By using Euler's notation, we will see that:
z^7 = 78,125*e^(-i*4.48)
How to get z^7?
We know that:
z = 4 - 3i
Remember that for a complex number:
w = a + bi
In Euler's notation, we can write this as:
w = √(a^2 + b^2)*e^(i*Atan(b/a))
Then, for z, we will get:
z = √(4^2 + (-3)^2)*e^(i*Atan(-3/4))
z = 5*e^(-i*0.64)
Now, if we apply an exponent of 7 to this number, we will get:
z^7 = ( 5*e^(-i*0.64))^7
z^7 = 5^7*e^(-i*7*0.64) = 78,125*e^(-i*4.48)
If you want to learn more about complex numbers, you can read:
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The length of a rectangle is 2ft longer than it’s width. If the perimeter of the rectangle is 32 ft, find it’s area
Answer:
Area of rectangle is 63 feet²Step-by-step explanation:
Given:
The length of a rectangle is 2ft longer than it’s width. If the perimeter of the rectangle is 32 ftTo Find:
Area of the rectangle.Solution:
Let's assume Width of rectangle be x feet and length be 2 +x. to Find the are of the rectangle firstly we need to the length and width of the Rectangle:
Using formula:
Perimeter of rectangle = 2(L + B)→ 32 = 2(x + 2 + x)
→ 32 = 2(2x + 2)
→ 32 = 4x + 4
→ 32 - 4 = 4x
→ 28 = 4x
→ 28/4 = x
→ 7 = x
Hence,
Length of the rectangle = 2 + x = 9 feetWidth of the rectangle = x = 7 feet.Now,
→ Area of rectangle = Length × Width
→ Area fo rectangle = 9 × 7
→ Area of rectangle = 63 feet²
Hence, Area of the rectangle is 63 feet²Answer:
63 sq.ft⠀
Step-by-step explanation:
⠀
As it is given that, the length of a rectangle is 2ft longer than it’s width and perimeter of the rectangle is 32 ft.⠀
So, let us assume the width of the rectangle as w ft and therefore the length will (w + 2) ft .
⠀
Now,
⠀
[tex]{\longrightarrow \qquad{ {{\boldsymbol {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad {\rm{2(w + 2 + {w})= 32 \ }}}[/tex]
⠀
[tex]{\longrightarrow \qquad {\rm 2({2w + 2= 32 ) }}}[/tex]
⠀
[tex]{\longrightarrow \qquad {\rm{4w +4= 32 \ }}}[/tex]
⠀
[tex]{\longrightarrow \qquad {\rm{4w = 28\ }}}[/tex]
⠀
[tex]{\longrightarrow \qquad {\rm{w = \dfrac{28}{4} }}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ \mathfrak{{\pmb{w = 7 }}}}}[/tex]
⠀
Therefore width of the rectangle is 7 ft .⠀
Now, We are to find the length of the rectangle:
[tex]{\longrightarrow \qquad{ {{\rm{Length = w + 2 }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ {{ \rm{Length = 7 + 2 }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ { \frak{ \pmb{Length = 9}}}}}[/tex]
⠀
Now, we are to find the area of the rectangle :
⠀
[tex]{\longrightarrow \qquad{ {{\boldsymbol{ Area_{(Rectangle)} = Length \times Breadth }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ {{ \rm{ Area_{(Rectangle)} = 9 \times 7 }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ { \pmb{\boldsymbol{ Area_{(Rectangle)} = 63 }}}}}[/tex]
⠀
Therefore,
The area of the rectangle is 63 ft².⠀
The square of a difference of numbers is the different of their squares?
Always true
Sometimes true
Never true
Answer:
Sometimes true
Step-by-step explanation:
This is only true for the numbers 0 and 1 because 0 squared is 0 and 1 squared is 1 making the different of their squares 1 and the difference of the numbers also 1.
For every other number combo this is untrue.
Shayla and Carlos each have a bag that contains five green marbles five red marbles and 10 yellow marbles the marvels are all the same size and shape which expression represents the probability that Shayla will select two red marbles
The probability that Shayla will select two red marbles from the bag is 1/16.
