the exponential form of the complex number \[ e^{17\pi i/60} e^{27\pi i/60} e^{37\pi i /60} e^{47 \pi i /60} e^{57 \pi i/60}\]
= (2+[tex]\sqrt{3}[/tex]) [tex]e^3^7^\pi^ i^/^6^0.[/tex]
How is the exponential form calculated?[tex]e^1^7^\pi ^i/^6^0[/tex] + [tex]e^2^7^\pi^ i^/^6^0[/tex]+⋯+[tex]e^5^7^\pi ^i^/^6^0[/tex]
=[tex]e^1^7^\pi ^i^/^6^0[/tex](1+[tex]e^\pi^ i^/^6[/tex]+....+[tex]e^4^\pi ^i^/^6[/tex])
=[tex]e^1^7^\pi ^i^/^6^0[/tex] (1−[tex]e^5^\pi ^i^/^6[/tex]) ÷ (1−[tex]e^\pi ^i^/^6[/tex])
=[tex]e^1^7^\pi ^i/^6^0[/tex] ([tex]\frac{1}{2}[/tex](2+[tex]\sqrt{3}[/tex]) + [tex]\frac{1}{2}[/tex](3+2[tex]\sqrt{3}[/tex])i)
=(2+[tex]\sqrt{3}[/tex])e17πi/60(12+([tex]\sqrt{3}[/tex]/ [tex]2[/tex]) i )
=(2+[tex]\sqrt{3}[/tex])[tex]e^1^7^\pi ^i^/^6^0[/tex] [tex]e^\pi ^i^/^3[/tex]
=(2+[tex]\sqrt{3}[/tex]) [tex]e^3^7^\pi^ i^/^6^0.[/tex]
To learn more about exponential form, refer
https://brainly.com/question/19864744
#SPJ4
1. What is the conclusion of the following conditional?
A number is divisible by 3 if the sum of the digits of the number is divisible by 3.
The number is odd.
The sum of the digits of the number is divisible by 3.
If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.
The number is divisible by 3.
Answer:
The number is divisible by 3.
Step-by-step explanation:
The conclusion is what a conditional statement ends with.
Use the expression 5x + 2y + 9 − 7 to identify: a. The terms, b. The coefficients, c. The constants.
The required answers are,
a. The terms - 5x, 27, 9, -7
b. The coefficients - 5 and 2
c. The constants - 9 and -7
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now the given expression is 5x + 2y + 9 − 7
Now the terms in the equation are 5x, 27, 9, -7
Therefore,
Terms = 5x, 27, 9, -7
Now coefficient is a number or any symbol representing a constant value that is multiplied by the variable.
So the variables in the given expressions are x and y.
And their multiples are 5 and 2, 5 is in multiplication of x and 2 is in multiplication of y.
Thus, coefficients are, 5 and 2
or, Coefficients = 5 and 2
Now th constants are the numbers that are not in multiplication with the variable. Thus, their value remains unchanged.
So in the given expression 9 and -7 are the constants that are not in multiplication with the variables.
Thus,
Constants = 9 and -7
Hence we get,
Terms = 5x, 27, 9, -7
Coefficients = 5 and 2
Constants = 9 and -7
Thus, the required answers are,
a. The terms -5x, 27, 9, -7
b. The coefficients - 5 and 2
c. The constants - 9 and -7
To learn more about expressions :
brainly.com/question/11568837
#SPJ1
At the beginning of the fall, the water level of a lake is 11 1/3
feet below normal level. After a drought, the lake's water
level dropped 7 2/3 feet. Where is the lake's current water
level in relation to its normal water level?
The lake's current water is dropped ( 55 / 3 ) feet below the normal water level.
A collection of ordered pairs having one item from each set makes up a relation between two sets. If the ordered pair (x,y) is present in the relation and the objects x and y come from different sets, then the objects are said to be connected. One kind of relation is a function.
Let x be the normal water level of the lake.
At the beginning of the fall, the level of water of the lake is [tex]11\frac{1}{3}[/tex] feet below the water level.
So, the change in water level [tex]-11\frac{1}{3}[/tex].
Then, the water level of the lake dropped [tex]7\frac{2}{3}[/tex] feet after the drought.
Again, the change in water level will be [tex]-7\frac{2}{3}[/tex].
