What is 5 Left-bracket cosine (StartFraction pi Over 4 EndFraction) + I sine (StartFraction pi Over 4 EndFraction) right-bracket raised to the 3rd power?
Answers
Answer:
C
Step-by-step explanation:
I took it on edg 2020
The Complex Alternative form to the expression (5[cos(π/4) + i sin(π/4)])^3 is given as: (Option C).
What is a complex Alternate form?A complex number of equations will take the form x + yi, where x and y are real numbers and i is an indeterminate that satisfies the rule i² = -1.
Hence, the solution to the above is given as follows:
Step 1 - Ludooph's number pi is given as:
π ≈ 3.14159265
Step 2 - Divide 3.14159265/4
= 0.78539816
Step 3
Cos (0.78539816)
= 0.70710678
It is assumed that the trigonometric angle argument is in radians.
Step 4
Divide: 3.14159265 / 4
= 0.78539816
Step 5 - find the Sin of the result of step 4
sin(0.78539816)
= 0.70710678
It is assumed that the trigonometric angle argument is in radians.
Step 6
Multiply i by the result of Step No 5
= i * 0.70710678
= 0.7071068i
Step 7 - Add the result of step no. 3 and the result of step number 6
= 0.70710678 + 0.7071068i
= 0.7071068+0.7071068i
Step 8 Multiply 5 by the result of step 7
= 5 * (0.7071068+0.7071068i)
= 5 * 0.70710678118655 + 5 * 0.70710678118655i
= 3.53553391+3.53553391i
= 3.53553391 +i(3.53553391)
= 3.5355339+3.5355339i
Step 9 - Exponentiate the results of Step 8 to the third power:
= (3.5355339+3.5355339i) ^ 3
= (5 × ei π/4)3 = 53 × ei 3 × π/4
= 125 × ei 3π/4
= -88.3883476+88.3883476i
If left in the Alternate Complex form, we have:
125[cos(3π/4) + i sin(3π/4)]
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Related Questions
PLEASE HELP!!!! What has to be true if you want to solve a quadratic?
Answers
Answer:
The quadratic formula helps you solve quadratic equations, and is probably one of the top five formulas in math. Then the formula will help you find the roots of a quadratic equation, i.e. the values of x where this equation is solved.
Find the slope of the line through each pair of points. (2,5) and (6, 8)
Answers
Y2-Y1 divided by X2-X1
8-5=3
———-
6-2=4
so your slope is 3/4
Please help me out with this
Answers
Answer: x=42
Step-by-step explanation:2x+2x+12=4x+12=180 so 180-12=4x
The expression 13b−13 factored is
Answers
Answer:
13(b - 1)
I hope it is. tell me if I'm wrong
Write the equation of the line passing through the point (-2, 2) that is parallel to the line y = 2x + 3
Answers
Hi there! :)
[tex]\large\boxed{y = 2x + 6}[/tex]
A line that is parallel to y = 2x + 3 must have the same slope of 2. Therefore:
We can use the given point as well as the slope-intercept formula y = mx + b to solve.
Plug in the x-coordinate for "x" and y-coordinate of the point into "y":
2 = 2(-2) + b
2 = -4 + b
6 = b
Rewrite the equation:
y = 2x + 6
Help pls its just math :(
Ik it sucks I hate math too, pls help tho
Answers
Answer: x = -1
Step-by-step explanation: Insert all the numbers into x, and when you insert -1 to x, you get 40.
Answer:
x = - 1
Step-by-step explanation:
Given
- 4(3x - 7) = 40 ( divide both sides by - 4 )
3x - 7 = - 10 ( add 7 to both sides )
3x = - 3 ( divide both sides by 3 )
x = - 1
The amount a basketball coach spends at a sporting goods store depends on the number of basketballs the coach buys. The situation is represented by the function rule a=16b.
A.) Make a table of values and graph the function rule. Is the graph continuous or discrete? Explain.
