cos 157 5"+ i sin 157 5"), 4(cos 202 5+ i sin 202 5"), 4(cos 292 5+ i sin 292.5%) *

Rosa bought a new car with a $23,529.52 sticker price. If the basic price was $18,450 and the destination charge was $685, what was the price of the options?

For any number n>1, is |(2-4i)^n| A. greater than 1? B. less than 1? C. equal to 1?

Find the midpoint between -7+4i and 3-2i

Perform the operation and get your answer in the form a + bi. (3+2i) (2-4i) 14+ [?]i

Find all the complex third roots of -3-3√3i, express argument in radians and write roots in exponential form.

Write the standard form equation of any vertically oriented ellipse with foci at (1,+-√5). For your ellipse, determine the length of the major and minor axes.

To help pay for culinary school, Chris borrowed money from a bank. He took out a personal, amortized loan for $57,500, at an interest rate of 5.9%, with monthly payments for a term of 10 years. For each part, do not round any intermediate computations and round your final answers to the nearest cent. If necessary, refer to the best of financial formulas. (a) Find Chris' monthly payment. (b) It Chris pays the monthly paythent each month for the full term find his total amount to repay me loan, (c) 11 Chris pays the monthly pasmant nach month for the full term find the total amount of interest the will pay

Given the function values f(2)=8 and g(2)=2, determine (fg)(2). OA)2fg OB)16 OC)32 OD)8

Expand log₂(2x³/y⁴z⁵) completely using properties of the logarithm.

In a marathon, Eileen ran four times as many miles as Alan and Susan ran two miles less than Alan. Together they ran a total of 28 miles. How many miles did Eileen run? a. 5 b. 3 c. 20 d. 16

The function f (x) = 4ˣ is dilated to become g (x)=1/3.4ˣ. What is the specific effect on f (x)?

Consider the functions defined by f(x)=6x-2, g(x)=x²-4x+1, k(x) = |x-2 g(0) k(2) g(2)

Evaluate the expression, or state that the expression is not a real number. √-1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The expression is a real number. √-1 = ____ (Simplify your answer.) B. The expression is not a real number.

Let P = (1/2,1/2) and Q = (-1/3,0). Write a formula for a hyperbolic isometry φ that sends P to 0 and Q to the positive real axis.

Is the function f(x) = 3 one-to-one? ∞ Yes ∞ No

Find the parametric equations of a unit circle with center (0,-4) where you start at point (-1,-4) at t = 0 and you travel clockwise with a period of 2π.

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?