Complex numbers Questions and Answers

Plot the intercepts to graph the equation. 3x-6y=-6 SIDE Use the graphing tool to graph the equation. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line.

Find the slope of the line. -7x-5y=3 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is (Simplify your answer.) B. The slope is undefined.

Which of the following sets are subspaces of R³? A. {(-5, y, z) | y, z arbitrary numbers } B. {(x, y, z) | x+y+z= -8} C. {(8x + 6y, 3x - 9y, -2x +9y) | x, y arbitrary numbers } D. {(x, y, z) | x+y+z=0} E. {(x, y, z) | 5x + 7y= 0,4x + 8z = 0} F. {(x, y, z) | x <y<z}

Find the slope of the line x = 6. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an integer or a simplified fraction.) A. The slope is B. The slope is undefined.

The equation d = 2sin (18t) measures the displacement of a swinging object in simple harmonic motion. t is measured in seconds and d is measured in centimeters. What is the displacement, to the nearest centimeter, when t = 10?

Find the value of z. √(z-5) = 2. 9 -49 -7 7

A planet rotates on an axis through its poles and 1 revolution takes 1 day (1 day is 26 hours). The distance from the axis to a location on the planet 30° north latitude is about 3671.5 miles. Therefore, a location on the planet at 30° north latitude is spinning on a circle of radius 3671.5 miles. Compute the linear speed on the surface of the planet at 30° north latitude

$5750 is invested at an annual interest rate of 3.5% for 25 years, find the balance if the interest is compounded on the following basis. (Round your answers to the nearest cent. Assume a year actly 365 days.)

A researcher performs an experiment to test a hypothesis that involves the nutrients niacin and retinol. She feeds one group of laboratory rats a daily diet of precisely 44.6 units of niacin and 33,100 units of retinol. She uses two types commercial pellet foods. Food A contains 0.19 unit of niacin and 155 units of retinol per gram. Food B contains 0.22 unit of niacin and 70 units of retinol per gram. How many grams of each food does she feed this group of rats each day? food A food B

Suppose that a culture of bacteria grows at a rate of 20.12e^t/32, where t is in minutes. If the initial population of bacteria was 2842, find the total number of bacteria in the culture after 10 minutes. Round to the nearest whole number. Answer =

Jake has $168,000 to invest. He chooses one money market fund that pays 6.8% and a mutual fund that has more risk but has averaged 7.2% per year. If his goal is to average 6.9% per year with minimal risk, how much should he invest in each fund? Jake should invest $ in the money market fund that pays 6.8%. (Simplify your answer.)

Savings Account: A woman deposits $600 in a savings account that pays 3% annually. If she withdraws all the money in the account after 120 days, how much does she withdraw (rounded to the nearest dollar)? She withdraws $ after 120 days.

Find all roots of the following. equation: z^4 = √3+i

Let f(x) = (x + 8)² Find a domain on which f is one-to-one and non-decreasing. Find the inverse of f restricted to this domain f-¹(x) =

In Problems 1-14, find the image of the given set under the mapping w = 2². Represent the mapping by drawing the set and its image. the line y = -3; f(2)= -z² +i

Evaluating and Solving an Equation Application Identify the information given to you in the application problem below. Use that information to answer the questions that follow. Round your answers to two decimal places as needed. The equation P= 450n - 11250 represents a computer manufacturer's profit P when n computers are sold. Identify the slope, and complete the following sentence to explain the meaning of the slope. Slope: The company earns $ per compute sold. Find the Vertical Intercept. Write your answer as an Ordered Pair: Complete the following sentence to explain the meaning of the Vertical Intercpet. If the company sells computers, they will not make a profit. They will lose $

The population of a town has been growing, following the equation P = 600t + 6000, where t is years after 2010. The number of restaurants in the town has been growing according to the equation R = 4t + 50. Complete an equation for the number of restaurants per capita (per person) How many restaurants per capita does this model predict for the year 2015?

The following chart shows "living wage" jobs in Rochester per 1000 working age adults over a 5 year period. Year 1997 1998 1999 2000 2001 Jobs 665 735 790 830 855 What is the average rate of change in the number of living wage jobs from 1997 to 1999? What is the average rate of change the number of living wage jobs from 1999 to 2001?

In 1812, an earthquake of magnitude 7.9 shook New Madrid, Missouri. Compare the intensity level of that earthquake to the intensity level of each earthquake below. 32. magnitude 7.7 in San Francisco, California, in 1906 33. magnitude 9.5 in Valdivia, Chile, in 1960 34. magnitude 3.2 in Charlottesville, Virginia, in 2001 35. magnitude 6.9 in Kobe, Japan, in 1995

Find the splitting field of x³ - 2 over the field Q of rational numbers and its degree over Q.

Find the 6 complex solutions for the equation z^6= -64. Give your exact answers in polar and standard forms.

Find the equation of the circle with the line segment (0, 1) and (4, 5) as its diameter. Draw and find its other y-intercept.

One of the next function is an even number: a) Csc x b) Tan x c) Cot (-x) d) Sec (2x) e) NA 2) Determine the period, amplitude, and horizontal shift of the function y= 2 cos (3x-pi)-2, and then graph over a full period.

