Complex numbers Questions and Answers

What is the volume, in cubic in, of a rectangular prism with a height of 5 in, a width of 12 in, and a length of 14 in?

T and K is the overlap so 8 + 23 = 31 C is 9+16 +23+15= 63 So (T and K) OR C is (T and K) + C- (overlap already accounted for). 31 +63-23

A plane has x = 2m, y = -3m + 5n, z = -1 - 3m - 2n, m, n ∈ R, as its parametric equations. a. By inspection, identify the coordinates of a point that is on this plane. b. What are the direction vectors for this plane? c. What point corresponds to the parameter values of m = -1 and n = -4? d. What are the parametric values corresponding to the point A(0, 15, -7)?

Find the volume of a sphere with a radius of 2. Hint: To add the pi symbol (TT), type "pi" Check

Write in terms of i. 7√-18

Read the following scenario: Sam knew that if he was going to save his money to rent a limo for prom that he would not be able to go out to eat with his friends every Friday night. What is the opportunity cost that Sam is trading to save his money? 1. Financial cost of his time 2. Financial cost of the limo 3. Personal cost of his time

Express in terms of i. √-64 √-64 = (Simplify your answer. Type an exact answer, using radicals and i as needed.)

The expression (3a²b⁴c⁴)² (2a²b³c²)³ equals naʳ bˢ cᵗ where n, the leading coefficient, is: and r, the exponent of a, is: and s, the exponent of b, is: and finally t, the exponent of c, is:

A rectangular swimming pool has a base that is10m by 20m. Water is being pumped into the pool at a rate of 30 m³. How fast is the water level rising after 12 minutes.

Application Toward the end of the year, to make room for next year's models, a car dealer may decide to drop prices on this year's models. Imagine a car that has a sticker price of $20,000. The dealer lowers the price by 4% each week until the car sells. (a.) Write a recursive rule to generate the sequence of decreasing prices. (b.) Find the 5th term and explain what your answer means in this situation. (c.) If the dealer paid $10,000 for the car, how many weeks would pass before the car's price would produce no profit for the dealer?

The direction cosines of the line passing through the two points (-2,4,-5) and (1, 2, 3) (A) ( 3 / √77 ) , ( -2 / √77 ) , ( 8 / √77 ) (B) ( -3 / √77 ) , ( -2 / √77 ) , ( -8 / √77 ) (C) ( 3 / √77 ) , ( 2 / √77 ) , ( 8 / √77 ) (D) ( 3 / √77 ) , ( 2 / √77 ) , ( -8 / √77 )

You owe $561.54 on your credit card. Your average daily balance is $220.77, the billing cycle is 32 days, and the interest rate on the credit card is 19%. What is your interest charge? (a) $3.86 (b) $4.02 (c) $3.68 (d) $4.89

The profits for a company were $18.2 million in 2008 and have increased each year by $1.6 million. Let t represent the years since 2008. Set up and solve a linear equation to find the year when the profits would reach $29.4 million.

Multiply (8 +8i)(7 + i). (8 +8i)(7 + i) = _______ (Simplify your answer. Type your answer in the form a +bi.)

What is the parent function for this graph? (a) f (x)= 2^x Exponential (b) f(x) = x Linear (c) f(x)=1/x Rational (reciprocal) (d) f(x) = x² Quadratic

What is the total variance of the following portfolio consisting of 2 assets invested in the ratio of 1:2. Asset A: E(r) = 0.2. σ= 0.5 Asset B: E(r) = 0.4, σ=0.7 Correlation: -0.8 rf = 0.1 A) 0.14 B) 0.12 C) 0.10 D) 0.08

What is the product z₁z₂ in polar form? z₁=3cis(π/2) z₂=6cis(π/4) a. 18 cis(3π/4) b. 3cis(3π/4) c. 3cis (π/4)) d. 3cis(π/4) e. 18cis(π/4)

Given the expressions 24m⁶n³p⁵ and 18m⁷n²(m + 5n)⁶, find the GCF. Provide your answer below:

Graph: y < x - 3 Make sure to choose the correct type of line - either solid or dotted. Click on two points to specify the line and then click on the side of the line that needs to be shaded.

Your purchase costs $4,900.25, including tax. You sign an installment loan to pay $1,200 as a down payment. The remainder including the finance charge will be paid in 40 monthly installments of $102.58. What is the total amount repaid? O $5333.02 O $5,303.20 O $5,230.03 O $5263.30

Multiply (√ + 2i)(√ - 2i) (√ + 2i)(√ - 2i) = ________

Find all solutions to 2 cos(θ) = -1 on the interval 0 <= θ < 2π. θ =______

Solve the following linear equation for x 4(5x-2)-3(x-8)= - 137 A. X = -6 B. X = -9.9 (rounded to tenths) C.x = -9 D. X = -7.1 OE.X = -7.5 (rounded to tenths)

Write in terms of i 6√-(20). 6√-(20) = ______ (Simplify your answer. Type an exact answer, using radicals and i as needed.)

Multiply. -9i + 8i - 9i + 8i = _____ (Simplify your answer. Type your answer in the form a + bi.)

a-9≤16 A) a ≤-144 : -144 -140 B) a ≤-7: -8 -6 -4 -2 0 C) a ≤-25: -30 -28 -26 -24 -22 -20 D) a ≤- 16/9 : -8 -6 -4 -2 0

Write the quotient in the form a + bi. (7-i) / (8-9 i) (7-i) / (8-9 i) = ______ (Simplify your answer. Type your answer in the form a +bi. Use integers or fractions for any numbers in the expression.)

Rockafella Savings and Loans offers its most esteemed depositors an APR of 2.45% compounded continuously. Both Jay and Nelson deposited $50,000 into such an account, but Jay plans to let it accrue interest for 15 years, while Nelson plans to withdraw his money in 20 years. Compared to Jay's final amount, how much more money will Nelson have when he withdraws all his money?

How many four-digit numbers may be formed using elements from the set {1, 2, 3, 4, 5, 6} if elements may be used more than once in a number and the number must be even?

Convert the exponential equations into logarithmic form: 6³ 216 is equivalent to log C = D. C = and D =

Five years ago, you acquired a 30-year loan of $130,950, charging 6.7% annual interest, compounded monthly, and requiring monthly payments. At this time, interest rates on 15-year loans have dropped to 2.2% APR, compounded monthly, and you wish to refinance what you still owe with a new loan at this new rate. (a) How much (in dollars) will you be refinancing? Round your answer to the nearest dollar. $ (b) How much (in dollars) will your new monthly payment be after refinancing? Round your answer to the nearest cent. $

Write the name of the element family to which each of the elements in the following table belongs. Your answer should be a word or a short (2 or 3 word) phrase, with no numbers in it. element family sodium _____ bromine _____

In sketching the graph of y = 2 sin {3x - (π/5)} + 1. Find the ordered pair of the graph. A. {(17π/15), 1} B. {(17π/15), -1} C. {(17π/30), -1} D. {(17π/30), 1}

How many valence electrons are in As²‾?

Find the area of the region lying to the right of x = y² + 7y + 10 and to the left of x = 2y + 6, (Use symbolic notation and fractions where needed.)

Solve. √b-2 = 8 One or more solutions, b= No solution

A translation maps (x, y) to (x + 5,y + 3). In which quadront does the point (-3. -2) be under the same translation

Sketch the curve given by y=√x and use transformations to sketch each of the following curve. 2.1.2 y = √x - 2 2.1.3 y = √(x-2) 2.1.4 y = -√x 2.1.5 y = j√x

What is the simplest form of (2+3i )+(4 - i) ? (A) None of the choices are correct. (B) 6 + 2i (C) −2+41 (D) 2i (E) 2

Find the VERTEX of the given equation to the nearest tenth y = 3x² + 4x-1 (a) (0.3,1) (b) (-0.7, -2.3) (c) (-1.5, 0.2) (d) (0.7,0.3)

What is the solution to √(9x-28) = i , excluding extraneous roots? x = 3i x = 3 None of the choices are correct. x =1 or 3 x = -1 or -3.

In order to add or subtract imaginary and complex numbers one must None of the choices are correct. use the order of operations and only add the imaginary parts, leave the real parts alone. use the order of operations and only add the real parts, leave the imaginary parts alone. use the order of operations and only subtract the real parts, leave the imaginary parts alone. use the order of operations and add and subtract all terms from left to right regardless of the term.

Data from the Federal Bureau of Investigation show that the number of hate crimes in the United States decreased between two recent years, from 7785 incidents to 6606 incidents. What was the percent decrease in hate crimes between these two years?

If the denominator is in the form a-bi , then the conjugate is: (A) None of the choices are correct. (B) (a, b) (C) a-bi (D) a + bi (E) (a, -b)

Use linear approximation to estimate the following. Also estimate the maximum error (with sign) in your approximation. (a) (1.999)⁴ (b) sin 1º (c) ∛1001 tan 44° (d) 1/4.002 (e) tan 44° (f) √99.8

If x³ = 63, then: (A) x = 8 (B) x = 21 (C) None of the choices are correct (D) x= 10.5 (E) x= √63

Write the sum as the logarithm of a single expression. Assume that variables represent positive numbers. log2 (3)+ log 2(Z)

Using f(x)= (x/2)-30, determine f(-20) A. -20 B. 20 C. 40 D. -40

Find all solutions of the equation 2 sin x + √3 = 0. The answer is A + Bkπ and С+ Dkπ where k is any integer, 0<A <C< 2π,

Consider the graph of the function f(x) =(x² - 81)/(x²-5x-36) . Find the x-value of the removable discontinuity of the function.