The complex number Z = (20 + 120i) can be expressed in polar form as Z = 2√370(cos(1.405) + isin(1.405)).
To express the complex number Z = (20 + 120i) in polar form, we need to find its magnitude (r) and argument (θ).
The magnitude of a complex number Z = a + bi is given by the formula:
|r| = √(a^2 + b^2)
In this case, a = 20 and b = 120.
Therefore, the magnitude of Z is:
|r| = √(20^2 + 120^2) = √(400 + 14400) = √14800 = 2√370.
The argument (θ) of a complex number Z = a + bi is given by the formula:
θ = arctan(b/a)
In this case, a = 20 and b = 120. Therefore, the argument of Z is:
θ = arctan(120/20) = arctan(6) ≈ 1.405 radians.
Now we can express Z in polar form as Z = r(cosθ + isinθ), where r is the magnitude and θ is the argument:
Z = 2√370(cos(1.405) + isin(1.405)).
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How many solutions does 4(−5x+8)= 4(−5x+8) have?
Answer:
infinity
Step-by-step explanation:
In the exercise, X is a binomial variable with n = 5 and p = 0.4. Compute the given probability. Check your answer using technology. HINT [See Example 2.] (Round your answer to five decimal places.) P(X ≤ 2)
The probability of P(X ≤ 2) is 0.0135
We have the information available from the question:
Binomial variable is X
the value of n = 5
and, the value of p = 0.4
We are given to compute the probability P(X [tex]\leq[/tex] 2) and round the answer to five decimal places.
The binomial distribution formula is given by:
[tex]P(X)=nCx(p)^x(1-q)^n^-^x[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)!x!}[/tex]
We have to find the probability:
P(X [tex]\leq[/tex] 2) = P(X=1) + P(X=2)
P(X = 1) = [tex]5C1(0.4)^1(1-0.4)^5^-^1[/tex] = 0.0026
P(X= 2) =[tex]5C2(0.4)^2(1-0.4)^5^-^2[/tex] = 0.0109
P(X [tex]\leq[/tex] 2) = P(X=1) + P(X=2)
P(X [tex]\leq[/tex] 2) = 0.0026 + 0.0109
P(X [tex]\leq[/tex] 2) = 0.0135
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Solve −2|m|= −10.
What is m?
Answer:
|m| : -5Step-by-step explanation:
{ -2|m|= -10= |m| : -5 }can someone plz help me plz plz
Answer:
56.52
Step-by-step explanation:
C = 2 x pi x r
r = 9
C = 2 x pi x r
multiply 2 by 9
C = 18 x pi
C = 56. 52
Please help me with the question
Answer: 70
Step-by-step explanation: if you look at it hard enough they both look the same, this is called a vertical angle, I'm down for more questions lol. you keep on getting on my fyp
1. An exponential function is shown below.
f (x)= -2(2)
Which key attribute does the function not exhibit?
This question seems extremely odd to me. I don't really even understand what's being asked.
As far as exponential functions go, it's missing an exponent for one. The dependent variable is missing. This essentially saying f(x) = -4 or y = -4. Which is fine, but is definitely not an exponential function and in a very odd and incomplete form to begin with.
What is the answer for |-12| is positive or negative
Answer:
postitive
Step-by-step explanation:
|-a| = a, a>0
In myrtle beach, the maximum height off the water a parasailor can be is 500 feet. I the rope is 800 feet long, about how many feet from the boat is the parasailor to the nearest tenth?
Answer:
624.5 feet
Step-by-step explanation:
Calculation to determine how many feet from the boat is the parasailor
Based on the information given we would make use of Pythagorean theorem to determine how many feet from the boat is the parasailor using this formula
a²+b²=c²
First step is to plug in the formula by substituting the given value
500²+b²=800²
Second step is to evaluate the exponent
250,000+b²=640,000
Third step is to substract 250,000 from both side and simplify
250,000+b²-250,000=640,000-250,000
b²=390,000
Now let determine how many feet from the boat is the parasailor
Parasailor feet=√b²
Parasailor feet=√390,000
Parasailor feet=b=624.49
Parasailor feet=b=624.5 feet (Approximately)
Therefore how many feet from the boat is the parasailor will be 624.5 feet
how tall is the building in the picture shown
Answer: just figure out how many 8s are in 36 then multiply that by 66 :):)
Step-by-step explanation:
E B A G ord Теа F NOTE: Angles not necessarily drawn to scale.
help
Answer: x = 13
angel bge and angle agf are vertical meaning they’re equivalent
77 + 90 + x = 180 (180 because all of them added together are supplementary)
167 + x = 180
x = 13
Answer:
Step-by-step explanation:
X=13
YO PLEASE HELP, AREA OF A TRAPEZOID
which expression is equivalent to (4^2)(4^5)
Answer: Sorry I don't know the answer but I recommend an app that will help you is called Mathpapa is really helpful and have helped me get A on test and homework
Step-by-step explanation: is htis one https://www.mathpapa.com/algebra-calculator.html
A group of college students are going to a lake house for the weekend and plan on renting small cars and large cars to make the trip. Each small car can hold 4 people and each large car can hold 6 people. The students rented twice as many large cars as small cars, which altogether can hold 48 people. Graphically solve a system of equations in order to determine the number of small cars rented, x,x, and the number of large cars rented, yy.
Answer:
The students rented 3 small cars and 6 large cars.
Step-by-step explanation:
Since a group of college students are going to a lake house for the weekend and plan on renting small cars and large cars to make the trip, and each small car can hold 4 people and each large car can hold 6 people, and the students rented twice as many large cars as small cars, which altogether can hold 48 people, to determine the number of small cars rented, X, and the number of large cars rented, Y, the following calculation must be performed:
4X + 6Y = 48
4x4 + 6x8 = 16 + 48 = 64
4x3 + 6x6 = 12 + 36 = 48
Thus, the students rented 3 small cars and 6 large cars.
20. An airport, a factory, and a shopping center are at the vertices of a right triangle formed by three highways. The airport and factory are 6.0 miles apart. Their distances from the shopping center are 3.6 miles and 4.8 miles, respectively. A service road will be constructed from the shopping center to the highway that connects the airport and factory. What is the shortest possible length for the service road? Round to the nearest hundredth
A circular opening of an ice cream cone has a diameter of 23 centimeters. The height of the cone is 17 centimeters, what is the
volume of the cone?
round to hundredth decimals if necessary.
Answer:[tex]2355.31\ cm^3[/tex]
Step-by-step explanation:
Given
diameter of the cone is [tex]d=23\ cm\quad [r=\frac{d}{2}=11.5\ cm][/tex]
The height of the cone is [tex]h=17\ cm[/tex]
The volume of a cone is [tex]V=\dfrac{1}{3}\pi r^2h[/tex]
Insert the values
[tex]\Rightarrow V=\dfrac{1}{3}\times \dfrac{22}{7}\times 11.5^2\times 17=2355.309\\\\\Rightarrow V\approx 2355.31\ cm^3[/tex]
Thus, the volume of the cone is [tex]2355.31\ cm^3[/tex]
47. Brainliest will be given, need answer asap
Answer:
Look below.
Step-by-step explanation:
45. B
46. D
47. B
Answer:
45.A 46. Bike A 47.C
Step-by-step explanation:
You are going to install a 15-metre long fence. If the posts are 3 metres apart, how many fence posts will you need? Select the best way to demonstrate the answer to students
Answer : 6 fence posts. The best way to demonstrate the answer to students is to use the formula
Explanation: To install a 15-metre long fence, the posts are 3 metres apart, how many fence posts will you need? The best way to demonstrate the answer to students is to use the formula: Total number of posts = (Length of fence ÷ Distance between posts) + 1
Where;Length of the fence = 15 metres, Distance between posts = 3 metres
Total number of posts = (15 ÷ 3) + 1 Total number of posts = 5 + 1 = 6 Therefore, you will need 6 fence posts.