B.) Suppose the coach spent $128 before tax. How many basketballs did she buy?
Answers
Answer: 0,16,32,48,64
Step-by-step explanation: the equation 16b means you will multiple 16 by whatever is in the b box. For the first b is equal to 0 so 16x0 = 0, the second b is equal to 1 so 16x1 = 16
The discrete graph for the function rule is plotted and the coach will buy 8 basketballs for $128.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is the amount which a basketball coach spends at a sporting goods store and it depends on the number of basketballs the coach buys. The situation is represented by the function rule a = 16b.
The given equation is -
a = 16b
where -
[a] represents the amount spend by the basketball coach.
[b] represents the number of basketballs buyed.
PART - AThe table is given as follows -
[b] [a]
0 0
1 16
2 32
3 48
4 64
The graph of the representing the function rule - a = 16b is attached with the answer. The graph is discrete as number of basketballs cannot exist in fractions. This means the possible values of [b] will be whole numbers only.
PART - B
If coach spent $128, then the number of footballs bought will be -
b = 128/16
b = 8
Number of footballs bought were 8.
Therefore, the discrete graph for the function rule is plotted and the coach will buy 8 basketballs for $128.
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the awnser is 15 i did it by steep like there is 16 ones then you multiply and thye awnser i got was 15.
there you go :D
Answers
Answer:
What is the question
Step-by-step explanation:
Upload a picture
-49b + 35
What is the answer simplified, without actually solving the problem?
Answers
Answer:
-24b
Step-by-step explanation:
I think (Please give me Brainliest!)
Simplify the expression.
: 8 - 2(3)
Answers
Answer: the answer is just 2
What is 7x1??????????????????????????
Answers
Answer:
7
Step-by-step explanation:
A small bookstore is downsizing and has lost employees at a steady rate. The company started with 30 employees but lost 3 employees each month for the past 4 months. Identify key features of the graph of this function.
Answers
Answer:
Join Zoom Meeting
Meeting ID: 385 546 8984
Passcode: icecream4
Step-by-step explanation:
How do you graph y = x + 1 and y = -x + 21
Answers
Answer:
whatever x is, add one and that is y.
-x? add 21 and that is also y.
do not change x, and plot the point.
A translation of (x - 4, y + 5) means
Answers
Answer:
it means left 4 and up 5
Step-by-step explanation:
I took the test
The Newtown Telephone Company advertises that if you use their 10-10 service, you will always pay only 9c per minute, no matter where you call within the country. Its major rival, Tryus Telephone Company, charges only 3c per minute, but you must pay a 36 c "connection fee" per call.
Create a cost equation for each telephone company where y is the total cost for each phone call (in cents), and x is the number of minutes the phone call lasts. Write a system of equations.
Answers
Answer:
y = 9x cents
y = (36 + 3x) cents
Step-by-step explanation:
Given that:
Newtown telephone company :
Fee per minute = 9c
Tyrus company :
Fee per minute = 3c
Connection fee = 36c
Cost equation :
y = total cost for each phone call:
x = minutes phone call last ;
Newton Company :
y = (fee per minute * minute phone call last)
y = 9 * x
y = 9x cents
Tyrus Company:
y = (connection fee + (fee per minute * minute phone call last))
y = (36 + (3 * x))
y = (36 + 3x) cents
You are adding to rational numbers with different signs. How can you tell if the sum will be positive, negative, or zero? #24
Answers
Answer:
it would be positive
Step-by-step explanation:
Answer:
Step-by-step explanation:
A positive plus a negative equals a negative:
4 + (-3) = 1
A positive plus a positive equals a positive:
4 + 4 = 8
A negative plus a negative equals a negative:
(-2 )+ (-2) = -4
If two number have the same absolute value, they will equal zero:
-3 + 3 = 0
- 2 + 2 = 0
Tell me if this is correct?
