5. Find all complex number solutions of the equation. 3 x + 125 i = 0 Choose the correct solution set below. A) . {125(cos 270° + i sin 270°), B) 125(cos 390° + i sin 390°), C) 125(cos 510° + i sin 510°
Answers
The correct solution set is A) {125(cos 270° + i sin 270°)} . The complex number -125i/3 can be expressed in polar form as -125i/3 = (125/3)(cos(-1.3963) + i*sin(-1.3963)).
To find all complex number solutions of the equation 3x + 125i = 0, we need to solve for x.
Dividing both sides of the equation by 3, we get:
x = -125i/3
Now, we can express -125i/3 in polar form. The polar form of a complex number is given by r(cosθ + isinθ), where r is the magnitude and θ is the argument.
The magnitude of -125i/3 can be calculated as:
|r| = sqrt((-125/3)^2) = 125/3
To find the argument θ, we can use the arctan function:
θ = arctan(-125/3)
Using a calculator, we find:
θ ≈ -1.3963 radians or approximately -79.91 degrees
Therefore, the complex number -125i/3 can be expressed in polar form as:
-125i/3 = (125/3)(cos(-1.3963) + i*sin(-1.3963))
Comparing this with the answer choices, we can see that the correct solution set is:
A) {125(cos 270° + i sin 270°)}
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Related Questions
This is 2 parts of one of my practice problems. The current age used for the first question is 30 and the retirement age is 58. The amount wanted to save is $1,060,123.
a) You and your family would like to have a $X saving at the end of the year you retire. You are planning to retire at the age of Y. Given your age today (please specify an age, which doesn’t have to reflect your true age), and planning to make $400 monthly deposits, what rate should you earn annually to reach your retirement goal? (Hint: Use Rate function)
b) You would like to buy a car with a loan that charges APR of 3.69% per year compounded monthly, (3.69%/12 per month). You borrow $40,000 and promised to pay monthly in 5 years (5*12=60 months). What would be your monthly payments?
Thank you!
Answers
A retirement savings goal of $1,060,123 by the age of 58, while starting at the age of 30 and making monthly deposits of $400, an annual interest rate of 3.69% compounded monthly and agrees to make monthly payments over a period of 5 years.
a) To determine the required annual interest rate to reach the retirement savings goal, the Rate function can be used in financial calculations. The known values in this scenario are the starting age (30), the retirement age (58), the desired savings amount ($1,060,123), and the monthly deposits ($400). By using the Rate function, the interest rate required to achieve the goal can be calculated. The formula for the Rate function is Rate(Nper, PMT, PV, FV). In this case, Nper represents the number of periods (in years), PMT represents the monthly deposit amount, PV represents the present value (initial savings), and FV represents the future value (retirement savings goal). By plugging in the given values, the function can determine the required interest rate.
b) To calculate the monthly payments for a car loan, the known values are the borrowed amount ($40,000), the annual percentage rate (APR) of 3.69%, and the loan term of 5 years (or 60 months). The monthly interest rate is calculated by dividing the APR by 12 (to reflect monthly compounding). Using the loan formula for monthly payments, which is PMT = (P * r * (1 + r)^n) / ((1 + r)^n - 1), where PMT represents the monthly payment, P represents the principal amount (borrowed amount), r represents the monthly interest rate, and n represents the number of periods (in this case, the total number of months).
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give me an answer i dont need an explanation both would be nice thank you
Answers
The surface area of the triangular prisms are:
1. 116 cm²
2. 82 cm².
How to Find the Surface Area of a Triangular Prism?To find the surface area of the triangular prism, add the areas of all the faces or shapes that make up the net of the triangular prism.
Problem 1: The triangular prism net consists of 2 identical rectangles, 2 identical triangles and 1 different rectangle.
Area of rectangle = length * width
Area of triangle = 1/2(base * height)
Therefore:
Area of the two identical rectangles = 2(7 * 4) = 56 cm²
Area of the larger rectangle = 6 * 7 = 42 cm²
Area of the two identical triangles = (6 * 3) = 18 cm²
The surface area= 56 + 42 + 18 = 116 cm²
Problem 2:
Area of the rectangle 1 = 6 * 3 = 18 cm²
Area of the rectangle 2 = 6 * 4 = 24 cm²
Area of the rectangle 3 = 6 * 5 = 30 cm²
Area of the two identical triangles = (5 * 2) = 10 cm²
The surface area = 18 + 24 + 30 + 10 = 82 cm²
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Assuming that no one is born on Feb. 29 (leap day), how many people should be selected to guarantee that at least 4 were born on the same day, not considering the year?