What is the probability?Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that Shayla will select two red marbles = (number of red marbles / total number of marbles) x (number of red marbles / total number of marbles)
5/20 x 5/20 = 1/16
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Gabrielle used 7 1/5 inches each of 6 different colors of embroidery floss to make one friendship bracelet. Each package of floss contains 12 feet. How many friendship bracelets can Gabrielle make if she has one package of each color?
The number of friendship bracelets Gabrielle can make is 20 bracelet
Conversion of feet to inches1 feet = 12 inches
12 feet = 144 inches
Number of colors of floss = 6
Quantity of each floss = 12 feet = 144 inches
Total quantity of floss = 6 × 144
= 864 inches
Quantity of each floss used for bracelet = 7 1/5 inches
Total floss used for each bracelet = 6 × 7 1/5
= 6 × 7.2
= 43.2 inches
Number of bracelet Gabrielle can make = Total quantity of floss ÷ Total floss used for each bracelet
= 864 ÷ 43.2
= 20 bracelet
Learn more about conversion of feet to inches:
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Help me the question 1 in my picture
Answer:
Number 1 is b
I found the answer on a website
Unit 10: Circles Homework 4: Inscribed Angles
Find each angle measure
Answer:
6. ∠GHJ ≅ ∠GIJ = 73°
10. ∠Q = 89°, ∠R = 123°, ∠S = 91°
Step-by-step explanation:
The relations applicable to these problems are ...
the measure of an inscribed angle is half the measure of the intercepted arcthe sum of the arc measures in a circle is 360°Opposite angles of an inscribed quadrilateral intercept arcs that total 360°, so those opposite angles must total 360°/2 = 180°.
__
6.The missing arc measure GJ is ...
68° +31° +115° +GJ = 360°
GJ = 360° -214° = 146°
Both of inscribed angles GHJ and GIJ intercept arc GJ, so both will have measure ...
∠GHJ ≅ ∠GIJ = 146°/2 = 73°
__
8.∠Q intercepts arc PSR, which is shown as ...
arc PSR = arc PS +arc SR
arc PSR = 137° +41° = 178°
The measure of angle Q is half this:
∠Q = (1/2)×arc PSR = 178°/2 = 89°
__
∠R is opposite ∠P in the inscribed quadrilateral, so is supplementary to it:
∠R = 180° -57° = 123°
__
∠S is opposite ∠Q in the inscribed quadrilateral, so is supplementary to it:
∠S = 180° -89° = 91°
Answer quickly please !!
Answer: 65 degrees
Using the property of vertical angles, the measurement of angle x is going to be 65 degrees.
Single angle x is directly opposite of the 65° angle given, we can figure out what angle x will be as they will be congruent.
By using the Vertical Angle Theorem, we can say
--> x = 65
Definition of Vertical Angle Theorem: states that the opposite (vertical) angles of two intersecting lines are congruent.
Question 1 of 10
Is the graph a linear function, nonlinear function, or relation?
AY
O A. Nonlinear function
OB. Relation
C. Linear function
PREVIOUS
Answer:
A. Nonlinear function
Step-by-step explanation:
It is not a linear function because :-
You cannot write an equation because change in y-value for every x-value is not consistentIt cannot be relation as there is no correlation between the x and y values in the graphIt is a nonlinear function20 POINTS!!!
If A varies directly as B and inversely as C and when A = 6, B = 10 and C = 15. Calculate C when A = 92 and B= 107
Answer:
C = [tex]\frac{963}{92}[/tex]
Step-by-step explanation:
given A varies directly as B and inversely as C then the equation relating them is
A = [tex]\frac{kB}{C}[/tex] ← k is the constant of variation
to find k use the condition A = 6 , B = 10 , C = 15 , then
6 = [tex]\frac{x10k}{15}[/tex] ( multiply both sides by 15 )
90 = 10k ( divide both sides by 10 )
9 = k
A = [tex]\frac{9B}{C}[/tex] ← equation of variation
when A = 92 and B = 107 , then
92 = [tex]\frac{9(107)}{C}[/tex] ( multiply both sides by C )
92C = 963 ( divide both sides by 92 )
C = [tex]\frac{963}{92}[/tex]
Answer:
C = 963/92
Step-by-step explanation:
Given :
A ∝ BA ∝ 1/CFinding the constant of variation, k
A = kB/C6 = k(10)/(15) [Given in 1st part of question]6 = 2k/3 2k = 18k = 9Finding C
Using the same equation, and new values of A and B, we can find CA = kB/CC = kB/AC = 9 x 107 / 92C = 963/92What is the first term of the arithmetic series?
a1 =
143
⇒ 8
What is the 20th term of the arithmetic series?
a20 =
⇒ 46
How many stitches are in the first 20 rows of the shawl?