How many parts is the
whole divided into?
Solve this too?
Divided into ____ Equal Parts
Answers
Answer:
Divided into five equal parts
Linda will spend more than $26 on gifts. So far, she has spent $12. What are The possible additional amounts she will spend?
Answers
She will need to spend more than $14 now
Answer:
Step-by-step explanation:
14
If a person rolls two dice, what is the probability of getting a five as the sum of the two dice?
Answers
Answer:
The probability of throwing any given total is the number of ways to throw that total divided by the total number of combinations (36)
The length of a tarpaulin is 3ft. more than thrice its width and its area is 126ft². What is the length of the tarpaulin?
Answers
Answer:
Length = 22 ft
Width = 6 ft
Step-by-step explanation:
Let the width of the tarpaulin be x meters.
Therefore, length = 3x + 3
Area of tarpaulin = 126 ft²
[tex]x(3x + 3) = 126 \\ \\ 3x(x + 1) = 126 \\ \\ {x}^{2} + x = \frac{126}{3} \\ \\ {x}^{2} + x = 42 \\ \\ {x}^{2} + x - 42 = 0 \\ \\ {x}^{2} + 7x - 6x - 42 = 0 \\ \\ x(x + 7) - 6( {x + 7)} = 0 \\ \\ (x + 7)(x - 6) = 0 \\ \\ x + 7 = 0 \: \: or \: \: x - 6 = 0 \\ \\ x = - 7 \: \: or \: \: x = 6 \\ \\ \because \: x \: is \: side \: length \\ \therefore \: it \: can \: not \: be \: negative \\ \implies \: x \notin - 7 \\ \\ \implies \: x = 6 \\ \\ 3x + 3 = 3 \times 6 + 3 \\ \\ 3x + 3 = 18 + 3 \\ \\ 3x + 3 = 21 \\ \\ length \: of \:the \: tarpaulin \: = 21 \: ft \\ \\ width \: of \: the\: tarpaulin \: = 6 \: ft \\ [/tex]
Is -4pi a rational number
Answers
Answer:
no
Step-by-step explanation:
Pi is irrational
Answer:
No it is a irrational number
Step-by-step explanation:
-4pi is not a whole number, integer number, or a rational number. It is only a irrational number.
ill give the right answer brainliest!
Answers
Answer:
C=84, D=80,b=99 and a=81
Step-by-step explanation:
In a quadrilateral, it's opposite measurements has to be equal to 180 degrees. So, for example if one side is 100 then the opposite side has to be equal to 80 so that if you add them there sum would be 180 degree.
Sorry, but I am not sure about a but you can try 81 degrees if you want. Hope this helps you!
solve for u and simplify the fraction 2/5u=4
Answers
Answer:
u=10 the fraction simplified once you plug in u would be 4
7x-5=8(x*3) what value of x makes this equation true
Answers
The given equation is:
[tex]\displaystyle 7x-5=8(x+3)[/tex]
The first step you need to do is open the parentheses and distribute the 8 to x+3. It will be 8 times x and 3 times x.
[tex]8(x+3)=8 \times x+ 8 \times 3\\\\8 \times x=8x\\8 \times 3=24[/tex]
[tex]8(x+3) \rightarrow 8x+24[/tex]
Rewrite the equation:
[tex]7x-5=8x+24[/tex]
Now you need to move one of the variables to the other side.
If you move 7x to the other side, then:
You can move the variable by doing the opposite of it. Since 7x is positive, you can move it by subtracting 7x, which is negative. Subtract 7x on both sides:
[tex]7x-5-7x=8x+24-7x\\-5=x+24[/tex]
Now you need to leave x alone. x is being added to 24, so remove it by subtracting both sides by 24. Remember that when you're subtracting from a negative number, you're actually adding while keeping the negative sign.