Answers
On the basis of birthday problem or scenario, the number of people should be selected to guarantee that at least 4 were born on the same day, not considering the year is equals to the 1096.
The worst case scenario is one of the many possible cases where the desired outcome comes after every other probable outcome has already occurred. The number of people who ensure that at least 7 people have a birthday on a single day of a non-leap year (365 days) can be determined by ensuring that in the number of people selected in each trial, two people do not have a birthday on a day. the same day. There are 365 days in a year.
Assuming everyone was born on a different day, then you could have 365 people where no one was born on the same day, but those 366 people would have to be born on the same day as someone else in the group. So the minimum number of people in a group would have to be 366 to guarantee that at least 2 people were born on the same day. But we wanted to guarantee that at least 4 people were born on the same day.
So, assuming we had 3 × 365 people together, with every 3 of them being born on the same day. Then would have a total of 365× 3 = 1095 people, with no more than 3 people being born on the same day. Now as we select one more person, the number of people born on a day for one of the days in the year will increase to 4. Hence the number of people that should be selected to guarantee that at least 4 were born on the same day are 1095 +1 = 1096. Hence, required value is 1096.
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What is the sale price on an item that is $50 with a 54% markdown?
Answers
The sales price on an item that is $50 with a 54% markdown is $23
How to determine the sale price on an item that is $50 with a 54% markdown?The given parameters are
Item price = $50
Markdown = 54%
The sales price on an item that is $50 with a 54% markdown is calculated as
Sales price = Item price * (1 - Markdown)
So, we have
Sales price = 50 * (1 - 54%)
Evaluate
Sales price = 23
Hence, the sales price on an item that is $50 with a 54% markdown is $23
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if the probability of detective bolt is 0.1, find the mean and the standard deviation for the number of defective bolts in a total of 400 bolts.
Answers
The mean and standard deviation for the number of defective bolts in a total of 400 bolts is 40 and 6.32 (approx), respectively.
The mean and standard deviation for the number of defective bolts in a total of 400 bolts if the probability of defective bolt is 0.1 can be calculated using Poisson distribution.
Poisson distribution is used to predict the number of events that occur over a specified interval of time when the probability of an event occurring is known.
The formula for calculating the mean (μ) and standard deviation (σ) is given as follows:
μ = λσ = √λ
Where λ = np, where n is the number of trials and p is the probability of success.
Here, the probability of a defective bolt is 0.1. So the probability of a non-defective bolt is 0.9. The total number of bolts is 400, so the expected number of defective bolts can be calculated as follows:
μ = λ = np = 400 x 0.1 = 40
The mean number of defective bolts is 40. The standard deviation can be calculated as follows:
σ = √λ = √40 = 6.32 (approx)
The standard deviation is 6.32 (approx).
Therefore, the mean and standard deviation is 40 and 6.32 (approx), respectively.
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Jane, ahmad, and miguel served a total of 84 orders monday at the school cafeteria. ahmad served 2 times as many orders as miguel. jane served 8 fewer orders than miguel. how many orders did they each serve?
Answers
Miguel served 23 orders, Ahmad served 46 orders, and Jane served 15 orders at the school cafeteria on Monday.
To solve this problem, let's assign variables to represent the number of orders served by each person. Let's say Miguel served x orders.
According to the information given, Ahmad served 2 times as many orders as Miguel, so Ahmad served 2x orders.
Jane served 8 fewer orders than Miguel, so Jane served (x - 8) orders.
The total number of orders served by all three is 84, so we can set up the equation:
x + 2x + (x - 8) = 84
Simplifying the equation, we have:
4x - 8 = 84
Adding 8 to both sides of the equation:
4x = 92
Dividing both sides by 4:
x = 23
Now we can find the number of orders served by each person:
Miguel served 23 orders.
Ahmad served 2 * 23 = 46 orders.
Jane served 23 - 8 = 15 orders.