⇒ 540 stitches
I don't think this is wrong
Given vectors
ā=(-1,-2), b=(-2,3), C = 3,-1),d =(-3,2)
find the dot product of b and c.
3
0-3
09
0-9
Answer:
-9
Step-by-step explanation:
b={-2,3)
c=(3,-1)
dot product b.c
=(-2×3) + (3×-1)
=-6+(-3)
=-6-3
=-9
What is the value if X? and how to find exterior angles.
Pleade god help me find a person that is sweet enough to help me thank you to anyone who will help me
Answer:
I will help you.
but first what is the problem
give brainliest
Answer:
Help you with what??
whats the question????
Allen was making trail mix, but he only wanted to make of the recipe. If the whole recipe called for of a cup of peanuts, how many cups will he need to make of the recipe? Choose the model that matches the situation.
It can be inferred that the amount of nuts that Allen requires depends on the amount of the recipe that he wants to make.
How many cups of nuts does Allen require to make the recipe?According to the information provided, one serving of the recipe calls for one cup of nuts. According to this, it can be inferred that to make a smaller or larger portion of the recipe, this amount must be divided or multiplied.
For example, if Allen calls for making two servings of the recipe, he would use two cups of nuts, while if he calls for making a half serving, he would use half a cup of nuts.
Note: The question is missing because there is some missing information. However I can answer it based on my general prior knowledge.
Learn more about recipes in: https://brainly.com/question/1320828
Answer:
1/6
Step-by-step explanation:
A motorcycle travels 20 miles west and then turns and goes 52° north of west another 38 miles. How far is the motorcycle from its starting point? Round to the nearest tenth.
Answer:52.7
Step-by-step explanation:
1) Find the angle inside the triangle by subtracting 52 from 180 getting you 128
2)Then we input everything into the law of cosines
4² - 5² × 2³ what is the value of the expression.
[tex]4 {}^{2} - 5 {}^{2} \times 2 {}^{3} [/tex]
[tex]16 - 25 \times 8[/tex]
[tex]16 - 200[/tex]
[tex] - 184[/tex]
Hello!
Let's evaluate this expression.
4²-5²×2³
4²=16
16-5²×2³
5²=25
16-25×2³
2³=8
16-25×8
According to PEMDAS, the next operation is multiplication (M)
16-200
Subtract:
-184
Hence, the simplified expression is equal to
[tex]\boxed{\boxed{\bold{-184}}}[/tex]
Hope everything is clear.
Let me know if you have any questions!
#KeepLearning
:-)
Answer this frequency distribution Question. I will make Brainelist + 50 points
Answer:
(i) 41-45 mins
(ii) 40 mins
(iii) 75 workers
(iv) Rs10500
Step-by-step explanation:
(i) The modal class is the class with the highest frequency.
Therefore, from inspection of the frequency table, the modal class is 41-45 mins since if has the highest frequency of 14.
(ii) As the data is grouped, to find an estimate of the mean, assume that every worker takes the value of the class mid-point. As the data is discrete, there are gaps between the classes, and so we also have to use lower and upper class boundaries to calculate the mid-points.