[tex]-5-24=x+24-24[/tex]
Subtract:
[tex]\bf-29=x[/tex]
If you move 8x to the other side, then:
8x is positive, so you can move it by subtracting 8x, which is negative. Subtract 8x on both sides:
[tex]7x-5-8x=8x+24-8x\\-x-5=24[/tex]
You need to leave the variable alone, so move -5 to the other side. You can do this by adding 5 to both sides.
[tex]-x-5+5=24+5\\-x=29[/tex]
Lastly, x is negative, but you're looking for the value of positive x. Divide both sides by -1 to remove the negative sign.
[tex]\displaystyle \frac{-x}{-1} =\frac{29}{-1}[/tex]
Remember that a positive number divided by a negative number is negative. Divide:
[tex]\bf x=-29[/tex]
The answer to your question is x = -29.
Step-by-step explanation:
Question:-Solve for x
[tex]\\ \tt{:}\leadsto 7x-5=8(x+3)[/tex]
SOLUTION:-[tex]\\ \tt{:}\leadsto 7x-5=8(x+3)[/tex]
[tex]\\ \tt{:}\leadsto 7x-5=8x+24[/tex]
[tex]\\ \tt{:}\leadsto 7x-8x=24+5[/tex]
[tex]\\ \tt{:}\leadsto -x=29[/tex]
[tex]\\ \tt{:}\leadsto x=29[/tex]
Tracy is borrowing $10,700 on a six-year, %, add-on interest loan. What will Tracy's monthly payments be?
Answers
Answer:
Step-by-step explanation:
Use the formula I=prt. (Interest = principle x rate x time)
So, I = 10700 x 0.07 (7% as a decimal) x 6
So, I = 749(6)
I = 4494
Now, divide 4494 by 6(12)
4494/71
This = 63.3 dollars.
Therefore, she is paying 63 dollars per month.
Tracy's monthly payments is $62.41.
What is Simple Interest?The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more. When you pay back a loan, the monthly interest is deducted first, and any remaining funds are applied to the principle.
Amount (A) = Principal (P) + Interest (I)
and, Simple Interest = PRT/100
Given:
P= 10700
Time= 6 year
Interest = 7%
Now, using simple interest
SI = P x R x T/100
SI = (10700 x 0.07 x 6)
SI = $4494
So, Tracy's yearly payments
= 4494/6
= 749
and, Tracy's monthly payments
= 749 / 12
= 62.41
Hence, Tracy's monthly payments is $62.41.
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y=+/-√bx+c+d Use the inverse of the function y= x2 -18x to find the unknown values.
Answers
Answer:
a=1
b=81
c=9
Step-by-step explanation:
here you go, have a great day!
List the factors that are divisible by 33,424,380. 2 3 4 5 8 9 10
Answers
Answer:
The factors are 2,3,4,5,8,10
Step-by-step explanation:
Here, we want to list out the factors that can divide 33, 424 and 380
The factors include;
2, 3 , 4 , 5, 8, 10
Kindly note that each of these factors can divide at least one of the listed numbers
someone please answer these for me i’ll mark brainlist
1. Belinda has a box of 48 bananas.
5/8 if them are ripe.
How many bananas does she have?
Find the following amounts:
A) 2/3 of 12=
B) 5/6 of 24=
C) 4/9 of 45=
D) 3/5 of 55=
E) 2/7 of 35=
F) 9/10 of 40=
Answers
Answer:
She has 30 ripe bananas.
A) 8
B) 20
C) 20
D) 55
E) 10
F) 36
Buying three tires at $80 each and getting a fourth tire free
Answers
Answer
3 x 80=240
240 / 4=$60 effective unit rate for each tire.
Step-by-step explanation:
mark me as brainliest!
Which values from the given replacement set make up the solution set of the inequality?
m+7<18 ; {8, 9, 10, 11}
{9, 10, 11}
{8, 9, 10}
{8, 9}
{10, 11}
Answers
Answer:
B: 8,9,10
Step-by-step explanation: