Complex numbers Questions and Answers

Given the following information of a triangle ARST S 124 ZT 28 a Calculate the measure of the unknown angle s ZR b Classify the triangle by angle measure and by side length

ort Answer 1 For what values of x will the expression log x be undefined 2 Evaluate log 625 log 32 3 Put the following in order from smallest to largest log 16 log 100 log 30 log 40 log20 200 4 If you invested money into an account that pays 9 a compounded weekly how many years would it take for your deposit to double 5 Solve 10 2 10 9900 for x 6 What is the hydrogen ion concentration of a glass of orange juice with a pH of 2 8 blem 7 Given the parent function f x log 0x a state the transformations that must be applied to produce the function f x 3 log 0 2x 8 5 b state the x intercept and the equation of the asymptote c state the domain and range 8 Explain the difference in the process of solving exponential equations where both sides can be written as powers of the same base and solving exponential equations where both sides can not be written as powers of the same base 9 The function S d 86 logd 112 relates the speed of the wind S in miles per hour near the centre of a tornado to the distance the tornado travels d in miles Estimate the rate at which the speed of the wind at the centre of the tornado is changing the moment it has traveled its 50th mile

o find the distance across a small lake a surveyor has taken the measurements shown Find the distance across the lake using this information Assume points A and B are exactly along the shoreline a hat a 2 42 miles and b 3 81 miles Round your answer to two decimal places mi C 40 3 b B A

As Drake s OVO Private Jet approched Toronto s airport its horizontal distance From the airport is 22 miles when his altitude is 2 2 miles To the nearest degree what is the angle of depression of Drake s Plane using the diagram write an equation and solve

Set up a trip equation missing side length of the triangle C 5 B 90 x A 12 trigonometric function Sin A OS A Tan A A Find the sine cosine and tangent of referenced angle and solve for the Ratio

D 3 8 A candle is burning at a constant rate The height of the candle is 12 5 inches after 3 hours After 7 hours the height of the candle is 10 5 inches Assuming the decrease is linear which equation describes the relationship between the height of the candle and the time in hours it burns A y 2x 18 5 By 2x 6 5 C y x 14

Consider the planes II₁: 2x - 4y -z = 3, II₂ : -3x + 6y + 3z/2 = 6 . Give a reason why the planes are parallel. Also, find the distance between both planes.

Deborah takes 45 minutes to stitch a skirt and a shirt. She takes 70 minutes to stitch a shirt and two skirts. How long is she taking to stitch a skirt? 25 minutes 40 minutes 35 minutes

Evaluate the quotient, and write the result in the form a + bi. (Simplify your answer completely.)

The heights of a group of people are normally distributed with a mean of 62 inches and a standard deviation of 1.5. What percent of the group is between 62 and 65 inches tall?

I need an example of a critical point of a nonlinear system of differential equations that satisfy the limit condition for asymptotaclly stable? We know from the definition of asymptotaclly stable critical point that the point must be stable and must satisfy the limit condition (I.e. all the trajectories must approach to the critical point as t goes to infinity), so the limit condition does not mean the asymptotic stability without the fact that the point is stable. I need an example in which the limit condition holds but the critical point is not stable.

Rewrite the system of inequalities, adding slack variables or subtracting surplus variables as necessary. X₁ + x₂ + x3 = 84 x₁ + x₂ + x3 ≥ 60 X₁ + X₂ 2 56 What is the corresponding system of equations?

7. Find the area of the shaded region. All work must be shown on this page for full credit. A. 34.77 cm² B. 40.24 cm² C. 88.56 cm² D. 106.75 cm²

A bacteria culture initially contains 3000 bacteria and doubles every half hour. Find the size of the baterial population after 20 minutes. Find the size of the baterial population after 10 hours.

A new car is purchased for 24000 dollars. The value of the car depreciates at 8% per year. To the nearest tenth of a year, how long will it be until the value of the car is 10300 dollars?

Bartholomew is grocery shopping. The probability that he buys chicken is 0.85. The probability that he buys beef is 0.52. The probability that he buys both is 0.42. What is the probability that he buys chicken or beef?

Describe the procedures for solving linear inequalities using a graphing method. What are some of the pitfalls you would watch out for? Are there some linear inequalities you cannot solve with the graphical method? Give one example.

Determine if 81x² - y² = 81 is an ellipse. Ellipse Not an Ellipse If it is an ellipse, write the equation of the ellipse in standard form not an ellipse, leave the rest blank. Where:

The school students are planning to conduct an exhibition. They need to collect a minimum of $5000 by selling tickets. The adult ticket cost $25 and a student ticket for $20. They estimate that at most 250 tickets will be sold. Form the system of inequalities representing the given situation. x+y ≤ 250, 250x+ 200y ≥ 5000, x ≥ 0 and y20 x+y> 5000, 250x + 200y <250, x ≥ 0 and y≥0 x+y> 250, 250x + 200y > 5000, x>0 and y>0

Given f(x) = 3(4), determine the following. 1) The parent function from which the graph of the function given above can be obtained. y = 2) Find f(10) = 3) Solve for x if f(x) = 10. Round the answer(s) to three decimal places. A N

Question 5 Points 3 Solve using graphical method: -2x + 9 = y; 5x = 18+ 2y. O (4,1) O (1,2) O (1.1)

IM 6.5 1. Write the (x, y) coordinates for P in terms of cosine and sine. 2. If cos(0) = 0.6, what are the coordinates of P? Explain your reasoning. YA 0 X P IM 6.6 1. If cos (0) = -0.5 and angle is in quadrant 2, what are the values of sin(0) and tan(0)?

Find the complex zeros of the following polynomial function using the techniqu 3 f(x) = x³ - 6x² +61x-106 The complex zeros of f are 0. (Simplify your answer. Type an exact answer, using radicals and i as needed. Use the complex zeros to factor f. f(x) = (Type your answer in factored form. Type an exact answer, using radicals and

Identify all of the following that are roots of f(z) = − 112²2² +18. 0-√2 3 0√2 -3

P(x) = x³ - 5x² + 24x - 20 and one root of P(x) is 2 + 42, which of the following is another root? 04+ 2i -2 - 4i 2 - 4i 04-2i

Total blood cholesterol level was measured for each of 7 adults. Here are the 7 measurements (in mg/dL). 186, 141, 253, 131, 206, 206, 206 Send data to calculator (a) What is the mean of this data set? If your answer is not an integer, round your answer to one decimal place. 0 (b) What is the median of this data set? If your answer is not an integer, round your answer to one decimal place. (c) How many modes does the data set have, and what are their values? Indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s), if applicable. zero modes one mode: two modes: and 0

Define a sequence (an)1 as follows. Let a₁ = 1 and an+1 = 0.5an + 1/n for n ≥ 2. Which of the following statement is true? (a) limn→∞o an = 1. (b) limn→∞an = ∞0. (c) limn→∞ an/n = 0. (d) Σ1 nan <∞0. (c) None of the above statements is truc.

How do we generate (find the expression giving y in terms of x) a random variable Y from another random variable X, where X is uniformly distributed between 0 and 1, and Y is Rayleigh distributed with a cdf Fy(y) = 1-expl-y²/b) fory 20

Write the complex number in standard form. √-11 ✓-22 .

(10 points) Derive the affine transformation that maps the triangle with (0, 1), (1, 2), and (2,0) as its vertices to a triangle with (1.2), (0, -1), and (3,3) as its ver- tices. Hint: Look for the affine transformation in R³ that is uniquely defined by mapping of three points.

Given the functions f (x) = x² - 1 1 and express it as a piecewise-defined function. and g(x) = |x| + 1, find f (g(x))

Solve 4 sin x + √5-2 sin x for 0 sx< 360°. Which of the following statements about the solution set is true? 240° is the larger of two solutions. O240 is the smaller of two solutions. O210" is the larger of two solutions. 210" is the smaller of two solutions.

The graph of the function f(x)=log6(x) is stretched vertically by a factor of 7, reflected over the x-axis, reflected over the y-axis, and shifted up by 2 units

Find two of the vertical asymptotes of y=tan(2x-). (Hint: find the period and vertical asymptotes before the phase shift, find the phase shift, and then find the vertical asymptotes by applying the effect of the phase shift to the vertical asymptotes you found before the phase shift.) (6 points)

Complete the squares to find the center and radius of sphere with equation x² + y² +2²-4x+2y-8z+30=0

Let X be any space, and let ACX. Let E = {(x, t) e Xx I|x A ift=0} Show that the projection p: E-X given by p(x, t) = x is a fibration.

Solve the equation by the square root property. (z+ 9)² = − 64

Rationalize the denominator. What is the first step to rationalize the denominator? Choose the correct answer below. A. Multiply by 1 using the conjugate of the numerator. B. Multiply by 1 using the opposite of the denominator. C. Multiply by 1 using the opposite of the numerator. D. Multiply by 1 using the conjugate of the denominator.

Complex numbers are used to describe current, I, voltage, E, and impedance, Z. These three quantities are related by the equation E = IZ. Given two of these quantities, solve the equation E = IZ for the missing variable. 1=5+3i, Z=7+4i

Select the equations that result from solving the absolute value equation. |x+51-7=3 Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. bx-2=3orx-2=-3 D x+5-7 3 orX+5-7=-3 P x+5=4 orx+5=-4 x+5=10 orx+5=-10

Find the positive integer k such that the roots of ³ - 15x² + kx - 1105 are three distinct collinear points in the complex plane.

Prove using the definition of locus that a horizontal hyperbola centered at the origin is defined by the equation (x2/a2)-(y2/b2)=1.

Suppose that the functions u and w are defined as follows. u(x)=x+5 w(x)=-3x-1 Find the following. (wou)(-5) = (uw)(-5) = 9. X 0,0 Ś ?

The times taken to assemble a clock at a factory are approximately normally distributed with a given mean μ = 3 hr and standard deviation σ = 0.5 hr. What percentage of the times are between 2 hr and 4 hr? 34% 47.5% 68% 95%

Use strong induction to prove that F₁ < 2" for all n € N.

Tyesha found that the z-statistic was 2.1 and that the critical z-values were -1.96 and 1.96. Which of the following is a valid conclusion based on these results? One can reject the null hypothesis. One can reject the alternate hypothesis. One can accept the null hypothesis. One cannot accept or reject the null hypothesis.

A small fire is sighted from ranger stations A and B. Station B is 1.6 miles due east of station A. The bearing of the fire from station A is N35°E and the bearing from the fire from station B is N50°W. How far, to the nearest tenth of a mile, is the fire from station A?

Consider the function defined by f(x,y)=√x-y. (a) Find the domain and range of f. (b) Draw a contour map of f for k=-1,0, 1. (c) Sketch the graph of f.

Opal is collecting data on water levels in different parts of town. She notices that her sample data has a low-value outlier. Which statement must be true? Removing the outlier will not change the spread of the graph of the data set. Removing the outlier will not change the variance of the data set. Removing the outlier will increase the variance of the data set. Removing the outlier will decrease the spread of the graph of the data set.

Sighting the top of a building, a surveyor measured the angle of elevation to be 27°. The transit (this is the piece of equipment used to measure the angles) is 5 feet above the ground and 325 feet from the building. Find the building's height to the nearest foot.