Answer:
D
Step-by-step explanation:
The value of z^3 is option (D) [tex]z^{3}=64 (cos(\frac{3\pi }{2} ) + isin (\frac{3\pi }{2} ) )[/tex] is the correct answer.
What is a complex number?A complex number is characterized by an ordered pair of numbers, the real and imaginary parts. It can be represented in multiple ways such as Standard form(rectangular form), Polar form, Exponential form.
For the given situation,
The complex number, z = 4 (cos (pi/ 2) + i sin (pi/2 ) )
[tex]z=4(cos(\frac{\pi }{2} ) + isin (\frac{\pi }{2} ) )[/tex]
⇒ [tex]z^{3}=4^{3} (cos(\frac{\pi }{2} ) + isin (\frac{\pi }{2} ) )^{3}[/tex]
By De Moivre's theorem,
[tex]{\displaystyle {\big (}\cos x+i\sin x{\big )}^{n}=\cos nx+i\sin nx}[/tex]
Thus, [tex]z^{3}=64 (cos(\frac{3\pi }{2} ) + isin (\frac{3\pi }{2} ) )[/tex]
Hence we can conclude that the value of z^3 is option (D) [tex]z^{3}=64 (cos(\frac{3\pi }{2} ) + isin (\frac{3\pi }{2} ) )[/tex] is the correct answer.
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The school in town is building a track around its football stadium. The principal must decide whether to build a track with 6 lanes or 7 lanes. A 6-lane track will be 28.68 feet wide, and a 7-lane track will be 28.98 feet wide. If all lanes are of equal width in each track, how much wider will the lanes be in a 6-lane track than in a 7-lane track?
Answer:
the 6 lane track will be 0.64 feet wider than the 7 lane track
Step-by-step explanation:
28.68÷6=4.78
28.98÷7=4.14
4.78-4.14=0.64
Density is also the slope of the relationship between mass and volume. If the density 7.2 g /mL, what is the slope?
Answer:
The slope for the substance = 7.2 g/mL
Step-by-step explanation:
Given that the density is also the slope relationship between mass and volume and that the density is equal to 7.2 g/mL, therefore, the slope of the equation of the line relating mass to volume is also equal to 7.2 g/mL
The density = Mass/Volume = 7.2 g/mL
The slope of mass volume relationship = (The change in mass)/(The equal change in volume)
Whereby the change is from the zero state, we have;
The slope of mass volume relationship = (Mass - 0))/(Volume - 0) = Mass/Volume
Therefore;
The value of the slope of the substance = The value of the density of the substance = 7.2 g/mL
The value of the slope for the substance = 7.2 g/mL.
What is 1.904 rounded to the nearest penny
Answer:
1.90 I believe this is the answer. Hope this helps! Have a great day!
The question is this: Rationalize the denominator and simplify.
Plssss hurry & answer this!!!!
9514 1404 393
Answer:
[tex]\dfrac{20+5\sqrt{3}}{13}[/tex]
Step-by-step explanation:
Multiply numerator and denominator by the "conjugate" of the denominator.
[tex]\dfrac{5}{4-\sqrt{3}}=\dfrac{5(4+\sqrt{3})}{(4-\sqrt{3})(4+\sqrt{3})}=\dfrac{20+5\sqrt{3}}{4^2-(\sqrt{3})^2}=\boxed{\dfrac{20+5\sqrt{3}}{13}}[/tex]
__
This is done in different scenarios in order to take advantage of the factoring of the difference of squares. Square root terms and imaginary terms in the denominator can be eliminated in this way.
a² - b² = (a -b)(a +b)
2(x + 0.7) = 6(x – 0.8) well what i got for this is 2x + 1.4 = 6x - 4.8 -2 -2 1.4 = 4x - 4.8 +4.8 +4.8 so i do i finish this equation i need the answer how do i finish this Equation?
Answer:
1.55
Step-by-step explanation:
[tex]2(x + 0.7) = 6(x – 0.8)[/tex]
Using the distributive property of addition over multiplication we get
[tex]2x+1.4=6x-4.8[/tex]
Take the like terms to one side and change their signs accordingly
[tex]1.4+4.8=6x-2x[/tex]
[tex]\Rightarrow 6.2=4x[/tex]
[tex]\Rightarrow x=\dfrac{6.2}{4}[/tex]
[tex]\Rightarrow x=1.55[/tex]
The value of [tex]x[/tex] is 1.55.
In order to make sure this value is correct we can substitute the value of x in the equation
[tex]2(1.55+0.7)=6(1.55-0.8)\\\Rightarrow 2\times 2.25=6\times 0.75\\\Rightarrow 4.5=4.5[/tex]
So, both sides are equal hence the value of [tex]x [/tex]is 1.55.
