Answer:
- 4 + 4√3 i, where a = -4 & b = 4√3
Step-by-step explanation:
z = 8 cis(2π/3)
z = 8 [cos(2π/3) + i sin(2π/3) ]
z = 8 [cos(π - π/3) + i sin(π - π/3)]
z = 8 [ - cosπ/3 + i sin(π/3)]
z = 8[ - 1/2 + i √3/2 ]
z = - 4 + 4√3 i [in a + bi form]
Note that: cis x = cosx + i sinx
Answer:
[tex]a + bi = - 4 + 4 \sqrt{3} i[/tex]
Step-by-step explanation:
we are given [tex]\displaystyle cis(\dfrac{2\pi}{3})[/tex]
recall complex number trigonometric form:
[tex] \displaystyle \: r( \cos( \theta) + i \sin( \theta) )[/tex]
we are already given that [tex]\theta=\dfrac{2\pi}{3}[/tex]
recall complex number rectangular form
[tex] \displaystyle \: a + bi[/tex]
where [tex]\displaystyle a=r\cos(\theta)\: and\: b=r\sin(\theta)[/tex]
let's work with a:
substitute the value of [tex]\theta[/tex] and r
[tex] \displaystyle \: a = 8 \times \cos( \frac{2\pi}{ 3} ) [/tex]
recall unit circle
so [tex]\cos(\dfrac{2\pi}{3})[/tex] should be in Q:II
[tex] \displaystyle \: a = 8 \times - \frac{1}{2} [/tex]
simplify multiplication:
[tex] \displaystyle \: a = - 4[/tex]
let's work with b:
substitute the value of [tex]\theta[/tex] and r:
[tex] \displaystyle \: b = 8\sin( \frac{3\pi}{2} ) [/tex]
recall unit circle so [tex]\sin(\dfrac{3\pi}{2})[/tex] should be in Q:II
[tex] \displaystyle \: b = 8 \times \frac{ \sqrt{3} }{2} [/tex]
simplify:
[tex] \displaystyle \: b = 4 \sqrt{3} [/tex]
so
[tex] \displaystyle \: b i= 4 \sqrt{3} i[/tex]
hence,
[tex]a + bi = - 4 + 4 \sqrt{3} i[/tex]
PLZ HELP I WILL MARK BRIANLIST Complete the table for 11, 15, and 19 days. Input your
answers. Then click done.
Number of Days
Total Number of
Trophies Won
80
slope
3
100 trophies
4 days
25 trophies
1 day
7
180
11
15
19
DONE
Answer:
275, 375, 475
Step-by-step explanation:
First, find the slope using the two pairs of values given.
Number of days = x
Total number of trophies = y
Using (3, 80) and (7, 180),
Slope = ∆y/∆x = (180 - 80)/(7 - 3) = 100/4 = 25
Slope/unit rate = 25 trophies per day
Multiply 25 by each given number of days to get each corresponding total number of trophies won.
Thus:
✔️Number of days = 11
Total number of trophies won = 11*25 = 275
✔️Number of days = 15
Total number of trophies won = 15*25 = 375
✔️Number of days = 19
Total number of trophies won = 19*25 = 475
Answer:
280
380
480
Step-by-step explanation:
If he gets 100 trophies every 4 days then you just add 100 to each column because in each one the days are increasing by 4
Your welcome ;)
Plzzzz help me thxs !!!
Answer:
b) 2 (x - 4) = 6x
Step-by-step explanation:
equation:
⇒ 2 (x - 4) = 6x
use distributive property:
⇒ 2 (x - 4) = 6x
⇒ 2x - 8 = 6x
subtract x from both sides:
⇒ 2x - 2x - 8 = 6x - 2x
⇒ -8 = 4x
divide both sides by 4:
⇒ [tex]\frac{-8}{4} = \frac{4x}{4}[/tex]
⇒ -2 = x
to check, substitute -2 for x: answer should be the same
2 (x - 4) = 6x
2 (-2 - 4) = 6 x -2
-4 - 8 = -12
-12 = -12
Answer:
i got A and B.
Step-by-step explanation:
for a, subtract 6 from both sides and your new equation should be 2x=-4
the divide -4 by 2 which is -2
for b, you multiply 2 by each number in the parenthesis so your new equation should be 2x-8=6x. then subtract 2x from 6x and get 4x then divide -8 by 4 to get -2. im 100% sure abt A but i was a little confused on B good luck tho
NEED MAJOR HELP PLEASE
Answer:
∠ BDC = 30°
Step-by-step explanation:
The angle on the circle is half the measure of the central angle subtended by the arc BC
∠ BDC = [tex]\frac{1}{2}[/tex] × 60° = 30°
w
What is the value of a?
