Answers
Answer:
We kindly invite you to see the result in the image attached below.
The number in polar form is [tex]z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}[/tex].
Step-by-step explanation:
A complex number is represented by elements of the form [tex]a + i\,b[/tex], for all [tex]a[/tex], [tex]b[/tex] [tex]\in \mathbb{R}[/tex]. The first part of the sum is the real component of the complex number, whereas the second part of the sum is the imaginary component of the complex number. The real component is located on the horizontal axis and the imaginary component on the vertical axis.
Now we proceed to present the point on the graph: ([tex]a = 6[/tex], [tex]b = 3[/tex]) We kindly invite you to see the result in the image attached below.
The polar form of the complex number is defined by:
[tex]z = r\cdot e^{i\cdot \theta}[/tex] (1)
Where:
[tex]r[/tex] - Magnitude of the complex number, dimensionless.
[tex]\theta[/tex] - Direction of the complex number, measured in radians.
The magnitude and the direction of the complex number are defined by the following formulas:
Magnitude
[tex]r =\sqrt{a^{2}+b^{2}}[/tex] (2)
Direction
[tex]\theta = \tan^{-1} \frac{b}{a}[/tex] (3)
If we know that [tex]a = 6[/tex] and [tex]b = 3[/tex], then the polar form of the number is:
[tex]r =\sqrt{6^{2}+3^{2}}[/tex]
[tex]r = 3\sqrt{5}[/tex]
[tex]\theta = \tan^{-1} \frac{6}{3}[/tex]
[tex]\theta \approx 0.352\pi \, rad[/tex]
[tex]z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}[/tex]
The number in polar form is [tex]z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}[/tex].
Related Questions
The median of 4 numbers is 48
3 of the numbers are:
42, 51, and 52
what is the other number
Answers
Answer:
45!
Step-by-step explanation:
why is 10 x 10 is 1 less than 9 x 11
Answers
Answer: It's the other way around and it is because 10 x 10 is adding 10+10+10+10+10+10+10+10+10+10, while 11x9 is just 9 11s added together.
Identify the property illustrated. (Commutative, Associative, Identity, Property of Zero, Property of -1)
1. -1 • (-6) =6
2. 0 • (-76.3) =0
3. (3x) y = 3 (xy)
4. 0.3 • (-3) = -3 • 0.3
Answers
-1 × (-6) = 6 ( because of multiplicative property of -1)
0 ×(-76.3) = 0 (zero property of multiplication)
(3x)y = 3(xy) (commuative property)
0.3 × (-3) = -3 × 0.3 ( commutative property)
As we know that,
The commutative property is a math rule that says that the order in which we multiply numbers does not change the product.
The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.
Identity property states that a number, known as the identity, can be added to, subtracted from, multiplied by, or divided into a number without changing the number.
Zero property of multiplication is defined as “when we multiply any number by zero, the resulting product is always a zero”.
Multiplicative property of -1 atates that any number multiplied by -1 gives the same but with its opposite sign.
From the given example we can say that
-1 × (-6) = 6 ( because of multiplicative property of -1)
0 ×(-76.3) = 0 (zero property of multiplication)
(3x)y = 3(xy) (commuative property)
0.3 × (-3) = -3 × 0.3 ( commutative property)
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When Suzy walks past the coffee shop, she can pick up their free wi-fi signal, which extends 60 ft from the shop. She starts walking toward the coffee shop at a rate of 3 ft/sec from her office building 180 ft away. After how many seconds will she pick up the signal? If she keeps on walking past the coffee shop, after how many seconds will she lose the signal?
Answers
The number of seconds Suzy will pick up the signal if she starts walking toward the coffee shop at a rate of 3 ft/sec from her office building 180 ft away is 40 seconds
DistanceSignal distance = 60 ftSuzy's speed = 3 ft/secDistance between her office building and the coffee shop = 180 ftAfter how many seconds will she pick up the signal between her office building and the coffee shop = (Distance between her office building and the coffee shop - Signal distance) / Suzy's speed
= (180 ft - 60 ft) / 3 ft/sec
= 120 ft / 3 ft/sec
= 40 seconds
After how many seconds will she lose the signal = Signal distance / Suzy's speed
= 60 ft / 3 ft/sec
= 20 seconds
Therefore, If she keeps on walking past the coffee shop, she will lose the signal after 20 seconds.
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Henri's bill at a restaurant is $19.62. He wants to leave a tip of 20%, or , of the bill. To find the exact amount of the tip, he should multiply the bill by ____. A good estimate for the amount of the tip is
$4.00. A good estimate for the total bill, including the tip, is
$24.00.
Answers
Answer:
0.2
Step-by-step explanation:
19.62*0.2
Multiply by 0.2
Hope this helps plz hit the crown :D
There are 3 boys for every 4 girls in Mrs. G.'s math class.
Find the constant of proportionality and write an equation to determine the number of boys in Mrs. G.'s class if you know the number of girls in Mrs. G's
class
Answers
Answer:
12 Step-by-step explanation:
Which of the following situations are equal to 40%? Select all that apply.
A) 5 out of 20
B) 6 out of 15
C) 10 out of 25
D) 45 out of 90
E) 32 out of 80
Answers
Answer:
C option
Step-by-step explanation:
please mark me brainliest
answer the following
Answers
Step-by-step explanation:
–(11/4) = 11 : (–4) = –11/4 = 11/-4
Expand $(2t - 7)^2.$
Answers
Answer:
4t^2 - 28t + 49
Step-by-step explanation:
(2t - 7)^2
Use FOIL.
(2t - 7)^2 =
= (2t - 7)(2t - 7)
= 4t^2 - 14t - 14t + 49
Combine like terms.
= 4t^2 - 28t + 49
(2t - 7)² on expansion results in 4t² - 28t + 49.
What are Algebraic Identities?The algebraic equations which can be used for all variables in the equation is called Algebraic identities. These identities used in factorization of polynomial expressions as well as in the computation of algebraic expressions.
Some of the standard algebraic identities are:
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
a² - b² = (a + b) (a - b)
Here we have the expression (2t - 7)².
Using the second identity (a - b)² = a² - 2ab + b², we can write,
(2t - 7)² = (2t)² - (2 × 2t × 7) + 7²
= 4t² - 28t + 49
Hence the expression (2t - 7)² is expanded to 4t² - 28t + 49 using the algebraic identity (a - b)² = a² - 2ab + b².
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A drone costs $300 plus $25 for each set of extra propellers. What is the cost of a drone and 4 extra sets of
propellers? (a) Write a function that will showthe cost.
300 + 4(25) = 400
(b) What is the independent variable in this situation?
are
Answers
b) 300 would be the unchanged or control variable, 25x would be the independent variable and 400 would be the dependent variable.
A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 55 pounds each, and the small boxes weigh 25 pounds each. There are 125 boxes in all. If the truck is carrying a total of 4775 pounds in boxes, how many of each type of box is it carrying?
Answers
There are 70 small boxes and 55 big boxes.
How to calculate the equation?Let x = small box
Let y = large box
The equation will be:
x + y = 125 ....i
25x + 55y = 4775 ..... ii
From equation i, y = 125 - x.
25x + 55y = 4775
25x + 55(125 - x) = 4775
25x + 6875 - 55x = 4775
Collect like terms
25x - 55x = 4775 - 6875
30x = 2100
x = 2100/30
x = 70
Since x + y = 125
y = 125 - 70 = 55
Therefore, there are 70 small boxes and 55 big boxes.
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i will mark you brainliest for answering
Answers
Answer:
28%
Step-by-step explanation:
Answer:
25% of the questions were correct
Step-by-step explanation:
14+42=56
14/56=0.25
Select the points that are solutions to the system of inequalities. Select all that apply. A(–2, 0)B (0, 10)C(–10, 10)D(1, 2)
Answers
Answer:
b and c
Step-by-step explanation:
i took the test
which expression is equivalent to 4(12+5)+3?
Answers
Answer:
I think it is 17/85
Step-by-step explanation:
1/5. = 2/10. = 3/15. = 4/20. = 5/25. = 6/30. = 7/35. = 8/40. = 9/45. = 10/50. = 11/55. = 12/60. = 13/65. = 14/70. = 15/75. = 16/80. = 17/85
Please help me with my homework :)
Answers
Step-by-step explanation:
x = 36
y = 48
z = 72
hope it helps
y is 48
z is 72
Which point is located at (0.25,-0.5)?
Answers
The answer that you're looking for is point C.
Hope this helps! <3
Answer:
The person above me is correct it is C
Step-by-step explanation:
Because it is the only one with a positive and negative. And of course coordinates are correct.
Hope this helps! :)
Priya bought x grams of flour. Clare bought 3/8 more than that. Select one equation that represent the relationship between the amount of flour that Priya bought, , and the amount of flour that Clare bought,
Answers
Answer:
The relationship ship equation:
y = x + 3/8xStep-by-step explanation:
Let 'x' be the grams of flour Priya bought
Let Clare bought 'y' grams of flour
As Clare bought 3/8 more than that.
so
y = x + 3/8x
Thus, the relationship ship equation:
y = x + 3/8xPLEASE HELP!! (QUESTION 1)
Answers
9514 1404 393
Answer:
a. reflection over the x-axis
b. vertical expansion by a factor of 2
c. right shift 3 units
d. shift upward 4 units
Step-by-step explanation:
It is a good idea to become familiar with what these various factors do. You will see them repeatedly.
__
a. Multiplying a function by a negative value reflects its graph over the x-axis.
__
b. A multiplier of 2 will expand the graph vertically by a factor of 2.
__
c. Subtracting 3 from each x-value will shift the graph right 3 units.
__
d. Adding 4 to each function value will shift the graph up 4 units.
Use vector operations to draw the resultant vector
Answers
Answer:
Draw an arrow from the origin to (4, 0)
Step-by-step explanation:
u-v+w
= <-3, -4> - <-4, -1> + <3, 3>
= <4, 0>
We want to perform a sum of vectors and draw the resultant vector. The resultant vector will be <4, 0> and its graph can be seen at the end.
If we see the image, we can write the vectors as:
w = <3, 3>u = <-3, -4>v = <-4, -1>Now we want to sum:
u - v + w
Remember that in the sum of the vectors we just add (subtract) the correspondent components, then we will have:
u - v + w = <-3, -4> - <-4, -1> + <3, 3> = <-3 + 4 + 3, -4 + 1 + 3> = <4, 0>
The graph of the resultant vector can be seen below.
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A player throws a bean bag from the height of 3 feet with an initial velocity of 34 feet per second at an angle of 30º.
The parametric equation that represents this situation is __
A. x = (34cos(30°)t and y = –16t2 + (34sin(30°))t
B. x = (34cos(30°)t and y = –16t2 + (34sin(30°))t + 3
C. x = (34cos(30°)t + 3 and y = –16t2 + (34sin(30°))t + 3
The bean bag’s path is part of a curve that is a __
To the nearest second, the bean bag was in the air for __
second(s).
Answers
Answer:
B, parabola, 1
Step-by-step explanation:
right on edge
The bean bag’s path is part of a curve that is a parabola and to the nearest second, the bean bag was in the air for 1 second(s).
What is projectile motion?Projectile motion is the motion of the body, when it is thrown in the air taking the action of gravity on it.
The parametric equation for x and y can be given as,
[tex]x =x_o+ v_o\cos(\theta)t \\y =y_o -\dfrac{1}{2}at^2 + (v_o\sin(\theta))t[/tex]
Here, (vo) is the initial speed, (h) is the height and θ is the angle of throw.
The player throws a bean bag from the height of 3 feet with an initial velocity of 34 feet per second at an angle of 30º.
Let suppose the time is t second. Thus, the parametric equation that represents this situation are,
[tex]x = (34\cos(30^o)t \\y = -16t^2 + (34\sin(30^o))t + 3[/tex]
The bean bag’s path is part of a curve. This path is in the form of parabola.
To the nearest second, the bean bag was in the air for 1 second(s).
Thus, the bean bag’s path is part of a curve that is a parabola and to the nearest second, the bean bag was in the air for 1 second(s).
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plz help thank you thank you
Answers
Answer:
B
Only one that goes over once and up twice
Answer:
b is the answer I believe
Can sum1 help plz!!
Answers
Answer:
5
Step-by-step explanation:
The rate is 5p/m
200 / 40 = 5 and so on...
Answer:
5 calories/minute.
Step-by-step explanation:
To find the rate, take one of the data sets (in my example, 40, and 200) and just divide the number of calories by the minutes to find your unit rate.
200/40
= 5
rs= 4x-9, st= 19, rt=8x-14
Answers
The value of x is 6
How to determine the valueFrom the information given, we have that;
Line RS = 4x - 9Line ST = 19Line RT = 8x - 14It is important to note that line RT is a line with segments RS and ST and S and the line between R and T
This can be expressed as;
RS + ST = RT
substitute the values into the equation, we have;
4x - 9 + 19 = 8x - 14
collect like terms
4x - 8x = -14 + 9 - 19
subtract like terms
-4x = -24
make 'x' the subject of formula
-4x/-4 = -24/-4
x = 6
Thus, the value of x is 6
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The diagram represents 6x² - 7x + 2 with a factor of 2x
1.
2x
6x
-4x
19
-3x
2
What is the other factor of 6x² - 7x + 2?
O 3x-2
O 3x-1
O3x + 1
O3x+2
Answers
The other factor of the quadratic equation [tex]6x^{2} -7x+2[/tex] is 3x-2. Since it is a quadratic equation we can get the other factor by factorization.
Factorization of quadratic equation is a way of finding the roots of the equation.The simple method of factorizing is we first find the product of the coefficient of [tex]x^{2}[/tex] and the constant, then we have to get the product by rearranging the coefficient of x, if the constant has a positive sign then we try to get the product by sum and if the sign is negative then we try to get the product by subtraction. After rearrangement we divide the equation in two parts and take the common factors from each part.
One of the factors of the equation is 2x-1, we have to find the other factor.
[tex]6x^{2} -7x+2=0\\6x^{2} -3x-4x+2=0\\3x(2x-1)-2(2x-1)=0\\(2x-1)(3x-2)[/tex]
The other factor of the equation is 3x-2.
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Determine the number of real solutions to the quadratic equation -9m^2-8m-3=0
Answers
Step-by-step explanation:
Let's solve your equation step-by-step.
−9m2−8m−3=0
For this equation: a=-9, b=-8, c=-3
−9m2+−8m+−3=0
Step 1: Use quadratic formula with a=-9, b=-8, c=-3.
m=
−b±√b2−4ac
2a
m=
−(−8)±√(−8)2−4(−9)(−3)
2(−9)
m=
8±√−44
−18
Answer:
No real solutions.
The given equation has no real solutions.
We have given that the quadratic equation
[tex]-9m^2-8m-3=0[/tex]
For this equation: a=-9, b=-8, c=-3
[tex]-9m^2-8m-3=0[/tex]
Step 1: Use quadratic formula with a=-9, b=-8, c=-3.
What is the formula for the quadratic roots?[tex]x=\frac{-b \±\sqrt{b^2-4ac}} {2a}[/tex]
Therefore we have,
[tex]x=\frac{-b \±\sqrt{b^2-4ac}} {2a}[/tex]
[tex]x=\frac{-(-8)\±\sqrt{(-8)^2-4(-9)(-3)} }{2(-9)}[/tex]
[tex]x=-\frac{4}{9} -i\frac{\sqrt{11} }{9}[/tex] and [tex]x=-4/9+i\frac{\sqrt{11} }{9}[/tex]
This equation has no real solutions.
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Consider a total of 1,000 people. If it was said that within 1 deviation (of the mean) of all people like MATH 123, how many of the group should like MATH 123?
Answers
Answer:
680 students
Step-by-step explanation:
The 68 - 95 - 99.7 rule (empirical rule) states that 68% of the population lies within one standard deviation of the mean, 95% of the population lies within two standard deviations and 95% of the population lies within three standard deviations.
Hence since it was said that within 1 deviation (of the mean) of all people like MATH 123, therefore the number of people that like MATH 123 is:
number of people that like MATH 123 = 68% of the population
number of people that like MATH 123 = 0.68 * 1000
number of people that like MATH 123 = 680 students
A process produces a certain part with a mean diameter of 3 inches and a standard deviation of 0.05 inches. The lower and upper engineering specification limits are 1.80 inches and 3.05 inches. What is the Cp (measure of potential capability)
Answers
Answer:
The correct answer is 4.167
Step-by-step explanation:
According to the given scenario, the calculation of the Cp i.e. measure of potential capability is as follows;
= (USL - LSL) ÷ 6 × standard deviation
= (3.05 inches - 1.80 inches) ÷ 6 × 0.05
= 1.25 ÷ 0.3
= 4.167
hence, the calculation of the Cp i.e. measure of potential capability is 4.167
Rebecca has 6 yards of ribbon. It takes 3/8 yard to wrap one package. How many packages can rebecca wrap
Answers
Answer:
16
Step-by-step explanation:
6 x 8 = 48
48 / 3 = 16
Rebecca can only wrap 16 packages with 6 yards of ribbon.
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what is one million + 1 ?
who made the song holy moly dounut shop?
what is eqivalent to 2x2
bonus question:
(five stars)
do you want brainlest
yes or no
i still have an answer slot open for my last question...........
Answers
blueface
4
yes
.............
Answer:
me
1,000,001
Blueface
4?
Yes
ok
Step-by-step explanation:
I will mark brainiest to whoever answers this!
Answers
Answer:
2
Step-by-step explanation:
......... . ........ .......