Which best describes the behavior of the graph of a polynomial function at a real zero that has multiplity 4? A) graph crosses x-axis and flattens B) graph has no x-intercept C) graph has a y-intercept D) graph bounces off x-axis and flattens E) graph bounces off x-axis and does not flatten F) graph crosses x-axis and does not flatten

Q3 Which of the following are correct? (i) Every rooted tree of height h has at least 2¹ nodes. (ii) Every rooted tree of height h has at most 2" nodes. (iii) Every tree can be rooted so that it has height at most [(n-1)/2]. (iv) If u, v are leaves of equal depth d in a rooted tree, then the length of the unique u-v-path (v0=u, V₁...,vi=v) is odd.

Find the difference between the complex numbers. (−4+8i)−(−6+8i)

The Sandersons are planning to refinance their home. The outstanding principal on their original loan is $150,000 and was to amortized in 240 equal monthly installments at an interest rate of 12% / year compounded monthly. The new loan they expect to secure is to be amortized over the same period at an interest rate of 8% / year compounded monthly. How much less can they expect to pay over the life of the loan in interest payments by refinancing the loan at this time? (Round your answer to the nearest cent.)

Find the value of x in this equation 2xr² +x³ =m

Find exact values without a calculator. Draw a reference triangle in the appropriate quadrant and show your work. (4 points each) a. sin [cos-¹(1/3)] b. cos [cot-¹(-3/7)]

From 2010 to 2012, the average selling price of tablets decreased by 30% This percent reduction amounted in a decrease of $198 Find the average selling price of tablets in 2010 and in 2012 In 2010, the average selling price was $ and in 2012, the average selling price was

The forces F₁, F2, F3, ..., Fn acting on an object are in equilibrium if the resultant force is the zero vector. F₁+F2 +F3+.+Fn = 0 The forces F₁ =7i-7j and F₂ = 6i+2j are acting on an object. a. Find the resultant force. b. What additional force is required for the given forces to be in equilibrium? a. The resultant force is (Simplify your answer. Type your answer in terms of i and j.) b. The additional force required for the given forces to be in equilibrium is (Simplify your answer. Type your answer in terms of i and j.)

Find the square roots of the complex number z = 16 cis 60°. Select all correct answers. Select all that apply: 4 cis 120° 4 cis 240° 4 cis 30° 4 cis 45° 4 cis 210⁰ 4 cis 180°

The equation N (t) = 450 / 1+49e-0.7t models the number of people in a town who have heard a rumor after t days. As t increases without bound, what value does N (t) approach? Interpret your answer How many people started the rumor? Number N (t) approaches Number N (t) is limited by the carrying capacity of the town. N (t) is limited by the rate at which the rumor spreads. N (t) is limited by the number of days it takes for the entire population to hear the rumor. N (t) is limited by the number of poeple who started the rumor. N (t) is not limited by any value and increases without bound.

Prove that 1, -1, i and i are the only units in the ring Z[i] of Gaussian integers.

Apply the alternative form of the Gram-Schmidt orthonormalization process to find an orthonormal basis for the solution space of the homogeneous linear system.

a culture is increasing according to the law of exponential growth. After 2 hours, there are 50 bacteria, and after 4 hours, there are 200 bacteria. How many bacteria will there be after 6 hours?

Classify as = 1,<1, or >1. For n>1. |i^n| A=1 B<1 C>1

A plane is flying with a velocity vector of <424.2, 474.2 >. The wind is blowing at a velocity vector of <-483.4, -814.5>. Units are in miles per hour. Add these vectors and find the resultant velocity of the plane. Round to the nearest tenth of a mile per hour.

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.) cos()-0.12 1.45+2nk, 4.83 + 2rk rad List six specific solutions. -1.56,4.94,1.67,5.05,1.45,4.83 rad

Determine the quadrant in which the terminal side of 0 lies. (a) sin0> 0 and tan0 < 0 quadrant II (b) sin0> 0 and cos0 > 0 quadrant I ▼

Use the Laplace transform to solve the given system of differential equations. d²x dx dy + + dt² dt dt d²y dy dt² dt + x(0) = 1, dx dt 16. = 0 = 0 x'(0) = 0, y(0) = -1, y'(0) = 17

Which of the following represents the mean of the data set below? 8, 12, 15, 35, 35

What is the mode of the following series of numbers? 3, 15, 9, 17, 14, 8, 3, 25, 10, 22

Solve the inequality set. Graph the solution on a numberline. |2x + 12| >13 x < -12.5 or x > 0.5 -12.5 x or x < 0.5 x>-12.5 or x < 0.5 -12.5 < x or x > 0.5 all real numbers no solution

If : X → Y is any function, : → :f → f • ô is a homomorphism. ring 1) prove that if (f)=0 then f=0. 2) show that if p is injective then p* is surjective?

Let F be a field and F is a fixed algebric closure of F. Suppose E≤ F is an arbitrary extension field of F and K is a finite Galois extension of F (called "normal extension" in the textbook). (a) Show that the joint K VE is a finite Galois extension over E. (b) Show that the restriction map Gal(KVE/E) → Gal(K/EnF) defined by ook is an isomorphism.

Find the particular solution of the following equation with y(2) = 1. xy3dx + (1 - x)dy = 0

Sketch the graph of y = 4 cos 2x over a period.

For n > 5, is there an arrangement of n circular disks where 2n intersection points of the associated circles lie on the edge of the union of the circular disks?

Examine the following graph of a function modeling damped harmonic motion. Find the equation for the function pictured in terms of y and t. Assume that a factor of e-te-t provides the desired damping effect and that the graph has no vertical or horizontal shifts.