The best way to demonstrate the answer to students is to use the formula: Total number of posts = (Length of fence ÷ Distance between posts) + 1
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does someone know the answer?
Answer:
I think it is the last answer.
Step-by-step explanation:
There can only be one vertex.
Please show me step by step how to do this
Answer:
The next three terms of the sequence are 17, 21 and 25.
The 300th term of the sequence is 1197.
Step-by-step explanation:
The statement describes an arithmetic progression, which is defined by following formula:
[tex]p(n) = p_{1}+r\cdot (n-1)[/tex] (1)
Where:
[tex]p_{1}[/tex] - First element of the sequence.
[tex]r[/tex] - Progression rate.
[tex]n[/tex] - Index of the n-th element of the sequence.
[tex]p(n)[/tex] - n-th element of the series.
If we know that [tex]p_{1} = 1[/tex], [tex]n = 2[/tex] and [tex]p(n) = 5[/tex], then the progression rate is:
[tex]r = \frac{p(n)-p_{1}}{n-1}[/tex]
[tex]r = 4[/tex]
The set of elements of the series are described by [tex]p(n) = 1 + 4\cdot (n-1)[/tex].
Lastly, if we know that [tex]n = 300[/tex], then the 300th term of the sequence is:
[tex]p(n) = 1 + 4\cdot (n-1)[/tex]
[tex]p(n) = 1197[/tex]
And the next three terms of the sequence are:
n = 5
[tex]p(n) = 1 + 4\cdot (n-1)[/tex]
[tex]p(n) = 17[/tex]
n = 6
[tex]p(n) = 1 + 4\cdot (n-1)[/tex]
[tex]p(n) = 21[/tex]
n = 7
[tex]p(n) = 1 + 4\cdot (n-1)[/tex]
[tex]p(n) = 25[/tex]
The next three terms of the sequence are 17, 21 and 25.
The 300th term of the sequence is 1197.
a - 2/3 = 3/5 how much is a?
Answer:
its 1 4/5 or 19/15
they are both the same
Step-by-step explanation:
so first you need to find the same common factor
A-10/15=9/15
then add 10/15 and 9/15 to find a
19/15-10/15=9/15
or
1 4/15-2/3=3/5
yw :)
What is the surface area of this right rectangular prism with dimensions of 8 inches by 4 inches by 14 inches?
Answer:
400 inches
Step-by-step explanation:
Area of all sides and add them
Due soon !!!!!!!...
Answer:
50m^2
Step-by-step explanation:
Which describes the cross section of the square prism that passes through the vertices A, B, C, and D shown below?
A square prism. The front left points are labeled A and D. The back right points are labeled B and C.
a rectangle
a square
a kite
a trapezoid
Answer:
its not that i got it wrong
Step-by-step explanation:
The figure below is a net for a triangular pyramid.
If all the triangles are equilateral, what is the surface area of
the pyramid, in square centimeters?
Answer:
339.36 cm^2
Step-by-step explanation:
14*12.12=169.68
169.68/2=84.84
84.84= the area of one triangle
(84.84)4=339.36
I'm pretty sure, but check my math if it's wrong
what is the ratio of 12
12 to 1
is the ratio :)
120, 60, 30, 15, ...
8th term:
10th term:
Answer:
8th term would be .9375
10th term would be .234375
Step-by-step explanation:
Please help, GodBless.
Answer:
(A) seems to have the least amount of slope with a slope of -6, compred to all, its the least one.
Step-by-step explanation:
Follow slope formula
(y2-y1) / (x2-x1)
Or calculate using rise over run method
Angela bought a dress that cost $22.50. If the sales tax is 6.5%, how much tax did she pay? I need help with this one
If one of my angles is 130 degrees, what is the measure of the blue angle that is supplementary to it?
Step-by-step explanation:
[tex]180 - 130 = 50[/tex]
How to solve -3x+1<7
Answer:
x > − 2
Step-by-step explanation:
If your motive was to solve for x thats your answer, if not good luck!