In conclusion, Miguel served 23 orders, Ahmad served 46 orders, and Jane served 15 orders at the school cafeteria on Monday.
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how many solutions are there to square root x =9
Answers
Answer:
There are 2 solutions to square root x = 9
They are 3, and -3
Step-by-step explanation:
The square root of x=9 has 2 solutions,
The square root means, for a given number, (in our case 9) what number times itself equals the given number,
Or, squaring (i.e multiplying with itself) what number would give the given number,
so, we have to find the solutions to \(\sqrt{9}\)
since we know that,
\((3)(3) = 9\\and,\\(-3)(-3) = 9\)
hence if we square either 3 or -3, we get 9
Hence the solutions are 3, and -3
State the domain and range of the graph below:
Answers
Answer:
domain [-1, ∞)
range [ -3, ∞)
Step-by-step explanation:
Help plssssss! Thnx!
Answers
Answer:
$55.48
Step-by-step explanation:
nice to help you.hope it helps
The length of a rectangle is 7inches more than 4 times the width. The perimeter is 74 inches. Find the length and the width.The length is ? inches and the width is ? inches.
Answers
L = lenght = 4w + 7
W = width
Perimeter = 2L + 2W
74 = 2 (4W + 7 ) + 2 W
74 = 8W + 14 + 2 W
74 = 10W + 14
74-14 = 10W
60 = 10W
60/10 = W
6 = W
L = 4W + 7
L= 4(6) +7
L= 24+7
L= 31
Answer:
Lenght = 31 inches
Width = 6 inches
Answer:
6
Step-by-step explanation:
Riddle: a half is a third of it. What is it?
Answers
Answer:
\(\frac{3}{2}\)
Step-by-step explanation:
let n be the number , then
\(\frac{1}{3}\) n = \(\frac{1}{2}\) ( multiply both sides by 3 )
n = 3 × \(\frac{1}{2}\) = \(\frac{3}{2}\)
7 3/4 + 3 5/6 - 1 3/4
Answers
Answer:
This does not have to be complicated.
Just subtract 1 3/4 from 7 3/4 to get 6. Now add the 3 5/6 to that for a total of 9 5/6
Step-by-step explanation:
The tensile strength of a metal part is normally distributed with mean 40 pounds and standard
deviation 5 pounds.
a. What is the probability of failing to meet the specification limit of 45-pounds tensile strength? b. Based on the probability of a, if 50,000 parts are produced, how many would parts would not
meet the specification?
Using the standard normal distribution.
Answers
a) The probability of failing to meet the specification limit of 45-pounds tensile strength 15.87%.
b) The number of parts that would not meet the specification is 7,935.
a) Given that the tensile strength of a metal part is normally distributed with mean 40 pounds and standard deviation 5 pounds.
We have to find the probability of failing to meet the specification limit of 45-pounds tensile strength.
Using the standard normal distribution, we can find the probability of failing to meet the specification limit of 45 pounds as follows:
z = {45 - 40}/{5}
= 1
The probability of failing to meet the specification limit of 45 pounds is the probability that the standardized variable Z is greater than 1, which is given by:
P(Z > 1) = 0.1587
Therefore, the probability of failing to meet the specification limit of 45-pounds tensile strength is 0.1587 or 15.87%.
b) If the probability of failing to meet the specification is 0.1587, the probability of meeting the specification limit is
1 - 0.1587 = 0.8413
.If 50,000 parts are produced, then the expected number of parts that meet the specification limit is:
0.8413* 50,000 = 42,065.
Therefore, the number of parts that would not meet the specification is: 50,000 - 42,065 = 7,935.
Hence, about 7,935 parts would not meet the specification.
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Round the number to the place of the underlined digit. The underlined digit is supposed to be the 7.
42.76
Answers
Answer:
42.80
Step-by-step explanation:
5 or up you round up. 4 or down, you round down. So since 6 is bigger than 5, you round up.
Runtime function T(n)=2n
2
+4n+40 in which of the Collowing rentime classes? Setect all that apply 1) Q(
2
1
n
2
) 2) O(
2
n(n+1)
) 3) θ(n) 4) θ(n
2
) 5) 0(2
n
) 6) Ω(n
2
) 7) θ(10n
2
+5n+40) 8) Ω(n
3
) 9) Ω(1) 10) O(n)
Answers
The function T(n) has a quadratic term (n^2), which means it grows with the square of the input size. Therefore, it belongs to the runtime class O(n^2).
Additionally, the function has a linear term (n), indicating a linear growth rate, which makes it fall into the runtime class θ(n). The presence of a constant term (40) does not affect the overall growth rate, so it does not change the runtime class. Finally, the function can also be classified under the runtime class O(n) because the quadratic term dominates the growth rate.
The function T(n) = 2n^2 + 4n + 40 can be explained in two paragraphs based on its runtime classes. Firstly, the function belongs to the runtime class O(n^2) because it has a quadratic term (n^2). This means that the function's runtime grows quadratically with the input size. As the input size increases, the runtime of the function will increase at a faster rate, proportional to the square of the input size.
However, it's important to note that the function also has linear and constant terms. While these terms contribute to the overall runtime, they do not dominate the growth rate when compared to the quadratic term.
Secondly, the function also falls into the runtime class θ(n) because of its linear term (n). In this case, the linear term represents a linear growth rate of the function. As the input size increases, the runtime of the function will increase proportionally to the input size.
The presence of the quadratic and constant terms does not change the growth rate significantly. Therefore, the function T(n) has a combined growth rate of both quadratic and linear terms, making it belong to the runtime class θ(n).
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Determine f(–3) for A piecewise function f of x in three pieces. The function is defined by part 1, which is x cubed for x less than negative 3, part 2, which is 2 times x squared minus 9 for negative 3 is less than or equal to x which is less than 4, and part 3 which is 5 times x plus 4, for x greater than or equal to 4..
Answers
Answer:8
Step-by-step explanation:
What is the monthly repayment on the following hire-purchase agreement? A colour TV costs £640. The deposit was £200. The interest rate was 10% p.a. and it was paid off in two years.
Answers
The monthly repayment on the following hire-purchase agreement is £22.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a colour TV costs £640. The deposit was £200. The interest rate was 10% p.a. and it was paid off in two years.
The monthly repayment will be calculated as,
Total interest for two years = ( 640 - 200 ) x 1.2
Total interest for two years = ( 440 x 1.2 )
Total interest for two years = £528
The value of monthly repayment = 528 / 24 = £22
Therefore, the monthly repayment on the following hire-purchase agreement is £22.
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helpppp this is due in 5 mins
Answers
A perimeter of 6 inches - Scalene Triangle
A perimeter of 15 inches - Scalene Triangle
One leg length of 6 inches and area of 24 square inches - Right Triangle
Non-congruent side of 4 inches and perimeter of 8 inches - Isosceles Triangle
Whole number side lengths - Scalene Triangle, Isosceles Triangle and Equilateral Triangle
What are the triangle types?A scalene triangle is a type of triangle in which all three sides have different lengths. Additionally, all three angles of a scalene triangle are also different from each other.
An isosceles triangle is a type of triangle in which two sides have the same length, while the third side has a different length. The two angles opposite to the equal sides are also equal in an isosceles triangle.
An equilateral triangle is a type of triangle in which all three sides have the same length.
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13 erasers in your backpack is considered
a what?
Answers
Is this suppose to be a riddle or sum
Write the number "five hundredths, six thousandths, forty-two millionths" as a decimal.
Answers
Answer:
0.0560042
Step-by-step explanation:
What is the image of the point (-2, 4) after a rotation of 180° counterclockwise
about the origin?
Answers
Answer:(2,-4)
Step-by-step explanation: The formula to find a point for a 180° rotation about the origin is (x,y)-> (-x,-y) Therefore -2->2 and 4-> -4
What is the equation of the line that passes through the point (6,-4) and has a
slope of - 1/6?
Answers
Answer:
y=(-1/6)x -3
Step-by-step explanation:
y=(-1/6)x + b, plug in (6,-4) to solve for b
-4 = (-1/6)(6) + b
b = -4 + 1 = -3
What is the value of x?
Answers
I need help with these please not number 3
Answers
Answer: A) -4.6
b) 4.6 spaces left from the original spot
c) the totaal distance travled was 18.2 cm
Step-by-step explanation:
for a you add the amounts together, if you go left that's negative so you use subtraction
for b you count the amount you have from zero
for c you add all the numbers together and forget the signs
a bag contains 5 red balls and 6 green balls. if two balls are taken out successively, without replacement, what is the probability that green is picked on the first pick given that at least one red is chosen? g
Answers
The probability of picking a green ball on the first pick, given that at least one red is chosen, is 11/19.
The probability of picking a green ball on the first pick, given that at least one red is chosen, can be calculated by finding the total number of possible outcomes and then dividing by the number of outcomes that include at least one red ball. In this bag, there are 11 green balls and 5 red balls, for a total of 16 balls. Since two balls are taken out successively without replacement, the total number of outcomes is 16 choose 2, or 120. Of those, there are 10 outcomes that include at least one red ball, so the probability of picking a green ball on the first pick, given that at least one red is chosen, is 11/19. This can be calculated by dividing the number of outcomes that include at least one red ball (10) by the total number of outcomes (120).
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Find the distance between the points (-10, 9) and (2, -7).
Hint: Use the Pythagorean theorem
Answers
Hope this helps
median of integers between 1 and 1000 divisible by 28
Answers
In order to find the required median, you first list the number divisible by 28 in between 1 and 1000. These numbers are:
28, 56, 84, 112, 140, 168, 196, 224, 252, 280, 308, 336, 364, 392, 420, 448, 476, 504, 532, 560, 588, 616, 644, 672, 700, 728, 756, 784, 812, 840, 868, 896, 924, 952, 980
Thus, you have 35 numbers divisible by 28. In this case you have an odd number of data. The median is the number at the position 18, which by the list above is 504.
Hence, the median is the integer 504
BC = 40; CD= 30. What is the value of BD - AC?
Answers
The value of BD - AC is 60.
Given BC = 40; CD = 30.
To find the value of BD - AC, we need to find the value of BD and AC and then subtract the value of AC from BD.
We know that,
BD = BC + CD
Substitute the given values of BC and CD.
BD = 40 + 30
BD = 70
We also know that,AC = AD - CD
We need to find the value of AD to find AC.
Let's use Pythagoras theorem in ΔABC to find AD.
a² + b² = c²
where a = AC, b = BC and c = AB
c² = a² + b²c² = AC² + BC²
c² = AC² + 40²
We know that CD = 30.
Substituting in ΔACD we get,
AD² = AC² + CD²AD² = AC² + 30²
Now let's use Pythagoras theorem in ΔABD to find AD.
c² = a² + b²c²
= AD² + BD²
c² = AD² + 70²
We have two equations to find AD.
AD² = AC² + 30²
c² = AD² + 40² - 2×40×AD² - AD²
= 40² - AC²
AD² + AD² = 1600 - AC²2
AD² = 1600 - AC²
AD² = (1600 - AC²)/2
Substitute the value of AD² in c² = AD² + 70².
(1600 - AC²)/2 = AC² + 900
1600 - AC² = 2AC² + 1800
AC² = 100
Thus,
AD² = (1600 - 100)/2
AD² = 750
AC = √100 = 10
Now we can find the value of BD - AC.
BD - AC = 70 - 10
BD - AC = 60
Therefore, the value of BD - AC is 60.
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need help! just need the answer!
Answers
Answer:
A
Step-by-step explanation:
k=1 ,i THINK
A
I need this ASAP! When David was asked how old he was, he said: "I'm three times younger than my dad, but twice as old as Rebecca." Then little Rebecca ran up to him and declared "I am 30 years younger than my dad." How old is David?
Answers
Answer:
David is 12 years old.
Step-by-step explanation:
Let r = Rebecca's age
Let d = David's age
let p = Dad's age
David is 3 times as younger than his dad:
d = \(\frac{p}{3}\)
David is 2 times older than Rebecca:
d = 2r
Rebecca is 30 years younger than the dad:
r = p-30
All three equations can be solved by a system
2r = \(\frac{p}{3}\)
r = p-30
multiplying r = p-30 by negative 2 and adding it to 2r = \(\frac{p}{3}\)
0 = (-2p + p/3) + 60
multiplying new equation by 3
0 = (-6p + p) + 180
5p = 180
p = 36
d = 36/3 = 12