# Complex numbers Questions and Answers Algebra
Complex numbers
The point (5, pi/4) can also be represtend by which of the following polar coordinates? Select ALL that apply. A) (5, -pi/4) B) (-5,5pi/4) C) (-5, 9pi/4) D) (5, 3pi/4) . Algebra
Complex numbers
Determine whether the given equation is a parabola: x = 7y². O Parabola O Not a parabola If it is a parabola, write the equation in standard form: (y– k)² = 4p(x - h) or (x – h)² = 4p(y – k) Otherwise, leave the rest blank. h= k= p= Algebra
Complex numbers
Solve the triangle. The Law of Cosines may be needed. (Standard notation for triangle ABC is used throughout. Use a calculator and give your answers as decimals to tenth at the end of the computation. If no such triangle exists, enter 'NONE' in each of the answer blanks.) b= 31.9°, c = 14.7°, C = 27.8° A = B= a= Algebra
Complex numbers
The point (5, pi/4) can also be represented by which of the following polar coordinates? Select ALL that apply. Algebra
Complex numbers
An oblique cylinder has a radius of 11 units and a volume of1815π cubic units. What is the height of the cylinder? Algebra
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Find the solution to the lines x = y +5 and x = 8 + 2y. O (2, -3) O (-2, 3) O (2, 3) Algebra
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Solve the following y"(t) - 4ty'(t) - 8y(t) = 4 y(0) = 0, y'(0) = 0 Initial value problem. Algebra
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We will only need one fact: • 4.5 pabs = 5 teeps Now, perform the conversion and give your answer as a decimal number. Do not round your answer. 66.34 pabs²=__teeps² Algebra
Complex numbers
Sophia's grades have been updated online. Sophia's mom has seen the grades and has started texting her about them. The data is shown in the table. Hours since grades were posted 0 1 2 3 Number of texts 2 6 18 54 Which algebraic expression represents Sophia's mother's attempts to contact her? ○ 3x ○ 2ˣ⁻¹ ○ 2(3)ˣ ○ 2(3)ˣ⁻¹ Algebra
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Let f(x) = ln(x² + 3) and g(x) = √eˣ +1. Find formulas for (a) g(f(x) and (b) g‾¹(). Algebra
Complex numbers
Find the solution of xy" + 5xy' + (4 – 1x)y = 0, x > 0 of the form y₁ = x^r ∑ Cn x^n ( n=0 to ∞ ) where C₀ = 1 Enter r=____________ Cn=__________ , n=1,2,3,............ Algebra
Complex numbers
Determine the equations of the planes that make up the tetrahedron with one vertex at the origin and the other vertices at (5,0,0), (0,-6,0), and (0,0,2). Draw the diagram Algebra
Complex numbers
Alaina has a spherical balloon that has a diameter of 12 centimeters. Edgar has a spherical balloon that holds 3 times as much air as Alaina's balloon. What is the diameter of Edgar's balloon? Algebra
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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? Algebra
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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 Algebra
Complex numbers
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)? Algebra
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Find the volume of a sphere with a radius of 2. Hint: To add the pi symbol (TT), type "pi" Check Algebra
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Write in terms of i. 7√-18 Algebra
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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 Algebra
Complex numbers Algebra
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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: Algebra
Complex numbers
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. Algebra
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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? Algebra
Complex numbers
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 ) Algebra
Complex numbers
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 Algebra
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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. Algebra
Complex numbers Algebra
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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 Algebra
Complex numbers
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 Algebra
Complex numbers
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) Algebra
Complex numbers
Given the expressions 24m⁶n³p⁵ and 18m⁷n²(m + 5n)⁶, find the GCF. Provide your answer below: Algebra
Complex numbers
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. Algebra
Complex numbers
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 Algebra
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Multiply (√ + 2i)(√ - 2i) (√ + 2i)(√ - 2i) = ________ Algebra
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Find all solutions to 2 cos(θ) = -1 on the interval 0 <= θ < 2π. θ =______ Algebra
Complex numbers
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) Algebra
Complex numbers Algebra
Complex numbers Algebra
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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 Algebra
Complex numbers
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.) Algebra
Complex numbers
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? Algebra
Complex numbers
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? Algebra
Complex numbers
Convert the exponential equations into logarithmic form: 6³ 216 is equivalent to log C = D. C = and D = Algebra
Complex numbers
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. \$ Algebra
Complex numbers
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 _____ Algebra
Complex numbers
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} Algebra
Complex numbers
How many valence electrons are in As²‾? Algebra
Complex numbers
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.) Algebra
Complex numbers
Solve. √b-2 = 8 One or more solutions, b= No solution Algebra
Complex numbers
A translation maps (x, y) to (x + 5,y + 3). In which quadront does the point (-3. -2) be under the same translation