Find the argument of the complex number z=1+iv3
Given:
The complex number is:
[tex]z=1+i\sqrt{3}[/tex]
To find:
The argument of the given complex number.
Solution:
If a complex number is [tex]z=x+iy[/tex], then the argument of the complex number is:
[tex]\theta=\tan^{-1}\dfrac{y}{x}[/tex]
We have,
[tex]z=1+i\sqrt{3}[/tex]
Here, [tex]x=1[/tex] and [tex]y=\sqrt{3}[/tex]. So, the argument of the given complex number is:
[tex]\theta =\tan^{-1}\dfrac{\sqrt{3}}{1}[/tex]
[tex]\theta =\tan^{-1}\sqrt{3}[/tex]
[tex]\theta =\tan^{-1}\left(\tan \dfrac{\pi}{3}\right)[/tex]
[tex]\theta =\dfrac{\pi}{3}[/tex]
Therefore, the argument of the given complex number is [tex]\theta =\dfrac{\pi}{3}[/tex].
Which is the solution for the system of equations? Y = 2x-3
Y = -x
A. (1, -1)
B. No solution
C. (-1, 1)
D. (-1, -1)
Answer:
(1,-1)
Step-by-step explanation:
[tex] \large{ \begin{cases} y = 2x - 3 \\ y = - x \end{cases}}[/tex]
Since both are y-isolated equation. We can combine both.
[tex] \large{2x - 3 = - x}[/tex]
Since we want to solve for x-term, we need to isolate x-term.
So we move from -x which is the right side to x.
[tex] \large{2x - 3 + x = 0} \\ \large{3x - 3 = 0} \\ \large{3x = 3} \\ \large{x = 1}[/tex]
But we are not done yet. Solving system of equations, you must solve for y-term as well. (Because we have to answer in ordered pairs which are (x, y))
Substitute x = 1 in any given equations but I will substitute x = 1 in y = -x
[tex] \large{y = - x} \\ \large{y = - 1}[/tex]
Since we have got y-value. Therefore the answer is (1,-1)
Math grade 9 ,I need the answer fassstt
Answer:
Step-by-step explanation:
i dont know sorry
Answer:
a) section c
b) at a constant rate
c) below
A. 3m/s^2
B. 0 m/s^2
C. -3m/s^2
D. 1 m/s^2
Step-by-step explanation:
a) This graph models the change in velocity of time. Since when the velocity decreases over time, the acceleration is negative. This relationship is modeled in the interval from the 9th to 11th seconds which is section c.
b) If the graph is flat, it means the car is traveling at the same amount of meters per second. This means the car is traveling at a constant rate during section b.
c) During section A, the velocity in second 0 to second 4 increases by 12m/s. So, the acceleration is 3m/s^2. This is identical to finding the slope.
During section B, the velocity does not change at all, so the acceleration(and slope) is 0 m/s^2
During section C, over 2 seconds, from 9 to 11, the velocity goes from 12 m/s to 6 m/s, which is a change of -6 m/s. Therefore, the acceleration is -3m/s^2
During section D, over a span of 4 seconds(11 - 15), the velocity changes from 6 m/s to 10 m/s. That means a change of 4 m/s and the acceleration would be 1 m/s^2.
Only answer if you’re sure, will give Brainly :) thank you
Help me out! I’ll give Brainly :) thank you!!
Answer:
f(5) = 15
Step-by-step explanation:
To evaluate f(5) substitute x = 5 into f(x) , that is
f(5) = 5² - 2(5) = 25 - 10 = 15
juan creates a new recipe for brownies. For each pan of brownies, he adds 7 dashes of cinnamon. How many dashes of cinnamon will he use for 8 pans of brownies?
Answer:
56 dashes of cinnamon
Step-by-step explanation:
7 dashes of cinnamon = 1 pan of brownies
And we need to make 8 pans of brownies so...
7 dashes of cinnamon x 8 pans of brownies = 56 total dashes of cinnamon :)
What is the sum of the first ten terms in a geometric series
with a1=
6 and r = 2?
Answer:
[tex]S_{10} = 682[/tex]
Step-by-step explanation:
Given
[tex]a_1 = 6; r = 2[/tex]
Required
[tex]S_{10[/tex]
This is calculated as:
[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex]
So, we have:
[tex]S_{10} = \frac{6 * (2^{10} - 1)}{10 - 1}[/tex]
[tex]S_{10} = \frac{6 * (1024- 1)}{9}[/tex]
[tex]S_{10} = \frac{6 * 1023}{9}[/tex]
[tex]S_{10} = 682[/tex]
If x = 3 cm and z = 5 cm, what is the length of y?