Class 21-25 : lower 20.5 | upper 25.5 | mid-point 23
Class 26-30 : lower 25.5 | upper 30.5 | mid-point 28
Class 31-35 : lower 30.5 | upper 35.5 | mid-point 33
Class 36-40 : lower 35.5 | upper 40.5 | mid-point 38
Class 41-45 : lower 40.5 | upper 45.5 | mid-point 43
Class 46-50 : lower 45.5 | upper 50.5 | mid-point 48
Class 51-55 : lower 50.5 | upper 55.5 | mid-point 53
Class 56-60 : lower 55.5 | upper 60.5 | mid-point 58
Mean = (sum of frequency x class mid-point) ÷ total frequency
⇒ Mean = (2 x 23 + 5 x 28 + 7 x 33 + 10 x 38 + 14 x 43 + 8 x 48 + 3 x 53 + 1 x 58) ÷ 50
⇒ Mean = 40 mins
(iii) 8 hours = 8 x 60 = 480 mins
Total time ÷ average time to make one doll = 480 ÷ 40 = 12
If the mean time to make a doll is 40 minutes, then one person can make 12 dolls in 8 hours.
Therefore, to calculate the number of workers required to make 900 dolls in 8 hours, divide the total number of dolls needed by 12:
900 ÷ 12 = 75
So 75 workers will be needed to make 900 dolls in 8 hours, given the mean time for a worker to make a doll is 40 mins.
(iv) Overtime is paid in excess of 6 hours. Therefore, each worker will be working 2 hours overtime.
Total amount of overtime pay = hours x rate x workers
= 2 x Rs70 x 75
= Rs10500
What is a polygonal curve
Answer: It is a connected series of line segments such as the image shown below.
Hope this helps!
Complete the equation that represents the proportional relationship shown in the table.
Enter your answer in the box.
y =
x y
2 8
3 12
7 28
Answer:
The x side is multiplying four each time to get the y side example 2x4=8 and so on
The equation would be x x 4= y
So hope this helps
The equation that represents the proportional relationship from the table is y=4x.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
The given table is
x y
2 8
3 12
7 28
Here, we can see when x increases y value also increases.
So, x and y are directly varies
Now, y∝x
y=kx -----(i)
k=y/x
k=8/2
k=4
Substitute k=4 in equation (i), we get
y=4x
Therefore, the equation that represents the proportional relationship from the table is y=4x.
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Which pair of functions are inverses of each other?
Answer:
D
Step-by-step explanation:
f(x) = 10x - 5 → x = 10g(x) - 5 → x + 5 = 10g(x) →
g(x) = (x + 5)/10
The diameter of a circular field is 56 cm. Find the length of wire required to
fence it? How
many times it can be fenced with 704 m of wire ?
Answer:
176cm
400 times
Step-by-step explanation:
-
In the diagram below, UV is parallel to RS. If UT = 4, TS = 9.6, and TV = 6,
find the length of RT. Figures are not necessarily drawn to scale.
Check the picture below.
Eric bought 8 pounds of flour for $5. How many pounds of flour did he get per dollar? If necessary, round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
8 pounds of flour = 5 dollars
1 pound of flour = x
Cross multiply
8x = 1*5 Divide by 8
8x/8 = 5/8
5/8 = 0.625
Therefore x = 0.625 dollars will buy 1 pound of flour.
Rounded x = 0.63
Solve on [0,2pi). Answer in order from smallest to biggest
cos x sin x = sin x
Answer:
0, π
Step-by-step explanation:
cos x sin x = sin x
cos x sin x - sin x = 0
sin x (cos x - 1) = 0
sin x = 0, x = 0, π
cos x - 1 = 0
cos x = 1, x = 0
So answers: 0, π
A business analyst has determined that the selling price per unit for a laser printer is $1600. The cost to make one laser printer is $950, and the fixed cost is $211,250. Find the break-even point.
please show the work thank you
Answer:
Solve the following equation
Step-by-step explanation:
You need to make an equation of this
Let x be the number of computers made
1600 × x = (950 × x) + 211250
When both sides are equal, that is the break even
One of the legs of a right triangle measures 2 cm and the other leg measures 17 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
17.1
Step-by-step explanation
a^2+b^2=c^2
2^2 + 17^2 = c^2
4 + 289 = c^2
293 = c^2
square root of 293 or 17.1
(12 pts) Choose whether the graphs of the following situations would have a positive slope, a negative slope, or a slope of zero
a. The amount of water in a bathtub as it is being filled
b. The temperature of a hot drink that you left sitting on your desk
c. The number of light bulbs on the Halloween string lights around your window
d. Power in your cell phone battery as you stream a video
Answer:
a. positive
b. negative
c. zero
d. negative
Step-by-step explanation:
You want a description of the sign of the slope of a graph of ...