Hence, the total change in water level will be:
[tex]=-11\frac{1}{3}-7\frac{2}{3}[/tex]
= ( - 33 + 1 ) / 3 - ( 21 + 2 ) / 3
= ( - 32 / 3 ) - ( 23 / 3 )
= ( - 55 / 3 )
Therefore, the lake's water level dropped ( 55 / 3 ) feet below the normal water level.
Learn more about feet here:
https://brainly.com/question/28315767
#SPJ9
solve: 5/3x+1/3x=21 2/3+7/3
Answer: x = 12
Step-by-step explanation:
1) Convert mixed numbers into improper fractions: [tex]21\frac{2}{3} =\frac{21*3+2}{3} =\frac{65}{3}[/tex]
New equation written as: [tex]\frac{5}{3}x+\frac{1}{3}x=\frac{65}{3}+\frac{7}{3}[/tex]
2) [tex]\frac{5}{3}x+\frac{1}{3}x=\frac{65+7}{3}[/tex]
3) Add the numbers 65 + 7 = 72: [tex]\frac{5}{3}x+\frac{1}{3}x=\frac{72}{3}[/tex]
4) Divide 72/3 = 24: [tex]\frac{5}{3}x+\frac{1}{3}x=24[/tex]
5) Multiply both sides by 3. Note: * = multiply: [tex]\frac{5}{3}x*3+\frac{1}{3}x*3=24*3[/tex]
6) Simplify: 6x = 72
7) Divide both sides by 6: [tex]\frac{6x}{6}=\frac{72}{6}[/tex]
x = 12
name the sides of the angle.
a cell phone company charges an initial price of $400 for a new phone and then $50 each month after the purchase. if c (t) is a rational function that represents the average monthly cost of owning the cell phone, what is the range of the function? r: ℝ r: (–[infinity], [infinity]) r: (0, 400) r: (50, 450)
The range of the average cost function of a cell phone that has an initial and monthly costs $400 and $50 is r:(50, 400)
Which method can be used to find the range of the average cost function?Initial price for the cell phone = $400
Charges per month after purchase = $50
The rational function representing the average monthly cost = c(t)
Required; The range of the average monthly cost function, c(t)
Solution:
The total cost of owning the cell phone, C, is therefore;
C = 400 + 50•∆tWhere;
∆t = The number of months after purchase
The average monthly cost is therefore;
[tex]c(t) = \frac{C}{ \Delta t} [/tex]
At ∆t ≈ 0, we have;
C ≈ 400
The cost for the month at ∆t ≈ 0, is therefore, c(t) = $400
At ∆t ≈ ∞, we have;
[tex] \lim\limits_{∆t→∞} \frac{400}{ ∆t} = 0[/tex]Therefore;
[tex] \lim\limits_{∆t→∞} c(t) = \frac{400+ 50× ∆t}{ ∆t} ≈ 50[/tex]
Which gives;
The range of c(t) is (50, 400)
The correct option is therefore;
r: (50, 400)Learn more about the domain and range of a function here:
https://brainly.com/question/28279808
#SPJ1
Please help
------------------------------------------
Answer:
(-5,5) and (0,-0.1) , solutions to the equation
(5,5) and (10,5) ...not solution to the inequality
Step-by-step explanation:
5,5) and (0,-0.1) ,,,they are solutions to the inequality since they lie in the required region (unshaded region)
(5,5) and (10,5) ,,,they lie in the shaded region which is the required region hence not among the required points.
URGENT!! ILL GIVE BRAINLIEST! 100 POINTS
San Diego's family took a road trip to Mount Rushmore San Diego fell asleep 44% of the way through the trip if the total length of the trip was 400 miles how many miles have they traveled when he fell asleep
The number of miles that they traveled when San Diego fell asleep will be 176 miles.
How to illustrate the information?It should be noted that from the information, San Diego's family took a road trip to Mount Rushmore and San Diego fell asleep 44% of the way through the trip.
In this case, the total length of the trip was 400 miles.
Therefore, the number of miles that they traveled when he fell asleep will be:
= Percentage × Total miles
= 44% × 400
= 0.44 × 400
= 176 mile
Therefore, the number of miles that they traveled when San Diego fell asleep will be 176 miles.
Learn more about percentages on:
brainly.com/question/24877689
#SPJ1
3. Jason and Eric discovered that the
means of their grades for the first
marking period in their math class
were identical. They also noticed that
the standard deviation of Jason's
grades is 20.7, while the standard
deviation of Eric's grades is 2.7. Which
statement must be true?