A.
3 cm
B.
0.5 cm
C.
4 cm
D.
5 cm
A researcher wishes to test whether the mean of a normally distributed population is greater than 1.06 at the 5% significance level. Based upon 22 independent observations, she observes a sample mean of 1.77 and a sample standard deviation of 0.84. Determine the critical value of the test rounded to the nearest hundredth. (Rounding counts!).
Answer:
t- critical value =1.721
Step-by-step explanation:
Given
Sample size =n=22
Degree of freedom = sample size -1 = 22-1 =21
The significance level is 5%. This indicates that the test is right tailed.
The alpha value = 0.05
For given right tailed test, with value of alpha = 0.05 and degree of freedom = 21, the t- critical value =1.721
5. What is the value of 8 in the unit circle below?
30°
600
b.
45°
d.
90°
9514 1404 393
Answer:
θ = 60°
Step-by-step explanation:
The angle is more than 45° and less than 90°. The only viable choice is ...
θ = 60°
__
We can only read the x-coordinate of the point on the terminal ray. It is 1/2, which is the cosine of 60°. The angle must be 60°.
2x^2-13=x Write the quadratic equation in standard form:
Answer:
2xˆ2-x-13=0
Step-by-step explanation:
Answer:
Below.
Step-by-step explanation:
2x^2 - 13 = x
Subtract x from both sides:
2x^2 - x - 13 = 0 is the standard form.
A bottle of mayonnaise holds 500ml. How many litres is this?
Convert x=-3 to polar equation
Draw the image of figure RSTU after a translation 2 units left and 2 units down and a reflection across the y-axis.
Answer:Just slide it to the left and 2 units down then plot the points Step-by-step explanation:
Answer:
Step-by-step explanation:
Slide it to the left and 2 units down
Who can do this I confused except for number 1
Find the Area of the figure below, composed of a rectangle with a semicircle
removed from it. Round to the nearest tenths place.
Answer:
Area of the figure = 25.7 units²
Step-by-step explanation:
Area of the given figure = Area of rectangle ABCD - Area of the semicircle with diameter CD
Area of the rectangle ABCD = Length × Width
= BC × AB
= 8 × 4
= 32 units²
Area of the semicircle = [tex]\frac{1}{2}\pi r^{2}[/tex]
Here, r = radius of the semicircle
r = [tex]\frac{\text{Diameter}}{2}[/tex]
r = [tex]\frac{1}{2}(CD)[/tex]
r = [tex]\frac{4}{2}[/tex]
r = 2 units
Therefore, area of the semicircle = [tex]\frac{1}{2}\pi (2)^2[/tex]
= 2π
= 6.28 units²
Area of the given figure = 32 - 6.28
= 25.72 units²
≈ 25.7 units²
Please helppppppppppppppppppp
Answer:
50 feet
Step-by-step explanation:
Perimeter is the sum of all of the lengths of the sides.
A triangle has three sides, and three lengths are given, therefore all the sides are given.
The sum of the sides is 20 + 20 + 10 = 50
So the Perimeter is 50 feet
Answer:50
Step-by-step explanation:20+20+10=50
Una persona compra borregos, cabras y puercos jabalí. Son 100 animales vivos en total y paga $100 mil pesos. Cada borrego costó $500 pesos, tres cabras cuestan $4000 y cada puerco jabalí $3500.
Si denotamos con la variable xel número de borregos comprados por la persona, con y el número de cabras y con z el número de puercos jabalí, escribe las ecuaciones que representan las relaciones entre x,y,zde acuerdo a la información proporcionada.
Answer:
I'm sorry I just need points
Step-by-step explanation:
Help Plis....................
Answer:
1.30
2. 0 im pretty sure
Step-by-step explanation:
if im wong sry
It is known that screws produced by a certain company will be defective with probability 0.01, independently of each other. The company sells the screws in packages of 10 and offers a money-back guarantee that at most 1 of 10 screws are defective. That is, the package would have to be replaced if greater or equal to 2 screws are defective. What proportion of packages sold must the company replace
Answer:
The company must replace 0.0042 = 0.42% of packages.
Step-by-step explanation:
For each screw, there are only two possible outcomes. Either it is defective, or it is not. The probability of an screw being defective is independent of any other screw. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
It is known that screws produced by a certain company will be defective with probability 0.01.