amount of water in a filling bathtubtemperature of a cooling drinknumber of lights in a stringpower in a battery being usedSlopeThe slope of a graph is the "rise" divided by the "run." Generally, we choose the direction of "run" to be to the right, so the "rise" will be positive when the graph shows an increasing value, and it will be negative when the graph shows a decreasing value. When the rise is zero (the value is neither increasing nor decreasing), the slope is zero.
WaterA graph of the volume of water in a filling tub will show it starts at some low value and increases over time. Generally such a graph will have volume on the vertical axis, and time on the horizontal axis. Since the volume is increasing, the slope is positive.
TemperatureAs a hot drink cools, its temperature decreases. The graph of temperature will generally be drawn with temperature on the vertical axis, and time on the horizontal axis. Since the temperature is decreasing, the slope will be negative.
LightsWe presume there is no process going on that is changing the number of light bulbs in the string of lights, so the value is constant. It is neither increasing nor decreasing, so the slope of its graph will be zero.
PowerIf we presume your cell phone is not connected to a charger while it is streaming video for you, then we can assume the power in the battery is decreasing. The slope of the graph of battery power will be negative.
(If the phone is connected to a charger, the slope may be zero or positive, depending on the power output of the charger. One of my phone chargers is "low power," so the battery power does not increase unless the phone is turned off (not playing video).)
One of the construction workers likes to listen to music on the job. Unfortunately, he
also has a bad habit of accidentally dropping his music player into the ravine! Luckily,
his daughter is good with physics and has built a safety balloon for his latest music
player that will release after the music player has been falling for 1 second.
The time it takes for the music player to fall from the bridge to the bottom of the
ravine can be modeled by the following equation:
1-
81 +24
16
where tis the amount of time since the construction worker dropped his music
player
Will the safety balloon release in time?
6. First, how long will it take for the music player to fall to the bottom of the ravine?
Solve the equation and find the values of t. (2 points: 1 point for each value)
The equation of the ravine function is an illustration of a quadratic function
It will take 1.5 seconds for the music player to fall to the bottom of the ravine
How to determine the time the music player will fall to the bottom?The equation of the function is given as:
[tex]t = \sqrt{\frac{8t + 24}{16}}[/tex]
Take the square of both sides
t² = (8t + 24)/16
Multiply both sides by 16
16t² = 8t + 24
Divide through by 8
2t² = t + 3
Set the equation to 0
2t² - t - 3 = 0
Expand the equation
2t² + 2t- 3t - 3 = 0
Factorize the equation to 0
2t(t + 1)- 3(t + 1) = 0
Factor out t + 1
(2t- 3)(t + 1) = 0
Expand
2t- 3 = 0 or t + 1 = 0
Solve for t
t= 1.5 or t =- 1
Time cannot be negative.
So, we have:
t = 1.5
Hence, it will take 1.5 seconds for the music player to fall to the bottom of the ravine
Read more about quadratic functions at:
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I need help ASAP, first one to get it correct gets 100 points.
Answer:
3D shape = cone
height = 3 units
diameter = 6 units
Step-by-step explanation:
3D shape = cone
height = 5 - 2 = 3 units
radius = 0 - (-3) = 3 units
diameter = 2 × radius = 2 × 3 = 6 units
A right angled triangle has hypotenuse 9cm and sides (x+5) and (x-3)cm. calculate x
Answer:
x= 3.95
Step-by-step explanation:
Hypotenuse = 9 cm
side = (x+5) cm
other side = (x-3) cm
Pythagoras theorem: Hypotenuse² = Base² + Base²
9² = (x+5)² + (x-3)²
81 = x² + 25 + 10x + x² + 9 - 6x
2x² + 4x - 47 = 0
Quadratic Formula
x = (-b±√b²-4ac) / 2a
x = (-4±√16+376) / 2(2)
x = (3.95 and -5.95)
We ignore the negative -5.95
So x = 3.95