Answer:
After solving the power:
[tex]\bold{2(cos60^\circ+isin60^\circ)}[/tex]
Rectangular form:
[tex]\bold{1+i\sqrt3}[/tex]
Step-by-step explanation:
Given the complex number:
[tex]2(cos20^\circ+isin20^\circ)^3[/tex]
To find:
The indicated power by using De Moivre's theorem.
The complex number in rectangular form.
Rectangular form of a complex number is given as [tex]a+ib[/tex] where a and b are real numbers.
Solution:
First of all, let us have a look at the De Moivre's theorem:
[tex](cos\theta+isin\theta )^n=cos(n\theta)+isin(n\theta )[/tex]
First of all, let us solve:
[tex](cos20^\circ+isin20^\circ)^3[/tex]
Let us apply the De Moivre's Theorem:
Here, n = 3
[tex](cos20^\circ+isin20^\circ)^3 = cos(3 \times 20)^\circ+isin(3 \times 20)^\circ\\\Rightarrow cos60^\circ+isin60^\circ[/tex]
Now, the given complex number becomes:
[tex]2(cos60^\circ+isin60^\circ)[/tex]
Let us put the values of [tex]cos60^\circ = \frac{1}{2}[/tex] and [tex]sin60^\circ = \frac{\sqrt3}{2}[/tex]
[tex]2(\dfrac{1}{2}+i\dfrac{\sqrt3}2)\\\Rightarrow (2 \times \dfrac{1}{2}+i\dfrac{\sqrt3}2\times 2)\\\Rightarrow \bold{1 +i\sqrt3 }[/tex]
So, the rectangular form of the given complex number is:
[tex]\bold{1+i\sqrt3}[/tex]
Consider the graph of the quadratic function. Which
interval on the x-axis has a negative rate of change?
3
0-2 to-1
2
O -1.5 to 0
O 0 to 1
-3
-2
21
2
3
x
О 1 to 2.5
Answer:
1 to 2.5
Step-by-step explanation:
A negative rate of change requires the instantaneous slope to be negative, and the interval from 1 to 2.5 is the only place segment where that can happen.
A la propiedad fundamental de las proporcionas, comprueba si las siguientes son o no hay elementos a) 5/7 a 15/21 b) 20/7 a 5/3 c) 16/8 a 4/2
Answer:
fucuvucybycych tcy bic ttx TV ubtx4 cub yceec inivtxr xxv kb
Step-by-step explanation:
t tcextvtcbu6gt CNN tx r.c tct yvrr TV unu9gvt e tch r,e xxv t u.un4crcuv3cinycycr xxv yctzrctvtcrzecycyvubr xiu nyfex tut uhyh
Find the surface area of the figure below round your answer to the nearest tenth in necessary
Answer:
1548.3 [tex]m^{2}[/tex]
Step-by-step explanation:
Answer:
A = 1548.3 m²
Step-by-step explanation:
Please help me!!Which of the following functions shows the linear parent function, Fx) = X,
shifted right?
5
F(x) = x
5
A. G(x) = x + 2
B. G(x) = 4x
C. G(x) = x - 9
D. G(x) = -x
Answer:
C. G(x) = x - 9
Step-by-step explanation:
You know that the transformation ...
g(x) = f(x -h) +k
causes parent function f(x) to be shifted right h units and up k units.
You're looking for a function that is shifted right, so you want something that looks like ...
g(x) = f(x -constant) = x - constant
Choice C has that form:
C. G(x) = x - 9
_____
A. the function is shifted up 2 units
B. the function is vertically expanded by a factor of 4 (no shift)
C. shifted right
D. the function is reflected over the y-axis (no shift)
Answer: C [G(x) = x-9]
Step-by-step explanation:
I got it right
Jonah read 5 1/2 chapters in his book in 90 minutes how long did it take him to read one chapter
Answer:
around 16 minutes. you partition an hour and a half (all out) by what number of sections he read (5.5
Step-by-step explanation:
PLEASE help me solve this!!!!
1. log2^64
2. log11^121
3. log8^512
4. log4^1/16
Here are all of the answers to these four questions:
1. log2^64=6, or 2 to the power of 6=64.
2. log11^121=2, or 11²=121.
3. log8^512=3, or 8³=512.
4. log4^1/16=-2, or 4 to the negative second (-2) power.
I hope that this answered your question.
Yeah, so the answer is 6, 2, 3, and -2.
I need help with the following question
Answer:
a. 2
b. x²+10x+26
c. x²+2x+2
Step-by-step explanation:
To find each value, you plug in the x value into the function and solve.
a. 2
f(2)=(2)²-2(2)+2 [combine like terms]
f(2)=4-4+2
f(2)=2
---------------------------------------------------------------------------------------------------------
b. x²+10x+26
f(x+6)=(x+6)²-2(x+6)+2 [use FOIL method and distributive property]
f(x+6)=x²+12x+36-2x-12+2 [combine like terms]
f(x+6)=x²+10x+26
---------------------------------------------------------------------------------------------------------
c. x²+2x+2
f(-x)=(-x)²-2(-x)+2 [combine like terms]
f(-x)=x²+2x+2
For the rhombus below, find the measures of ∠1, ∠2, ∠3, and ∠4.
Answer:
∠1 = 116 ° , ∠2 = 32° , ∠3 = 116 ° and ∠4 = 32°
Step-by-step explanation:
∠2 = 32° (The diagonals of a rhombus bisect pairs of opposite angles)
Opposite sides of a rhombus are parallel ,so
∠2 = ∠4 (Alternate interior angles )
∠4 = 32°
32° + ∠4 + ∠3 = 180° (angle sum property of a triangle)
64° + ∠3 = 180°
∠3 = 180 - 64
∠3 = 116°
∠3 =∠1 (in a rhombus opposite angles are equal )
∠1 = 116°
What is the constant of variation, k, of the line y=kx through (3,18) and (5,30)? 3 6
Answer:
6
Step-by-step explanation:
The constant of variation is the slope
k = (y2-y1)/(x2-x1)
= (30-18)/(5-3)
=12/2
= 6
The value of constant of variation, k, is,
⇒ k = 6
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Here, the constant of variation, k, of the line y = kx through (3,18) and (5,30)
Since, The constant of variation is the slope,
Hence, We get;
k = (y₂ - y₁)/(x₂ - x₁)
= (30 - 18)/(5 - 3)
= 12/2
= 6
Thus, the value of constant of variation, k, is,
⇒ k = 6
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What is the solution set for StartAbsoluteValue z + 4 EndAbsoluteValue greater-than 15? 11 less-than z less-than 19 Negative 19 less than z less-than 11 z less-than negative 19 or z greater-than 11 z less-than 19 or z greater-than 11
Answer:
z less-than negative 19 or z greater-than 11Step-by-step explanation:
Given the inequality [tex]|z+4|>15[/tex], we are to find the solution set of the inequality. Since the the function is an absolute value, this means that the function will be positive and negative.
For the positive value of the function;
[tex]z+4>15\\\\subtract\ 4\ from \ both \ sides\\z+4-4 > 15 -4\\\\z>11[/tex]
For the negative value of the function we have;
[tex]-(z+4) > 15\\\\-z-4> 15\\add\ 4 \ to\ both \ sides\\\\-z-4+4> 15+4\\\\-z> 19\\\\[/tex]
Multiplying both sides of the inequality by -1 will change the sense of the inequality sign;'
[tex]-(-z)< -19\\\\z<-19[/tex]
Hence the solution sets are [tex]z> 11 \ and \ z< -19 \\[/tex] OR z less-than negative 19 or z greater-than 11
Answer:
z less-than negative 19 or z greater-than 11
Step-by-step explanation:
Please help me on question 4 and 5 I am really stuck thank you I would really appreciate it
Answer:
1. 5/4
2. 7
Step-by-step explanation:
1) Lets call the width as w
Therefore length would be:
w+4
To find the perimeter you use the formula:
2 (l+w)
Now substitute our values into this formula:
2 (w+4+w)
2( 2w+4)
4w+8
Now make this equal to 13:
4w +8 = 13
4w = 5
w = 5/4
2. In this question we will call length l
Therefore width would be:
l-5
Now we will do the steps we did above:
2 (l+l-5)
2 (2l-5)
4l -10
4l - 10 = 18
4l = 28
l = 7
ASAP Which condition does not prove that two triangles are congruent? A. ASA ≅ ASA B. SAS ≅ SAS C. SSA ≅ SSA D. SSS ≅ SSS
Answer:
The answer is C. SSA ≅ SSA.
Step-by-step explanation:
To check for similar triangles, SSA congruence would not work because the other side can be any length. Also, there is not an SSA postulate because this theorem by itself cannot prove congruence.
The other three properties do work because they show congruence unlike the other congruent factors.
What is the value of x?
Answer:
58
Step-by-step explanation:
By the property of intersecting secants outside of a circle, we have:
x° = 1/2( 141° - 25°) = 1/2 * 116° = 58°
Therefore, x = 58
Is 3.6 a irrational or rational number?
Determine the value(s) for which the rational expression 2x^2/6x is undefined. If there's more than one value, list them separated by a comma, e.g. x=2,3.
Answer:
0
Step-by-step explanation:
Hello, dividing by 0 is not defined. so
[tex]\dfrac{2x^2}{6x}[/tex]
is defined for x different from 0
This being said, we can simplify by 2x
[tex]\dfrac{2x^2}{6x}=\dfrac{2x*x}{3*2x}=\dfrac{1}{3}x[/tex]
and this last expression is defined for any real number x.
Thank you
Find the inverse of f(x) = -3 -4/5x
Answer:
-5/4x -15/4 = y
Step-by-step explanation:
y = -3 - 4/5x
To find the inverse, exchange x and y
x = -3 - 4/5 y
Solve for y
Add 3 to each side
x+3 = -4/5y
Multiply each side by -5/4
-5/4(x+3) = -5/4 * -4/5(y)
-5/4x -15/4 = y
Solve for X: 1+1*12/80-2+3=56x
Answer:
NOT SURE
Step-by-step explanation:
what is the closest side lenght of this square area=111 square units
Let side be a
Area=111units^2We know
[tex]\\ \sf\longmapsto Area=(side)^2[/tex]
[tex]\\ \sf\longmapsto a^2=111[/tex]
[tex]\\ \sf\longmapsto a=\sqrt{111}[/tex]
[tex]\\ \sf\longmapsto a=10.3units[/tex]
Stella and Michael are helping their friend Austin move. Stella can move one box for every four boxes that Michael can move. If Stella moves ten boxes, how many boxes can Michael move?
Explanation:
Stella can move 1 box for every 4 boxes Michael moves.
She moves 10 boxes, so that must mean Michael moved 40 boxes (since 4*10 = 40).
Put another way, the ratio 1:4 bumps up to the equivalent form 10:40 after multiplying both parts by 10. The first value of each ratio is the amount of boxes Stella moves, and the second part is what Michael moves.
You could also solve it like this
1/4 = 10/x
1*x = 4*10
x = 40
In the second step, I used cross multiplication.
4(x+4) =2x-1
8
Show work
Answer:
4(x+4) =2x-18
4x+16=2x‐18
4x–2x= –18 –16
2x= – 34
x= –34/2
x= – 17
I hope I helped you^_^
Step-by-step explanation:
[tex]thank \: you[/tex]
Which graph is the result of reflecting f(x) = One-fourth(8)x across the y-axis and then across the x-axis?
Answer:
f(x) = -0.5x
Step-by-step explanation:
.25*8 = 2 which is really a slope of 2/1
place a negative in front flips it over the y axis and flipping the slope flips it over the x axis.
Simplify the following expression.
3(2k + 3) -8k + 5 + 5
Answer:
Step-by-step explanation:
3*(2k + 3) - 8k + 5 + 5 Remove the brackets on the left
6k + 9 - 8k + 5 + 5 Combine like terms
6k-8k+9 + 5 + 5
-2k + 19
2. Estimate the quotient: 6.31 x 105 - 2.085 x 103
Answer:
Estimate: Around 445 or 450
Step-by-step explanation:
If we multiply the whole expression we get [tex]447.95[/tex] =. Rounding it down gets us [tex]440[/tex] but we can also round up to [tex]450[/tex]. So, we can estimate the quotient as [tex]450[/tex] (or if your picky, then also 445)
(Hopefully this helped! If you think I misinterupted or if I got this wrong, please tell me and I will fix my answer as soon as possible.)
hello, if someone can give me a hand with this upper and lower bound excercise please? l get 3 marks of 5 but l cant find what l am missing please thanks
Answer: maximum "safe" Force = 415.58 N
Step-by-step explanation:
Length = 1.2 m
lower bound is 1.15 (because it rounds up to 1.2)
upper bound is 1.24 (because it rounds down to 1.2)
Note: 1.25 would round up to 1.3
width = 2.5 m
lower bound is 2.45 (because it rounds up to 2.5)
upper bound is 2.54 (because it rounds down to 2.5)
Note: 2.55 would round up to 2.6
Pressure = 150 N/m²
lower bound is 147.5 (because it rounds up to 150)
upper bound is 152.4 (because it rounds down to 150)
Note: 152.5 would round up to 155
Max "safe" Force means minimum Area and minimum Pressure (lower bounds)
Force = Area x Pressure
= length x width x Pressure
= 1.15 x 2.45 x 147.5
= 415.58
The length of a rectangle is twice the width. If the length is increased by 4 inches and the width is decreased by 1 inch, a new rectangle is formed whose perimeter is 198 inches. Find the dimensions of the original rectangle.
Answer:
Width: 32 inches.
Length: 64 inches.
Step-by-step explanation:
Let's say that the width of the rectangle is x inches, so the length is 2x inches.
If 2x + 4 and x - 1, the perimeter is 198 inches. That means that two times the width plus two times the length is 198 inches.
2(2x + 4) + 2(x - 1) = 198
4x + 8 + 2x - 2 = 198
6x + 6 = 198
x + 1 = 33
x = 32.
That means that the width of the original rectangle is 32 inches, and the length is 32 * 2 = 64 inches.
Hope this helps!
A football field has the shape of a rectangle with dimensions of 300 feet long and 160 feet wide. If a fan was to run diagonally from one end zone to the opposite end zone, how far would she run to the nearest foot? Enter only the number.
Answer:
340 feet
Step-by-step explanation:
we use Pythagora
d² = l² + w²
d = √300ft)² + 160ft)²
= √90000ft² + 25600ft²
= √115600ft²
= √(2⁴ₓ5²ₓ17²)ft²
= √(2²ₓ5ₓ17)ftₓ(2²ₓ5ₓ17)ft
= √340ftₓ340ft
= 340 feet
Find the area of the figure
A =
Answer:
207m
Step-by-step explanation:
(17+5)*6=132
(15*5)=75
132+75=207
For an ordered pair (x,y) in a relation, the y element represents the
a.) range
b.) domain
c.) function
d.) input
y represents the range for an ordered pair (x, y). Option A is correct.
For an ordered pair (x, y), What y represents is to determine.
Range of the function is the output value of the function.
Here, in ordered pair (x, y) x represents the values of independent variable terms as domain. And for every value of x their is exist or output values y this set of y values is called as range.
Thus, y represents the range for an ordered pair (x, y).
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6. Classify the traianle as scalene, isosceles or equilateral. Explain. Leave answers in square root form.
TAL
Answer:
isosceles
Step-by-step explanation:
The point B is located on the perpendicular bisector of AC. No calculation is necessary. AC has a slope of 1, so it is easy to count grid squares to see where the perpendicular bisector goes.
When the altitude of the triangle bisects the side opposite the vertex, it is an isosceles triangle.
_____
Apparently, you're to use the distance formula to determine the lengths of the sides of the triangle. Doing that, you would find ...
AB² = (6-4)² +(1 -6)² = 4 + 25
CB² = (6-1)² +(1-3)² = 25 + 4
At this point, it doesn't require much thought to realize these sides are the same length: √29.
Write each decimal as a fraction or mixed number in simplest form.
1 3/8
3/2
Step One: 1 3/8, transform the number into a improper fraction:
To have a mixed number in to a improper fraction, you need to use addition and multiplication. For 1 3/8, We first multiply the denominator (8, also know to be the bottom number of the fraction) to the whole number (1). 8x1= 8NOTE: The original denominator (8) will be use for are improper, again playing as the denominator, we only multiply the denominator for the numerator (which is the top number of a fraction).After multiplying, we'll add are product with the numerator (3) for the process. 8+3= 12 Now we have both numerator and denominator for 1 3/8, we can create the improper fraction. 12 as the numerator and 8 as the denominator. 12/8We still need to simplify the number. To that, we need the biggest whole number, or rather I call it the lowest number, that can be divide both in 12 and 8. 4 can be divide by both number so: 12/4= 3 and 8/4=2Now 3 is are simplify numerator and 2 is are simplify denominator.