Complex numbers Questions and Answers

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?

Write the expression in rectangular form, x + y i, and in exponential form, reiθ [√3(cos π/12 + i sin π/12)]^8

Find the indicated roots of the following. Express your answer in the form found using Euler's Formula, Iz|neino The cube roots of 64 (cos (3π/2) + isin ( 3π/2 ))

Let Z[√3] = {a +b√√3 : a and b € Z}. Then prove that Z[√3] is a FD.

What is the maximum profit? $126210.00 there is no maximum profit $210.00 $127170.00 $230.00

How much of the substance will remain after 10 years? Round to the nearest whole gram. 18 grams 184 grams 1 gram 490 grams 285 grams

A) Find the polar form of the complex number z=5-3i. B) Use the polar form above and DeMoivre's Theorem to find (5-3i)^6.

Find the greatest common divisors of the following set of integers and find r.s and t (such that the equation on the right is satisfied). 2+2+3+3 (c) c = 30,b= 75, a = 250, gcd(a, b, c) = 250r +75s + 30t (d) c= 51, b = 27, a = 6, gcd(a, b, c) = 6r+27s+ 51t

Find all the complex roots. Write the answer in exponential form. The complex cube roots of 17 + 17 i. Zo = (Simplify your answer. Type an exact answer, using as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than 2л. Use integers or fractions for any numbers in the expression.) Z₁ = (Simplify your answer. Type an exact answer, using as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than 2π. Use integers or fractions for any numbers in the expression.) 2₂= (Simplify your answer. Type an exact answer, using as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than 2л. Use integers or fractions for any numbers in the expression.)

Note: Triangle may not be drawn to scale. Suppose a = 5 and b = 6. Find: C A degrees degrees Give all answers to at least one decimal place. Give angles in degrees

Evaluate the line Integral ∫(x² + y²) ds where "C" is The line segment from (-1, -1) To (2; 2).

Perform the indicated operation and record answer in rectangle form 4 (cos 200° + i sin 200°)/2(cos 100° +isin 100°)

Write the following complex number in standard form, z = a + bi. Write the exact answer. Do not round. COS(7π/4)+isin(7π/4)

A point P is often identified in mathematics using the notation P(x, y) to reference a point at coordinates (x, y). If P(x, 6/7 ) is on the unit circle in quadrant II, then a =

Find a so that the vectors v=i-aj and w = 5i + 7j are orthogonal.

Let 12 be a set of all square summable sequences of complex numbers. Prove that- (i) (l³)* = l^3/2

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. x 4.5x3+10x2+30x-36=0 (-2, 1, 3+31, 3-31} (-2, 1, 3+ 4i, 3 - 4i} (2,-1, 3+√√3,3-√√3) (2,-1, 3+ 31, 3 - 31}

The distribution of the number of occurrences of the letter "a" on the pages of a book is found to be a normal distribution with a mean of 60 and a standard deviation of 15. If there are 600 pages in the book, what percentage of the time is "a" found 45 times or more on a page? Select one: a. 34% of the time b. 84% of the time c. 50% of the time d. 68% of the time

Find the expected value in % of an insurance bet if you have removed 6 small cards from a single deck (and the dealer has an ace up)