(1) In general, Eric's grades were lower
than Jason's grades.
(2) Eric's grades are more consistent than
Jason's grades
(3) Eric had more failing grades during the
marking period than Jason had.
(4) The median for Eric's grades is lower
than the median for Jason's grades.
Answer:
2
Step-by-step explanation:
MAD stands for mean absolute deviation.
The larger the MAD, the more spread out the data set is.
This means that Jason’s grades must vary more.
Q2) 1,-3, 9, -27, 81, -243, ...
Bobby was absent from school and called you to find out what he missed. You say to find the next
numbers in pattern 2 you would
Solving the Question
We're given:
1,-3, 9, -27, 81, -243, ...The first term is 1. It appears that, to get each consecutive term, we have to multiply the previous term by -3.
i.e. 1 x -3 = -3-3 x -3 = 99 x -3 = -27Therefore, to get each the next two terms, we have to multiply the previous term by -3.
AnswerTherefore, to get each the next two terms, we have to multiply the previous term by -3.
i neeed help 5(9/12−14)+0.5
can u solve
Answer:
[tex] \sf \large \: \frac{ - 263}{4} [/tex]
Step-by-step explanation:
5(9/12−14)+0.5
=5(3/4−14)+0.5
=5(−53/4)+0.5
=−265/4+0.5
=−263/4
A waitress is filling coffee mugs at a diner. She pours 350 milliliters into each of the 5 mugs from a full pot of coffee. If her coffee pot holds 2.5 liters, how many milliliters does she have left in her pot?
Answer:750 milliliters
Step-by-step explanation:
2.5 liters=2500 milli
5*350=1750 milli
2000-1750=750 milli
Please help
Isolate a variable in each system. You may need to use the distributive property to simplify the equation. Show your work.
Answer:
it's true, not false.
Step-by-step explanation:
it's true, not false.
Two boats are traveling in a canal in opposite directions, where x represents the distance, in feet, between the boats. the equation 4(x 1) = 4x 4 models the paths of the boats. solve for x. no solution 0 all real numbers 1
Answer: the answer would be all real numbers
Step-by-step explanation:
I got it right on the test
which of the following steps were applied to ABCD to obtain A'B'C'D'?
There is a translation of 3 units to the right and 4 units upwards to translate ABCD into A'B'C'D', then the correct option is C.
"Shifted 3 units right and 4 units up"
which of the following steps were applied to ABCD to obtain A'B'C'D'?
Let's just compare one of the vertices to identify the translation applied.
We can see that the coordinates of vertice A are (2, 3).
While the coordinates of the vertice A' are (5, 7)
If we take the difference between these two coordinate pairs, we will et
A' - A = (5, 7) - (2, 3)
Remember that this difference is computed component to component, so we have:
(5, 7) - (2, 3) = (5 - 2, 7 - 3) = (3, 4)
From this we can conclude that we hade a translation of 3 units to the right and 4 units upwards to translate ABCD into A'B'C'D', then the correct option is C.
"Shifted 3 units right and 4 units up"
If you want to learn more about transformations:
https://brainly.com/question/4289712
#SPJ1
if m<4=35 degrees, find m<2 and m<3
35, ∠2 and ∠4 are alternate interior angles, so m∠2 = m∠4.
What is alternate interior angles?
Two angles that are on the interior of and, but on different sides of the transversal, are said to be alternate interior angles. The alternate interior angles theorem states that the alternate interior angles must be congruent if two parallel lines are cut by a transversal.Given
m∠4=35
From the image given, angle 2 and angle 4 lie on opposite side of the line that intercepts the two parallel lines, AB and CD. Angle 2 and angle 4 both lie within the parallel lines.
Therefore, ∠2 and ∠4 are alternate interior angles.
Thus,
m ∠2 = m∠4 (alternate interior angles theorem)
since m∠4 = 35°
therefore m∠2 = 35°
Learn more about alternate interior angles
brainly.com/question/2656732
#SPJ9
Find the value of g(−6) if g(x)=−2x+3
Answer: g(-6)=15
Step-by-step explanation:
(x)= -6G(-6)=-2(-6)+3G(-6)=12+3G(-6)=15Broo someone help pllss
========================================================
Explanation:
15 - 2.5x is the same as 15 + (-2.5)x
Then we can swap the terms to get -2.5x+15
Therefore, the original equation is the same as -2.5x+15 = 40
To solve this equation, we follow PEMDAS in reverse. So instead of starting with the "P", we start with the "S". There's no subtraction operations to undo, so we move onto the "A". There is an additional operation to undo, which is the +15
To undo the +15, we subtract 15 from both sides
-2.5x+15 = 40
-2.5x+15-15 = 40-15
-2.5x = 25
The next step after this would be to divide both sides by -2.5 to undo the multiplication. The -2.5x means "-2.5 times x".
Find the dimensions and maximum area of a rectangle if its perimeter is 12
Is the answer 48?
Please help!
find the area of the triangle.
Answer:
2x^2 + 8x
Step-by-step explanation:
Area of triangle: base x height / 2
So: 2x(2x+8)/2
We cancel 2 so:
x(2x+8)
then = 2x^2 + 8x
Question 4 of 10
Which choice is equivalent to the product below for acceptable values of x?
√7x √x+2
The equivalent choice of √7x √x+2 is x√7 + 2√7x
How to determine the equivalent choice?The product expression is given as:
√7x √x+2
Rewrite as:
√7x * (√x + 2)
Expand the bracket
√7x^2 + 2√7x
Take the square root of x^2
So, we have
x√7 + 2√7x
Hence, the equivalent choice of √7x √x+2 is x√7 + 2√7x
Read more about equivalent expressions at
https://brainly.com/question/2972832
#SPJ1
PLEASE I NEED HELP TO PASS
Answer:
x = 17
Step-by-step explanation
the two interior angles add up to the exterior.
What is the value of x 2,8,9,7.6,x the mean is 6
The value of X is 3.4
Disclaimer:
We will consider arithmetic mean in this case as which mean is not mentioned.
The total number of terms are 5
thus, arithmetic mean= 6
6= (2+8+9+7.6+x)/5
30 = 26.6+x
x=30-26.6=3.4
Thus the value of X is 3.4
#SPJ9
Main Answer:x= 3.4
Concept and definitions should be there
The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers.
To calculate it:
• add up all the numbers,
• then divide by how many numbers there are.
Given data
the value of x 2,8,9,7.6,x the mean is 6
Solving part
As we know that
mean =(sum of the terms)/(Number of terms)
By substituting the values, we get
6=(2+8+9+7.6+x)/5
30= x+26.6
x= 30-26.6
x= 3.4
Final Answer: Thusx= 3.4 is the correct answer.
To learn about more about the visit:brainly.com/question/18590508 #SPJ9.
18:3:9 in it's simplest form
23+11x-5=39
What’s the answer
For each of the graphs below choose inequality that best represent the graph. explain your reasoning.
a. This graph represents an inequality that has:
A. No solution.
B. All real numbers as the solution.
One such inequality is:
A. x > x + 1.
B. x + 2 < 1.
C. x + 2 > 1.
D. x < x + 1.
Because solving it yields ___, an inequality which is:
A.True.
B.False.
for all real numbers x.
(Type an inequality. Simplify your answer).
The desired inequalities are given as follows:
A. A. x > x + 1. because solving it yields an inequality that is False for all real numbers x.
B. D. x < x + 1, because solving it yields an inequality that is True for all real numbers x.
Which inequality represents graph A?For graph A, as nothing is plotted on the line, we have a inequality with no solution.
The successor of a number(number plus 1), will always be greater than the number, hence the inequality that has no solution is:
A. x > x + 1. because solving it yields an inequality that is False for all real numbers x.
Which inequality represents graph B?For graph B, as the entire line is plotted, we have a inequality with all real values as solution.
From the same logic above, of the successor, the correct option is:
D. x < x + 1, because solving it yields an inequality that is True for all real numbers x.
More can be learned about inequalities at https://brainly.com/question/25235995
#SPJ1
Can someone please help mee (20 points
brainliest!!!)
Answer:
I may have mixed up the meaning of the variables...
Step-by-step explanation:
Every additional 1 card sold, price decrease $0.05 Known point, (6, 280). x is price, p is ... number of cards sold.
The measure of an angle is 81.1°. What is the measure of its supplementary angle?
Answer: 98.9°
Step-by-step explanation:
Supplementary angles are two angles whose measures add up to 180 degrees.
=180-81.1
=98.9°
| 7 + m | - 4 > 8
A m > 9 or m < -15
B m > -2 or m < -20
C m > 5 or m < -19
D m > 7 or m < 0
Answer:
C m > 5 or m < -19
Step-by-step explanation:
i took the test