4
5 units
C
Os units
O 6 units
O 7 units
Answer:
B.5 1/3
Step-by-step explanation:
got it right on edge
The value of a from the given triangle is [tex]5\frac{1}{3}[/tex] units. Therefore, option B is the correct answer.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
From the triangle we have WX=b, WZ=c, ZY=3, YX=a and WY=4.
By Pythagoras theorem,
c²=4²+3²
c²=16+9
c²=25
c=5 units
In triangle WXZ,
(3+a)²=5²+b² ----(i)
From the triangle WXY,
b²=4²+a² ------(ii)
From equation (i) and (ii), we get
(3+a)²=5²+4²+a²
9+6a+a²=41+a²
6a=32
a=32/6
a=[tex]5\frac{1}{3}[/tex] units
Therefore, option B is the correct answer.
To learn more about the Pythagoras theorem visit:
brainly.com/question/21926466.
#SPJ7
PLEASE I NEED HELP CLICK ON THIS IMAGE
Answer:
14 and 15
Step-by-step explanation:
A petri dish is a small, shallow dish of thin glass or plastic, used especially for cultures in bacteriology. A 2-inch-radius petri dish, containing nutrients upon which bacteria can multiply, is smeared with a uniform suspension of bacteria. Subsequently, spots indicating colonies of bacteria appear. The distance of the center of the first spot to appear from the center of the petri dish is a variable with density curve y= x/2 for 0 < x <2 and y=0 otherwise.
a. Graph the density curve of this variable.
b. Show that the area under this density curve to the left of any number x between 0 and 2 equals x2/4.
c. What percentage of the time is the distance of the center of the first spot to appear from the center of the petri dish
1. at most 1 inch?
2. between 0.25 inch and 1.5 inches?
3. more than 0.75 inch?
Answer:
a) attached below
b) Area = 1/2 ( base ) (height )
= 1/2 ( x ) ( x/2)
= x^2 / 4
C) i)25% ii) 54.69% iii) 85.94%
Step-by-step explanation:
Given density curve y = x/2 for 0 < x < 2 and y = 0
a) Graph the density curve of this variable
attached below
b) show that the area under the density curve to the left of any number x between 0 and 2 equals x^2/4
base of triangle = x
height = x/2
Hence to show the area under the density curve is equal to x^2/4 we will calculate the area to the left
Area = 1/2 ( base ) (height )
= 1/2 ( x ) ( x/2)
= x^2 / 4
c) Determine the percentage of the time of the distance of the center of the first spot to appear from the center of the petri dish
i) At most 1 inch
(area to the left of 1 ) = 1^2 / 4
= 1/4 = 0.25 ≈ 25%
ii) between 0.25 inch and 1.5 inches?
( area between 0.25 and 1.5 ) = ( area to the left of 1.5 ) - ( Area to the left of 0.25 )
= (1.5^2 / 4 )- ( 0.25^2 / 4 )
= 0.5469 = 54.69%
iii) more than 0.75 inch
( Area to the right of 0.75 ) = 1 - (0.75^ / 4)
= 0.8594 = 85.94 %
y =|x −3|+|x +2|−|x −5|, if x >5
Answer: maybe -1
Step-by-step explanation:
18 is ______percent of 40
Answer:
18 is 45% of 40
Step-by-step explanation:
Kennedy lives in the middle of the city. Her friend Zoe lives 8 miles to the west and her friend Shiloh lives 6 miles to the south. Approximately how far apart do Zoe and Shiloh live from each other?
Answer:
i would say about 16 miles.
Answer:
Step-by-step explanation:
Draw a picture. The lines between their houses forms a right triangle. Kennedy is at the 90°. The distance between Shiloh and Zoe is the hypotenuse of the triangle, so use the Pythagorean Theorem.
Distance² = 8² + 6² = 100
Distance = √100 = 10 miles
The table shows the prices for the same cereal, sold in different weights. Which size box is the best buy, in terms of price per ounce?
A. 9 oz
B.18 oz
C.28 oz
D.38 oz
Answer:
c
Step-by-step explanation:
ESPERO TE A YDUE :)
help me someone please
plssss help im stuck and this is worth 20 percent
Answer:
Percentile 2020 Percent Change
18% $4,480.43 30.8%
19% $5,378.37 24.0%
20% $6,368.35 24.3%
21% $7,363.47 22.4%
Step-by-step explanation:
Is 60.560 an irrational number or rational?
Answer: ratinal?
Step-by-step explanation:
What is the volume to the nearest thousandth? Does anyone know
4
Multiplying a number by and then dividing by is the same as doing what to the
number?
А
Dividing by 4
B
Multiplying by 2
С
Multiplying by 2
D
Dividing by 5
E
Multiplying by 5
Find the measure of an angle whose supplement measures two times its measure
Answer:
first angle = 60
second angle = 120
Step-by-step explanation:
Let the first angle x
Let the second angle = 2x
x + 2x = 180 Supplementary angles = 180 degrees
3x = 180 Divide by 3
3x/3 = 180/3
x = 60
2x = 120
1. Which fraction is equivalent to a repeating decimal? A. 2/6 B. 34 C. 9/12 D. 78
Answer:
Answer is A. 2/6
Step-by-step explanation:
Hope this helps! :)
Tayler works at a bicycle shop. When he sells a bicycle, he earns 6% of the sale price as a commission. One day Tayler sold 1 bicycle for $125 and 2 bicycles for $75 each. What was the total amount of commission he earned?
Please let me know asap
Answer:
100
Step-by-step explanation:
Hello There!
∠4 and ∠8 are corresponding angles
corresponding angles are congruent so if ∠4 = 100 then ∠8 also equals 100
What is the value of the expression below when a = 5?
9a - 7 + 6
Answer:
44
Step-by-step explanation:
Hello There!
To solve this one all we have to do is plug in 5 for a
so
9(5)-7+6
9x4=45
45-7=38
38+6=44
so when a=5 the value of the expression is 44
2. Which of these is a combination problem?
How many different ways can a manager review 3 out of 5 employees if he reviews them in a specific order?
In how many different ways can Maria choose 5 roses from a bunch of 10 roses.
How many license plates can be formed with the digits 3, 2, 7, 0?
How many different ways can the letters in the word 'seven' be arranged?
THAT SHOULD BE THE ANSWER
Ambitious
268 answers
76.4K people helped
This is a fundamental counting principle problem and can be solved by multiplying the number of choices you have for each digit of the license plate.
For the first digit you can choose from the numbers 0,1,2...,9 or 10 choices.
Now the next 5 digits will all be letters all being different.. recall there are 26 letters in the alphabet.. for our second digit we have 26 choices, for our third digit we have 25 choices(because we already used one of the 26 letters and we can't repeat), for our fourth digit we have 24 choices.... and well I'm sure you are catching on by now...
Here is what the whole calculation looks like:
10(26)(25)(24)(23)(22) = 78,936,000
Step-by-step explanation:
Answer:
The answer should be the one with roses
Step-by-step explanation:
What ordered pairs are the solutions of the system of equations shown in the graph below?
Answer:
(-3,1) and (-8,6)
Step-by-step explanation:
Hey gabymcarrillo!
The solution is always the place where the two lines intersect.
Our first answer: go 3 left on the x- axis, and then go 1 up on the y- axis. This results in (-3,1)
Our second answer: go 8 left on the x- axis, then go 6 up on the y- axis. This results in (-8,6)
Hope a helped, have a nice day!
-Aadi x
Please help me. I need help
Ms. Cathy bought a package of pens. Out of every 10 , pens, 7 are black. If there are 20 pens in the pack, what fraction of the pens in the pack are black? What percent of the pens in the pack are black? What fraction of the Owens in the pack is black?
Answer:
Step-by-step explanation:
7/10 are black therefore 14/20 are black
The cost of 7 pounds of berries is $16.38, what is the cost per pound of
Berries?
Answer:
2.34
Hope that helps!
Help please someone
What is 2/5 + 3/10 + 1/2?
The answer will be 1 and 1/5
I attached the work in the picture!
A line with a slope of 0 passes through the point (9,5). What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
if the slope is 0, it is horizontal. and remember, m is the slope. (0)
Step-by-step explanation:
x is 9, y is 5.
slope intercept form is y=mx+b, so you plug in the numbers.
5= 0*9+5
or, 5=5
Helppppp !!!!!!
During a 20 kilometer hike, Deana consumed 3 3/4 quarts of water.
What was Deana's average water consumption in quarts per kilometer?
Answer:
16.7
Step-by-step explanation:
The amount of water consumed is 334 quarts
The distance is 20km
Therefore the average water consumption can be calculated as follows
= 334/20
= 16.7
Hence the consumption rate is 16.7 quarts/km
At Brett's Swimwear, 9 out of the 45 styles at the store are bikinis. What percentage of
swimsuit styles at the store are bikinis?
Answer:
20%
Step-by-step explanation: