Can you help me find all the seventh roots of unity? what do they look like graphed?
Answers
Answer:
There are seven seventh roots of unity, e2πki7 , all on the unit circle, r=1 above.
The first one is at θ=2π7=360∘7=5137 ∘ , and there are others at 4π7,6π7,8π7,10π7,12π7 and of course at 0 radians, i.e. unity itself.
How to find?
There are 4 fourth roots of unity and they are 1, i,−1 and−i
Each of the roots of unity can be found by changing the value of k k k in the expression e 2 k π i / n e^{2k\pi i/n} e2kπi/n. By Euler's formula, e 2 π i = cos ( 2 π ) + i sin ( 2 π ) = 1.
Related Questions
The sum of the cubes of 3 numbers which are in the ratio 1:2:3 is 7776. Find the numbers
Answers
the numbers - [tex]x,2x,3x[/tex]
[tex]x^3+(2x)^3+(3x)^3=7776\\x^3+8x^3+27x^3=7776\\36x^3=7776\\x^3=216\\x=6\\2x=12\\3x=18[/tex]
6,12,18
Line R: 2x + 2y = 18 Line M: x + y = 9 Which statement is true about the solution to the set of equations?
Answers
Answer:
Step-by-step explanation:
2x + 2y = 18
-2x -2y = -18
0 = 0
infinite solution of equations
Para la función f(x) = x + 6, ¿ cuál es
resultado de la función si x=2 ?
Answers
Answer:
f(x) = 8
Step-by-step explanation:
Como x = 2, simplemente lo sustituiría por x en la función y sumaría.
f(x) = 2+6
f(x) = 8
-104=8x what is the answer?
Answers
Answer:
x=-12
Step-by-step explanation:
8x=-104
8x÷8=-104÷8
x=-104÷8
x=-13
Step-by-step explanation:
8x:-104
8÷8x:-104÷8
x:13
Graph the function f(x) = 2√x+2 .
All help is appreciated!
Answers
Answer:
Not sure which was your intended, but here are two options.
Step-by-step explanation:
HELP ASAP ILL GIVE BRAINLIST
In a study on the placebo effect on 100 students, 64 were found to perform better on tests after taking a fake pill to improve concentration. What is the experimental probability the placebo pill induced better concentration on the student exams?
Answers
Answer:
16/25 or 64%
Step-by-step explanation:
In this problem we see that 64 out of the 100 students did better on the exams. So, to find the answer we must find the percentage form of 64 out of 100.
Step one:
what exactly is 64 out of 100? Well, in the math world when we see 'out of' we know that means 'divided by'. So, 64 out of 100 is 64/100.
Step two:
now we have to turn 64/100 into a percentage. We know that 1/100 is 1% so lets multiply 1 by 64. 64*1 = 64. This means that 64/100 = 64%.
I'm not 100% sure what form you need your answer in but if you need it in percentage for the answer is 64%. If you need your answer in a fraction form the answer would be 64/100 or 16/25 if we simplify the answer.
I hope this helps!!
find the area of quadrilateral ABCD
Answers
Answer:
A ≈ 28.5
Step-by-step explanation:
a, b, c
P = a + b + c
Semiperimeter s = [tex]\frac{a+b+c}{2}[/tex]
A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
~~~~~~~~~~~~~~~
[tex]P_{ABC}[/tex] = 4.3 + 2.89 + 6.81 = 14
s = 14 ÷ 2 = 7
[tex]A_{ABC}[/tex] = [tex]\sqrt{7(7-4.3)(7-2.89)(7-6.81)}[/tex] = √14.75901 ≈ 3.84
[tex]P_{BCD}[/tex] = 8.59 + 7.58 + 6.81 = 22.98
s = 22.98 ÷ 2 = 11.49
[tex]A_{BCD}[/tex] = [tex]\sqrt{11.49(11.49-8.59)(11.49-7.58)(11.49-6.81)}[/tex] = √609.7343148 ≈ 24.6928
[tex]A_{ABCD}[/tex] = 3.84 + 24.6928 ≈ 28.5
FA is a line, line segment, and a ray
Answers
Answer:
False, FA can't be all three. (See explanation below to see which one FA is.)
Brainliest, please!
Step-by-step explanation:
A line has goes on and on forever in two different directions.
A line segment has two endpoints and does not go on and on forever.
A ray has one endpoint and goes on and on forever in one direction.
It is impossible for FA to be all three, or two even.
if the side length of a square can be represented by 4x + 4 and its area is 1024 square units, find the value of x
Answers
Answer:
x = 7
Step-by-step explanation:
Since it’s the area of a square, we can simply do square root of 1024. (Because to get area of square you do side x side). Which is 32.
So basically 4x + 4 = 32... x = 7
Answer:
x = 7
Step-by-step explanation:
A = 1024
side length of a square = 4x + 4
A = s²
s = √A
s = √1024
s = 32
using the side length to get the value of x
s = 32
4x + 4 = 32
4x = 32 - 4
x = 28 / 4
x = 7
check:
A = side length * side length
A = (4x + 4) * (4x + 4)
A = (4*7 + 4) * (4*7 + 4)
A = 32 * 32
A = 1024 ok
Each cat at the animal shelter gets
5/6 pound of food. Allie has 9 1/2
pounds of cat food. How many cats
can Allie feed?
A: 7
B:9
C: 11
D:13
Answers
Answer: C : 11
Step-by-step explanation:
So divide 9 1/2 by 5/6
So the answer is 11,4 and it round off to 11
So the answer is 11 option C
A police car is located 40 feet on a small straight road perpendicular to main highway. A red car is driving along a highway in the direction of an intersection with that small road and is 180 feet away from the intersection. The police radar reads that the distance between the police car and the red car (this distance is straight between them - not on either road) is decreasing at a rate of 100 feet per second. How fast is the red car actually traveling along the road
Answers
Answer:
the red car is traveling at 102.44 ft/s along the road
Step-by-step explanation:
From the given information:
Let consider p be how far the car is up the road and q be how far the police is off the road.
Also, suppose that r is the distance between the police and the car.
Then, we can have a right triangle in which we can use the Pythagorean Theorem to calculate the r (distance between the cop and the car)
NOW,
p² + q² = r²
r² = 40² + 180²
r² = 1600 + 32400
r² = 34000
r = [tex]\sqrt{34000}[/tex]
r = 184.39
If we consider q' to be how fast the car is traveling down the road.
And, p' be how fast the police is traveling toward the road.
r' be how fast the distance between the police and the car is changing.
then , the derivative of our equation, p² + q² = r² with respect to time can now be:
2p(p') +2q(q') = 2r(r')
p(p') +q(q') = r(r')
By replacing our values; we have:
40(0) +180(y') = [tex]\sqrt{34000} \times 100[/tex] (given that the police is not moving p' =0)
180(y') = [tex]\sqrt{34000} \times 100[/tex]
[tex](y') = \dfrac{\sqrt{34000} \times 100}{180}[/tex]
[tex](y') = \dfrac{184.39 \times 100}{180}[/tex]
[tex]\mathbf{(y') = 102.44 \ ft/s}[/tex]
the red car is traveling at 102.44 ft/s along the road
What happens when you subtract a greater positive
number from a lesser positive number?
Answers
Answer:
You get negatives
Step-by-step explanation:
Imagine that you have 67 and you need to subtract that by 107
you would do 67-107 or 107-67 then add a negative symbol.
67 - 107 = -40
Please help me solve this. With Reasoning
6 2/5 - 4 2/3
Answers
Answer:
1 and 11/15.
Step-by-step explanation:
To solve, we can separate the integers from the fractions.
(6 - 4) + (2/5 - 2/3)
= 2 + (6/15 - 10/15)
= 2 + (-4/15)
= 1 + 15/15 - 4/15
= 1 + 11/15
= 1 and 11/15
Hope this helps!
which has a steeper slope y=-2x or y=-3x
Answers
Answer:
y=-3x
Step-by-step explanation:
3>2. It doesn't matter if some or all of the numbers are negative.
Answer: y = -3x has the steeper slope
==========================================
Explanation:
Any linear equation is of the form y = mx+b, where m is the slope.
For y = -2x, the slope is -2. For y = -3x, the slope is -3.
We just look at the number to the left of x to find the slope.
To figure out which slope is steeper, we simply look to see which slope value is furthest from 0 on the number line. A slope of 0 itself is completely horizontal and flat. As the slope value moves away from zero, in either positive or negative direction, then the slope gets steeper and steeper.
In short, a slope of -3 is more steep compared to a slope of -2. Therefore, y = -3x is the answer.
The graph below helps visually confirm that y = -3x is indeed steeper. We drop one extra unit down each time we move to the right one space.
Darnell goes to the movies with his friends. The receipt on his phone
shows the cost of the tickets after a discount. What is the price of a ticket before the discount?
Answers
answer
8(+ - 0.75)=62.00
the price of the tickets before is 8.50
Step-by-step explanation:
8(+-.075)=62.00
+-0.75+0.23
+=8.50
3) Find f(3) for the function below.
f(x) = 2x² – 3x
Answers
Answer:
9
Step-by-step explanation:
f(x) = 2x² – 3x
Let x=3
f(3) = 2 * 3^2 - 3*3
= 2 *9 - 9
= 18-9
= 9
Answer:
f(3) = 9Step-by-step explanation:
[tex]f(x) = 2x^2 -3x\\ f(3) = ?\\\\ f(3) = 2(3)^2 -3(3)\\ f(3) = 2(9) - 9\\ f(3) = 18- 9\\ f(3) = 9[/tex]
Find the surface area of a
sphere with a diameter of
15 in.
Can someone please explain how?
Answers
Answer:
About 706.5 square inches.
Step-by-step explanation:
Surface area of a sphere is: [tex]SA=4\pi r^2[/tex]
The radius is half the diameter. So, the radius of the given sphere is 7.5 in.
15/2 = 7.5
Find the surface area:
I use 3.14 for pi.
[tex]SA=4*3.14*7.5^2\\\\SA=4*3.14*56.25\\\\SA=12.56*56.25\\\\\boxed{SA=706.5}[/tex]
The surface area is about 706.5 square inches.
Hope this helps.
Answer:
SA=706.86 in²
Step-by-step explanation:
surface area of a sphere = 4πr²
radius r=d/2=15/2=7.5
SA=4(π)(7.5)²
SA=706.86 in²
hello :) why is the first one wrong?
Answers
Answer:
The cube only belongs to the x and not 2x.
The statement will only be true if there is a bracket around the 2x.
log₃(2x)³= 3log₃2x
logarithm power rule:
logₐ(x)^y = y ∙ logₐ(x)
Answer:
see explanation
Step-by-step explanation:
Given
[tex]log_{5}[/tex] 2x³
= [tex]log_{5}[/tex] 2 + [tex]log_{5}[/tex] x³
= [tex]log_{5}[/tex] 2 + 3[tex]log_{5}[/tex] x
A piece of blue yarn is 5/ 3/7 yards long. A piece of pink yarn is 5 times as long as the blue yarn. How much longer is the pink yarn than the blue yarn?
Answers
Answer:
27 1/7
Step-by-step explanation:
Multiply 5×5=25 and afterwards multiply 3/7×5=2 1/7
Q.5(b) The population {(P) in millions} of a country is estimated by the function, P=125e0.035t, t = time measured in years since 1990. (a) what is the population expected to equal in year 2000 (b) determine the expression for the instantaneous rate of change in the population (c) what is the instantaneous rate of change in the population expected to equal in year 2000.