This means that [tex]p = 0.01[/tex]
The company sells the screws in packages of 10
This means that [tex]n = 10[/tex]
That is, the package would have to be replaced if greater or equal to 2 screws are defective. What proportion of packages sold must the company replace?
This is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which:
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.01)^{0}.(0.99)^{10} = 0.9044[/tex]
[tex]P(X = 1) = C_{10,1}.(0.01)^{1}.(0.99)^{9} = 0.0914[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.9044 + 0.0414 = 0.9958[/tex]
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.9958 = 0.0042[/tex]
The company must replace 0.0042 = 0.42% of packages.
At a local bodega, the cost of a banana at the corner store is $1.50, and the cost of a
bottle of soda is $1.20. What would it cost to get 5 bananas and 2 bottles of soda?
What would it cost to get x bananas and y bottles of soda?
Answer:
$7.5
Step-by-step explanation:
4 bottles cost = $5
Then 1 bottle costs:
$5/4 = $1.25
Then 6 bottles cost:
$1.25*6 = $7.5
Based on the figure below, what is the value of x? (look at picture \/)
Answer:
X = 9
Step-by-step explanation:
90 - ( 30 + 15 ) = 45
45/5 = 9
Gordon types 2,508 words in 38 minutes. Find the unit rate. Gordon types words per minute.
Answer:
66 words per minute
Step-by-step explanation:
In 38 minutes , words that can be typed by Gordon = 2508 words
In 1 minute, words that can be typed by Gordon = 2508/38
= 66 words
Therefore Gordon types 66 words per minute.
hope it helps :)
Answer:
66
Step-by-step explanation:
To find the unit rate you would need to find how many words Gordon can type in one minute. To do that, all you need to do is divide 2,508 by 38 (which would get you 66 words). If you set up a proportion to solve this it would look somewhat like 2,508/28 = 66/1.
~ ~
I needd help pleaseeeee
Correct answer will be marked brainliest
find the value of x
4x + 2 = 8
Answer: x = 6/4
Step-by-step explanation:
4x + 2 = 8
4x = 6
x = 6/4 or 1 1/2
Hope this helped :)
Answer:
x = 1.5, 1 1/2
Step-by-step explanation:
4x + 2 = 8
4x = 6
4x/4 = 6/4
x = 1.5
1.5 = 1 1/2
Have a nice day! :-)
I WILL GIVE BRAINLIEST IF YOU HELP
A museum has an aquarium in the shape of a right rectangular prism that is 22.9 meters long, 7.5 meters wide, and 5.6 meters high. What is the volume, round to the nearest cubic meter, of the aquarium?
A. 280
B. 623
C. 1288
D. 962
Answer:
D. 962
Step-by-step explanation:
The volume of a rectangular prism is the length x width x height.
22.9*7.5*5.6=961.8
961.8 rounds up to 962
is 2/5 greater than 3/7
Answer:
3/7 is greater than 2/5
Step-by-step explanation:
If you convert the fractions into decimals:
3/7=0.42
2/5=0.4
0.42 is greater than 0.4
Here is the next one jaded :))
Answer:
x = 5.56
Step-by-step explanation:
Sin(17) = [tex]\frac{x}{19}[/tex]
=> Isolate the "x"
Sin(17) * 19 = x
5.56 = x
Hope this helps!
These triangles are:
A) congruent,
B) similar or
C) neither
Answer:
there is no photo
Step-by-step explanation:
Complete the function table for each equation
Answer:
y=-32, 0, -16, -4, 16
Step-by-step explanation:
y=4(-6)-8= -32
y=4(2)-8 = 0
y=4(-2)-8 = -16
y=4(1) -8 = -4
y=4(6) -8= 16
For the given equation of the line, the complete table is attached below.
Use the concept of the equation of line defined as:
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.
The given equation of a line is,
y = 4x - x
To complete the table:
Put x = -6 in this equation,
y = (-4)(-6) - 8
y = 16
Put x = 2 in the equation,
y = (-4)(2) - 8
y = -16
Put x = -2 in the equation,
y = (-4)(-2) - 8
y = 0
Put x = 1 in the equation,
y = (-4)(1) - 8
y = -12
Put x = 6 in the equation,
y = (-4)(6) - 8
y = -32
The complete table is attached below.
To learn more about the equation of line visit:
brainly.com/question/18831322
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