Answer:
B
Step-by-step explanation:
did the course
The equivalent complex expression of [tex](\frac{1}{2}(cos(\frac{\pi}{5} )+i~sin(\frac{\pi}{5} )) )^5[/tex] is
[tex]\frac{1}{32} (cos(\pi)+i~sin(\pi))[/tex]
The correct answer is an option (b)
What is complex number?"The number of the form a + ib, where a, b are real numbers and [tex]i=\sqrt{-1}[/tex]"
What is De Moivre's theorem?"This theorem gives a formula for computing powers of complex numbers.
[tex](r(cos\theta+i~sin\theta))^n=r^n~(cos(n\theta)+i~sin(n\theta))[/tex] "
For given question,
We have been given a complex expression [tex](\frac{1}{2}(cos(\frac{\pi}{5} )+i~sin(\frac{\pi}{5} )) )^5[/tex]
Using the DeMoivre's theorem,
[tex](\frac{1}{2}(cos(\frac{\pi}{5} )+i~sin(\frac{\pi}{5} )) )^5\\\\=(\frac{1}{2})^5~((cos(\frac{\pi}{5} )+i~sin(\frac{\pi}{5} )) )^5\\\\=\frac{1}{32} (cos(\frac{5\pi}{5} )+i~sin(\frac{5\pi}{5} )) )\\\\= \frac{1}{32} (cos(\pi)+i~sin(\pi))[/tex]
Therefore, the equivalent complex expression of [tex](\frac{1}{2}(cos(\frac{\pi}{5} )+i~sin(\frac{\pi}{5} )) )^5[/tex] is
[tex]\frac{1}{32} (cos(\pi)+i~sin(\pi))[/tex]
The correct answer is an option (b)
Learn more about the De Moivre's theorem here:
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The students at Midtown Middle school sold flowers as a fundraiser in September and October. In October, they charged $1.50 for each flower. The October price was a 20% increase of the September price. Part A: What was the price of the flowers in September? Part B: The seventh-grade class earned 40% of the selling price of each flower. In September, they sold 900 flowers. In October, they sold 700 flowers. Did they earn more money in September or October? How much more?
what is the value of 8^4/12
Answer:
1024/3
Step-by-step explanation:
First we want to do 8^4 which is 4096/12. Now, we can factor this equation by factoring out 4: 4(1024)/12. Cancel the common factors to get 1024/3. This can also be written as 341. 3 (the decimal 3 has a line over it) or 341 1/3
Answer:
1024/3
Step-by-step explanation:
PLS Help! This is DUE! 50 Points
[tex]log_{6}(2x-7)=4[/tex]
Answer: x = 651.5
Step-by-step explanation:
First, we can re-write the equation as = 2x - 7.
Now, we simplify 6^4 = 1296.
1296 = 2x - 7
1303 = 2x
x = 651.5
Ştiind că a . b = 2 019 şi a c= 2019, calculați a. (b-c)
Answer: a × ba × c = a (bc) = 0
a × ba × c = 2019-2019 = 0
Step-by-step explanation:
1/8 × 2/3=?
4/5 × 3/8=?
8/9 × 1 1/4= ?
5 1/3 × 2 1/4=?
1/4 × 9 1/2
3/5 × 10/21
4/5 × 3
1/8 × 4 2/3
20 × 3 1/5
2 1/3 × 2 1/3
Answer:
1/12
3/10
22/9
357/4
91/8
2/7
12/5
7/4
124
49
hope this will help you
Answer:
i dont understand the question please be more precise
Step-by-step explanation:
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers,
Express in exponential form.
logo0.001 =3
In order to write log10(0.001) = -3 in index form, we have [tex]10^{-3} = 0.001[/tex].
Exponential form of logarithmThe logarithm of a number refers to the power to which a given base is raised to give the number. In this case, the base is 10 and the index is 3. Our task is to write log10(0.001) = -3 in index form.
Recall that;
[tex]a^{x}[/tex] = PHence, to write log10(0.001) = -3 in index form we have to write, [tex]10^{-3} = 0.001[/tex]
Learn more about logarithm: https://brainly.com/question/7302008
Joey makes 20 less dollars than Jeremy. If they make a total of $72, how much does
Joey make? You must write two let statements and an equation to solve this problem.
Answer:
Joey makes 52 dollars
Step-by-step explanation:
9) A 5 inch by 7 inch picture has a frame surrounding
it on all four sides of width w. The total area of the
picture frame and picture is 80 square inches.
a) Using the diagram and information, write an
expression for the total length, including the
frame, and with an expression for the total
width, including the frame.
Length expression:
Width expression:
b) Using the expressions for total length and width, write an equation for the total
area of the rectangular picture and frame (Hint: Area = l × w).
c) Using your knowledge of factoring, solve the equation from (b) for the width of
the frame surrounding the picture.
Answer:
w = 3/2
Step-by-step explanation:
Area of a Rectangle
The 5-inch by 7-inch picture has a frame of width w surrounding all four sides.
a)
The total length of the framed picture is 7 + 2w
The total width of the framed picture is 5 + 2w
b)
The total area of the framed picture is:
At = (7 + 2w)(5 + 2w)
c) We know the total area is 80 square inches, thus:
(7 + 2w)(5 + 2w) = 80
Operating:
[tex]35 + 14w + 10w + 4w^2=80[/tex]
Simplifying:
[tex]4w^2 + 24w -45 =0[/tex]
We now write:
[tex]4w^2 + 30w - 6w -45 =0[/tex]
Factor out 2w from the first two terms and -3 from the last two terms:
[tex]2w(2w + 15) - 3(2w + 15) =0[/tex]
Factor out 2w+15
(2w + 15)(2w - 3)=0
The solutions are:
w = -15/2
w = 3/2
The only feasible solution is the positive value, thus
w = 3/2
A marathon is 32 miles long. By noon, Roger had ran 3/4 of the distance. How many more miles did he need to run to finish the race? (You may choose your strategy)
PLEASE HELP! Is the following trinomial factorable why or why not
h=-4(4t^(2)-9t+2)
Answer:
h = -4(t - 2)(4t - 1)Step-by-step explanation:
Given trinomial
h= -4(4t² - 9t + 2)Let's try to factor 4t² - 9t + 2
First find it's zeros:
t = (9 ± √9² - 4*4*2)/(2*4) t = (9 ± √81 - 32)/8t = (9 ± 7)/8t = 2 and t = 1/4So yes, it is factorable:
4t² - 9t + 2 = 4(t - 2)(t - 1/4)or4t² - 9t + 2 = (t - 2)(4t - 1)The given trinomial factored:
h = -4(t - 2)(4t - 1)Answer: Yes, this trinomial -4(4t² -9t + 2) is factorable.
It is h =(-4)(4t -1 )(t -2) converted from the explanation
[tex]y\ =\left(-4\right)\left(4x\ -1\right)\left(x\ -2\right)[/tex]
A graph of the equation is in the attachment. There are two equations, but only one graphed parabola because they are identical.
Step-by-step explanation: I am using x in place of t in this explanation, and leaving out the factored (-4) to simplify.
Using the systematic new AC Method to factor trinomials (Socratic Search) Starting with a quadratic equation in the form
y = ax² + bx + c
This involves converting the equation by multiplying the leading coefficient, a, times the constant, c
y =4x² –9x + 2
=4(x + p)(x + q)
Converted trinomial:
y' = x² –9x + 8
= (x + p')(x + q').
Here p' and q' will have the same – signs because the b term is negative and the c term is positive.
Factor pairs of ac = 8 are -1 and –8. This sum is –9 = b. Then p' = -1 and q' = -8.
Then divide the second factor by the original coefficient, 4.
Replacing the original leading factor (-4) the factored equation looks like
y = -4(4x - 1)(x - 2)
To solve for x
p =p’/a = ¼ or 4x - 1 = 0 4x = 1 x = ¹/₄
and
q ='q/a
= 8/4 = 2 OR x -2 = 0 x = 2
The second attachment shows some other ways to set up the equation without the (-4) to solve, and then replace that factor. You get the same values for x.
I hope this helps and is not too confusing. There may be other ways to factor this equation.
HELP PLEASEEE !!! 50 POINTS
Answer:
haha
Step-by-step explanation:
first off thats not 50 points
Answer:
Step-by-step explanation For the first on 5 and -4 all u do is divide y over x so it wpuld be -4/5 which would be -0.8
just keep doing the process of dividing y over x
the second 1 would be 0/3 which is 0
just keep doing this process
Can someone help me please!!
A frog jumped 9.5 meters. Approximately how many feet did the frog jump if 1 meter is equivalent to about 3.28 feet?
Help me it is due Today!!!
solve;
i) X+10%of X =22
ii)x+20%of X=rs60
iii)X+25%ofx=rs120
iv)X=rs200+50%of X
v)X=180+10%of x
question from equation and inequality
Answer:
i) 20
ii) 50
iii) 96
iv) 400
v) 200
Step-by-step explanation:
Given equations, for which we have to solve for the variable.
i)
[tex]X+$10\% of X $=22\\\Rightarrow X + \dfrac{10}{100}X =22\\\Rightarrow \dfrac{11}{10}X=22\\\Rightarrow X = 20[/tex]
ii)
[tex]x+$20\% of x = Rs.\ 60 $\\\Rightarrow x+\dfrac{20}{100}x =60\\\Rightarrow \dfrac{6}{5}x = 60\\\Rightarrow x = 50[/tex]
iii)
[tex]x+$25\% of x = Rs. 120$\\\Rightarrow x + \dfrac{25}{100}x = 120\\\Rightarrow \dfrac{5}{4}x = 120\\\Rightarrow x = 96[/tex]
iv)
[tex]X= $ Rs. 200+50\% of X$\\\Rightarrow \dfrac{50}{100}X = 200\\\Rightarrow X = 400[/tex]
v)
[tex]X=180+$10\% of X$\\\Rightarrow X - \dfrac{10}{100}X = 180\\\Rightarrow \dfrac{9}{10}X = 180\\\Rightarrow X = 200[/tex]
Write -3.625 as a mixed number
Answer:
negative three five over eight
Step-by-step explanation:
HELP!!!..........................................
Answer:
A.) the function is increasing on the interval (-∞, 0) and decreasing on interval (0,∞)
Step-by-step explanation:
La serie de el 2 12 32 62 al 1902
Answer:
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Step-by-step explanation:
need help with this geometry question please!
Answer:
6√2
Step-by-step explanation:
According to the question
The equation is
Sin(45°)=6/x
√2/2=6/x
√2x=12
x=12/√2
x=12×√2/√2²
x=12×√2/2
x=6√2
Given f(X) =-X+ 6 write an equation for f(x + 3).
Answer:
3 - x
Step-by-step explanation:
f(x) = -x + 6
f(x + 3)
Substitute (x + 3) in for x;
f(x + 3) = -(x + 3) + 6
= - x - 3 + 6
= -x + 3
A father claims about snowfall last night. First daughter tells that the probability of snowfall on a particular night is 1/8. Second daughter tells that 5 out of 6 times the father is lying! What is the probability that there actually was a snowfall
Answer:
2.08%
Step-by-step explanation:
The probability of a snowfall on any given night is 1/8.
The probability that the father is telling the truth is 1 - 5/6, or 1/6.
Then:
1/6 x 1/8=1/48=0.0208, or 2.08% ............
Write down in terms of n the expression for the nth term of the following sequences : 12,10,8,6,4
Answer:
n-2
because 12-2=10
determine the value of x for which r parallels s. then find measure of angles one and two
measure of angle one= 30-4x
measure of angle two= 50-44x
the value for which r parallels s is .....
measure of angle one.....
measure of angle two ......
Answer:
[tex] m\angle 1 = 28\degree
m\angle 2 = 28\degree [/tex]
Step-by-step explanation:
[tex]\because line\: r || line\: s\\
m\angle 1 = m\angle 2\\(corresponding \: \angle s) \\
\therefore 30 - 4x = 50 - 44x\\
\therefore 44x - 4x = 50 - 30\\
\therefore 40x = 20\\
\therefore x = \frac{40}{20}\\
\therefore x = 0.5\\
m\angle 1 = 30 - 4x = 30 - 4(0.5) = 30 - 2 \\
m\angle 1 = 28\degree \\
\implies m\angle 2 = 28\degree [/tex]
Please help ME?!!!!!!
Answer:
29 is your answer. I hope this helps you! Let me know if I got something wrong or if you need more help :)
Step-by-step explanation:
First, apply distributive property to 3(2+8). 3×2 and 3×8.
[tex]15 + (6 + 24) - 4^2[/tex]
Add 6 and 24.
[tex]15 + 30 - 4^2[/tex]
Simplify [tex]4^2[/tex]. [tex]4^2[/tex] is the same as 4×4. 4 times 4 is 16.
[tex]15 + 30 - 16[/tex]
Add 15 and 30.
[tex]45-16[/tex]
Subtract.
[tex]29[/tex]
29 is your answer. I hope this helps you! Let me know if I got something wrong or if you need more help :)
Linda left home and drove for 2 hours. She stopped for lunch then drove for another 3 hours at a rate that is 10 mph higher than the rate before she had lunch. If the total distance Linda traveled is 250 miles, what was the rate before lunch
Answer:
44 mph
Step-by-step explanation:
Given that:
Before lunch :
Time taken = 2hrs ; at speed = x mph
After lunch :
Time taken = 3hrs ; at speed = x + 10 mph
Total distance covered = 250 miles :
Distance = speed * time
(2 * x) + (3 * (x + 10)) = 250
2x + 3x + 30 = 250
5x + 30 = 250
5x = 250 - 30
5x = 220
x = 220/ 5
x = 44 mph
Rate before lunch is 44mph
The price of some Beats by Dre were reduced from $125 to $100. By what percentage was the price of the Beats reduced?
Answer:
10% of 100=10
20%of 100=20
5% of 100=5
50%=50
125
Please help!! :( Needs to be done soon
Step-by-step explanation:
12x - 6 3x+3 6(2x-1)
1 = 6 1 = 6 1 = 6
2 = 18 2 = 9 2 = 18
3 = 30 3 = 12 3 = 30
The equivalent expressions are 12x-6 and 6(2x-1)
NEED HELP ASAP FIND the missing side of the triangle
Answer:
20
Step-by-step explanation:
using Pythagoras theorem:
29²-21²= 400
√400 = 20
5. If a = -6 and b = 7, then 4a(3b+5)+2b=?
A. 638
B. -485
C. 850
D.-610
Answer:
D.-610
Step-by-step explanation:
-6 ×4 =-24
7 times 3 =21
simplify the sum. d^2-5d+6/d^2+d-6 + d^2-4d-5/d^2+3d+2
Answer:
B. (2d^2 - 3d-21)/((d+2)(d+3))
Step-by-step explanation:
(d^2 - 5d + 6)/(d^2 + d - d) + (d^2 - 4d-5)/(d^2+3d+2)
(d^2 - 5d + 6)/(d^2 + d - d) = (d-3)/(d+3)
(d^2 - 4d-5)/(d^2+3d+2) = (d - 5)/(d+2)
(d-3)/(d+3) + (d - 5)/(d+2)
Least common Multiplier of d + 3 and d + 2 is (d+3)(d+2)
((d-3)(d+2))/((d+3)(d+2)) + ((d-5)(d+3))/((d+2)(d+3))
((d-3)(d+2)+(d-5)(d+3))/((d+3)(d+2))
(2d^2 - 3d - 21)/((d+2)(d+3))
Weston used the steps below to determine the percent equivalent to StartFraction 1 Over 40 EndFraction
Step 2: StartFraction 1 Over 40 EndFraction = StartFraction question mark Over 100 EndFraction. StartFraction 1 Over 40 EndFraction = StartFraction question mark Over 100 EndFraction. Multiply both sides by 2.5.
Step 3: 1 times 2.5 = 2.5
Step 4: StartFraction 2.5 Over 100 EndFraction = 25%
What was Weston’s ethe second fraction should have been out of a multiple of 40.
Weston's second fraction should have been 0.25.
How do we convert 1/40 to a percentage?Percentage can be described as a fraction out of an amount expressed as a number out of hundred. Percentages are a measure of frequency. The sign used to denote percentages is %.
1/40 x 100 = 2.5%
To learn more about percentages, please check: https://brainly.com/question/25764815
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Im not the smartest in Math and this is giving me a headache. Any ideas?