Answers
Answer:
Hello,
Step-by-step explanation:
Q.5(b) The population {(P) in millions} of a country is estimated by the function, P=125e0.035t, t = time measured in years since 1990. (a) what is the population expected to equal in year 2000 (b) determine the expression for the instantaneous rate of change in the population (c) what is the instantaneous rate of change in the population expected to equal in year 2000.
[tex]P(t)=125*e^{0.035*t}\\a)\\P(2000)=125*e^{0.035*(2000-1990)}=177.38...\\\\b)\\P'(t)=125*0.035*e^{0.035*t}\\\\c)\\\\P'(2000)=125*0.035*e^{0.035*(2000-1990)}=6.2084...[/tex]
what is the greatest common factor of 48,24,and 32
Answers
Answer:
8
Step-by-step explanation:
gcf
choose the function where the graph is given below
Answers
Answer:
B
Step-by-step explanation:
You could've graphed your choices and find which one is a perfect match.
This equation shows how the total number of necklaces Denise owns is related to the amount of money she spends on additional necklaces.
n = d + 74
The variable d represents the amount of money she spends on additional necklaces, and the variable n represents the total number of necklaces she owns. With $16 to spend on new necklaces, how many total necklaces can Denise own?
Answers
please mark brainliest
What is the percent change from 75 to 14?
Answers
Answer:
the change is -81.33% (the 3 is repeating)
the volume of a cube is 125cm cubed. The area of a square is 64cm squared. How does the length of one edge of the cube compare to the length of one side of the square? Explain
Answers
Answer:
One edge of the cube is 5 cm, one edge of the square is 8 cm, so the edge of the cube is 3 cm shorter than the edge of the square.
Step-by-step explanation:
The volume of the cube is found by the formula
V = s³,
where s is the side length (called the edge in this problem)
Since V = 125 cm³, we can take the cube root of 125 to find the edge length.
The cube root of 125 is 5, ( 5³ = 125)
So the edge of the cube is 5 cm
The are of a square is found by the formula
A = s² ,
where s is the side length (called the edge in this problem)
Since A = 64 cm², we can take the square root of 64 to find the edge length.
The square root of 64 is 8 (8² = 84)
So the edge of the square is 8cm
Comparing the two edges tells us that the edge of the cube is 3cm shorter than the edge of the square.
How do you simplify the square root of 64a^6
Answers
Answer:
it's (2a)^6
Step-by-step explanation:
so first you need to write 64a^6 in exponential form simplifying it to 2^6a^6
then multiply the bases which gives you (2a)^6
sorry if I didn't explain it very well but I hope I helped!
Answer:
[tex]\sqrt{64a^{6} } = 8a^{3}[/tex]
8*8 = 64
a^3*a63 = a^6
Step-by-step explanation:
(07.06A) Which scenario best matches the linear relationship expressed in the equation y = 13.50x + 300? Bobby has $300 in the yearbook fund and spends $13.50 on each yearbook. Bobby has $13.50 in the yearbook fund and spends $300 on each yearbook. Bobby has $300 in the yearbook fund and earns $13.50 for each yearbook sold. Bobby has $13.50 in the yearbook fund and earns $300 for each yearbook sold.
Answers
Answer:
Bobby has $300 in the yearbook fund and earns $13.50 for each yearbook sold.
Step-by-step explanation:
The value of the expression when x is zero is 300. For each increment of 1 in x, the value of the expression increases by 13.50. This best matches the scenario ...
Bobby has $300 in the yearbook fund and earns $13.50 for each yearbook sold.
5^-4 over 5^3
simplify
A. 5^7
B. 5^-1
C. 1/5
D. 1/5^7
Answers
Answer:
D is the correct answer.
Place the two large triangles around the square to form a triangle, a parallelogram ,and a trapezoid .Please answer it step by step
Answers
Answer:
Step-by-step explanation:
A sailboat has a large sail in the shape of a right triangle. The height of the sail measures 17 yards, and the width measures 8 yards
Answers
Answer:
68
Step-by-step explanation:
17x8 = 136
136/2 = 68