Lucas is making a wire sculpture for art class. For the sculpture, he needs to cut a wire into pleces that
are each 1/16 of a foot long. If the original wire is 3/4 of a foot long, how many pieces will Lucas have?
⟹Answer:
➧Lucas can cut the wire into 12 pieces.
Step-by-step explanation:
⟹Lets Solve!
⟹The first step is to convert [tex]\frac{3}{4}[/tex] into [tex]\frac{}{16}[/tex] !
To do this we must find what number multiplied by 4 equals 16.
16 ÷ 4 = 4
⟹Now we know our multiplier is 4. So lets multiply the numerator and denominator by 4.
[tex]\frac{3}{4} * \frac{4}{4} = \frac{12}{16}[/tex]
[tex]\frac{12}{16}[/tex]
⟹Next we just divide [tex]\frac{12}{16}[/tex] by [tex]\frac{1}{16}[/tex].
[tex]\frac{12}{16}[/tex] ÷ [tex]\frac{1}{16}[/tex] = 12
➧Lucas can cut the wire into 12 pieces.
Woohoo! Brainliest appreciated! Hope I helped!
Based on the original length of the wire and the length Lucas requires, he will have 12 pieces.
The wire is 3/4 feet long and each piece required will be 1/16 feet.
The number of pieces in total is:
= Length of wire / Length of pieces
Solving gives:
= 3/4 ÷ 1/16
= 3/4 × 16/1
= 48/4
= 12 pieces
In conclusion, Lucas will have 12 pieces.
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In AQPL, m
twelve more than twice m
each angle.
m
Answer:
Yes but I do not get what we are going to do here
Step-by-step explanation:
A group of friends equally split the dinner bill shown. If each person paid $16, how many friends paid?
Answer:
4
Step-by-step explanation:
Wait... this doesn’t make sense because it doesn’t tell you if there was tax, how many friends there were, or tips.
Answer:
16/y = x
Step-by-step explanation:
You cannot solve for the question yet. However, you can create an equation!
we know that each person paid 16 dollars.
We don’t know how much the bill was or how many people were there.
So out equation looks like;
z/y = x
or
z * x = y
z = how much each person paid.
y = how much each person paid.
x = how many people paid.
Substitute with what we know.
16/y = x
16 * x = y
Now you will be able to substitute for either x or y to find either answer.
I neeeeeeeeed heeeelp
PLZ PLZ PLZ PLZ HELP I NEED HELP PLEASE
Answer:
Open dot on positive 2, arrow going to the left <----0
Step-by-step explanation:
Answer:
x < 2
Step-by-step explanation:
write linear equation in slope intercept
In this figure of a protractor , which angle is a right angle?
Which table contains only values that satisfy the equation
y = 0.25x + 8?
Answer:
Step-by-step explanation:
y = 0.25x + 8
(0, 8) are coordinates of y=intercept
y = 0.25 × 2 + 8 = 8.50
(2, 8.50)
The last table represnts the given equation.
The fourth table among all the options contains values that satisfy the equation y = 0.25x + 8.
An equation is a combination of two or more expressions, all equal to each other.
Let's check every table if every point in them satisfies the equation y = 0.25x + 8,
Table 1:
To check if (0, 8) satisfies the given equation,
RHS: 0.25 × 0 + 8 = 0 + 8 = 8
LHS: 8 = RHS
This point satisfies the equation.
To check if (2, 8.25) satisfies the given equation,
RHS: 0.25 × 2 + 8 = 0.50 + 8 = 8.50
LHS: 8.25 ≠ RHS
This point does not satisfy the equation.
Table 2:
To check if (0, 0) satisfies the given equation,
RHS: 0.25 × 0 + 8 = 0 + 8 = 8
LHS: 0 ≠ RHS
This point does not satisfy the equation.
Table 3:
To check if (0, 8.25) satisfies the given equation,
RHS: 0.25 × 0 + 8 = 0 + 8 = 8
LHS: 8.25 ≠ RHS
This point does not satisfy the equation.
Table 4:
To check if (0, 8) satisfies the given equation,
RHS: 0.25 × 0 + 8 = 0 + 8 = 8
LHS: 8 = RHS
This point satisfies the equation.
Similarly, all the points can be verified that they satisfy the equation.
Thus, all values in Table 4 satisfy the given equation.
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Write the equation of the parabola in vertex form.
vertex (3,4), point (2,-2)
Answer:
y = - 6(x - 3)² + 4Step-by-step explanation:
The vertex form of the equation of the parabola with vertex (h, k) is:
y = a(x - h)² + k
So the equation of the parabola with vertex (3, 4):
y = a(x - 3)² + 4
The parabola passes through point (2, -2) so if x=2 then y=-2
- 2 = a(2 - 3)² + 4
- 2 -4 = a(-1)² + 4 -4
- 6 = a
So, the equation written in vertex form of a parabola with a vertex of (5, 7) that passes through (2, -2):
y = - 6(x - 3)² + 4
Put them in order 4, 1.5, 7.3, -5, -1
Answer:
-5, -1, 1.5, 4, 7.3
Step-by-step explanation:
in of least to greatest
Thanks! have a good day
Need Brainlyest
What is 3 1/3 times 3?
Answer:
10
Step-by-step explanation:
friend chicked for life
Somebody please help me with this question I don’t get it :(
Answer:
The rental costs $2 per mile (third from top answer)
Reasoning:
The graph on the side follows the slops of y=2x (rise of 2, run of 1) , therefore at x=1, we know that the y value must be 2.
Meaning The third option (The rental costs $2 per mile) is the only
correct answer
I hope this helps you and good luck!
In Euclidean geometric terms, which of the below would be the best description of a RAY? a. It is a straight object that consists of all of the points that are equal distance from a common point. b. It is a straight object that extends infinitely in opposite directions without any width or thickness. c. It is a straight object that begins at a point and extends forever in one direction. It could be considered half of a line. d. It is a straight object that consists of all of the points that exist between two different points.
Answer:
c. It is a straight object that begins at a point and extends forever in one direction. It could be considered half of a line.
Step-by-step explanation:
A ray is a line that begins at a point and extend forever in one direction. It has no end point. It has a start point but no end point. So, C is the correct answer.
who has watched crown lake?
Answer:
omg finally I can answer one of your questions meeeeeee!
Answer:
Not a bad movie
Step-by-step explanation:
what is the answer to the question 6*9+6+9?
Answer:
69
Step-by-step explanation:
6 × 9 + 6 + 9 = 69
Please give me Brainlest!
Answer:
69
Step-by-step explanation:
Original Equation:
6 · 9 + 6 + 9 = ?
Multiply 6 and 9
54
Plug this value back into the equation
54 + 6 + 9
Add 54 to 6
60
Plug this value back into the equation
60 + 9
69
Hope I helped :)
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Factor the expression.
x^2- 3x+2
O A (x+2)(x-1)
B. (x+2)(x+1)
O C. (x-2)(x-1)
D. (x-1)(x-3)
Answer:
Step-by-step explanation:
The answer would be O C. (x-2)(x-1)
xD
Take these points but plz answer the other question I asked.
Answer:
ok i will try my best to give your questions answer
Step-by-step explanation:
thankyou for free point
Questions 1-6 , need help ASAP , will award you brainiest
Answer:
1. 13+10i
2. 28-(-4i)
3. -14-1i
4. 4 -i
5. 15+ 10i
6.8 - 5i^2
Step-by-step explanation:
what is the inverse of f(x)= -4x+60
Step-by-step explanation:
let y= -4x+60
4x= 60-y
x= 3/2-y/4
f'(x) = 3/2- x/4
Answer:
I hope this is right
Step-by-step explanation:
y = (x + 6)(x – 7)
Distribution
Answer:
Y = [tex]x^{2}[/tex] - x - 42
Step-by-step explanation:
You can use the foil method
first, outside, inside, last
multiply the x’s together, the x times -7, the 6 times x, and then 6 times -7
Y = [tex]x^{2}[/tex] - x - 42
Here are 36 carpenters on a construction crew. On a certain day, 29 carpenters were present. Which proportion can be used to determine the percent of carpenters that were present?
Answer:
80.6%
Step-by-step explanation:
Given that :
Total construction crew = 36
Number present in a certain day = 29
Percentage present on that day :
(Number present / total number) * 100%
(29 / 36) * 100%
0.8055555 * 100%
80.555%
= 80.6%
Need help!!! Worth 40 points!!!
look on google
Step-by-step explanation:
go on google
search the answer
then BOOM!
Answer:
The answer is the first option x(x-4)(x-1)/2(x+4).
Step-by-step explanation:
because when you simplify after multiplying the denominator is 2x+8 when you simplify that its 2(x+4) and for the numerator after multiplying you get x^3−5x^2+4x when you simply that you get x(x-4)(x-1). Answer would be x(x-4)(x-1)/2(x+4).
Susan made $204 for 17 hours of work. At the same rate, how much would she make for 13 hours of work?
Answer:
156
Step-by-step explanation:
204/7 = 12
12 x 13 = 156
What is the equation of the line that passes through the points (-2, 1) and (1, 10
What is the answer of this math problem??
- 1/2 / 4/5
Answer:
-0.025
Step-by-step explanation: