The solutions to x^3 = 5 - 5i in polar form are √50cis(-π/12), √50cis(4π/3), and √50cis(5π/12).
Explanation:To find the solutions to the equation x^3 = 5 - 5i in polar form, we can start by converting the complex number 5 - 5i into polar form.
The magnitude (r) of the complex number can be found using the equation r = √(a^2 + b^2), where a is the real part and b is the imaginary part. In this case, the magnitude is √(5^2 + (-5)^2) = √(25 + 25) = √50.
To find the argument (θ), we can use the equation θ = tan^(-1)(b/a), where b is the imaginary part and a is the real part. In this case, the argument is tan^(-1)(-5/5) = tan^(-1)(-1) = -π/4.
Therefore, the complex number 5 - 5i in polar form is represented as √50cis(-π/4).
To find the solutions to x^3 = 5 - 5i, we can take the cube root of both sides of the equation. Using De Moivre's Theorem, we can express the cube root of the complex number in polar form as the cube root of the magnitude raised to the power of 3, and the argument divided by 3.
Therefore, the solutions to x^3 = 5 - 5i in polar form are:
a. √50cis(-π/12)
e. √50cis(4π/3)
i. √50cis(5π/12)
Answer:
[tex] \sqrt[6 ]{50} cis( \frac{7\pi}{12} ) \sqrt[6]{50} cis( \frac{23\pi}{12} ) \sqrt[6]{50} cis( \frac{5\pi}{4} )[/tex]
William only has 1 3/4 cups of flour, so he can only make 2/3 of a batch of biscuits. How much flour is needed for a full batch of biscuits?
Answer:
1 1/2 cups
Step-by-step explanation:
Subtract 1 3/4 and 2/3 and you get 1 1/2
Answer:
1 1/2 cups for a full batch
Order the numbers from least to greatest.
7.4 x 104
7.6 x 10-4
765,000
Answer:
dhccidifivivicickcvkvvkvk
HELPPP PLEASEEEEE!!!!!
Answer:
like 60 or something
Step-by-step explanation:
heyy does anybody know the answer please i need this to graduate
Answer:
i think it is de 1st one
Step-by-step explanation:
which is a bigger number 12 or 12
Answer:
neither they are the same as each other...
Answer:
they're equal to each other.. unless your trolling...
Step-by-step explanation:
which expression is equivalent to -1/4x+1/2?
(A) 1/4(-x+1/2)
(B) -1/4(-x+1/2)
(C) -1/4(x+2)
(C) 1/4(-x+2)
Will mark brainliest to first person.
Do you mean D for the last choice?
The answer is D, if that is what you meant.
The 1/4 must be positive since the 1/2 is positive in the equation and the second numbers are all positive in the choices.
Also, 1/4 of 2 is 1/2, so D has to be the answer.
I hope this helps.
A wire that is 48 centimeters long is shown below.
The wire is cut into two pieces, and each piece is bent and formed into the shape of a square.
Answer:
The sides of the square measure 6 cm
Step-by-step explanation:
If we cut the wire in half, we have to:
48/2 = 24
We would have two 24 cm wires
With each wire a square will be formed, therefore the question I suppose must be how much each side of the square measures.
We know that the square has 4 equal sides, therefore:
4/24 = 6
The sides of the square measure 6 cm
The sides of the square measure 6 cm.
Calculation of the sides of squares:Since A wire that is 48 centimeters long
In the case when we cut the wire in half so it should be 50% of 48 i.e. 24
Also, the square does have 4 equal sides
So, the sides of the square should be
[tex]= 24\div 4[/tex]
= 6 cm
hence, The sides of the square measure 6 cm.
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Which statement is true about the joint frequencies in
this table?
Twenty-three 9th graders and fifteen 11th graders
prefer math.
Fourteen 11th graders prefer math and eight 10th
graders prefer science.
Thirty-five 12th graders prefer math and nine 10th
graders prefer science.
Twenty-three 9th graders and thirty-two 12th
graders prefer math.
The statements Fourteen eleventh graders prefer math and eight tenth graders prefer English and Thirty-five twelfth graders prefer math and nine tenth graders prefer English are true.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
For the 12th graders, we have a total of 67 pupils with 32 preferring
English, therefore the number of the 12th graders that prefer math is 67 - 32 = 35 pupils
Similarly for the 11th graders we have total pupils = 29 with 15 preferring English, therefore the number of the 11th graders that prefer math is 29 - 15 = 14 pupils
Also for the 10th graders we have total pupils = 26 with 18 preferring math, therefore the number of the 11th graders that prefer English is 26 - 18 = 8 pupils
Finally for the 9th graders, we have a total of 63 pupils with 40 preferring English, therefore the number of the 9th graders that prefer math is 63 - 40 = 23 pupils
Hence, the statements Fourteen eleventh graders prefer math and eight tenth graders prefer English and Thirty-five twelfth graders prefer math and nine tenth graders prefer English are true.
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A survey was conducted with high school students in
each grade to see how many prefer math or science.
Some of the data are shown below.
Which statement is true about the joint frequencies in
this table?
40
11 | 12 |
Total
O Twenty-three 9th graders and fifteen 11th graders
prefer math.
O Fourteen 11th graders prefer math and eight 10th
graders prefer science.
O Thirty-five 12th graders prefer math and nine 10th
graders prefer science.
Twenty-three 9th graders and thirty-two 12th
graders prefer math.
Math
18
90
Science 40
15
95
Total
63
26
29
67
185
30 POINTS
Victoria has $103 earned from babysitting saved at home, and the amount is modeled by the function h(x) = 103. She reads about a bank that has savings accounts that accrue
interest according to the function s(x) = (1.03)* - 1. After combining the two functions, the new function is g(x) = 103(1.03)* - 1. Using complete sentences, explain what the 103 represents in this new function. What is the interest rate the bank is giving to Victoria?
103 represents how much money Victoria is depositing into the bank, or her principal.
The interest rate is 1.03, or 3%.
What Values of X will make x2 (Exponent of 2) =16 true? HELPPPPPP!!
A)4 AND -4
B)2
C)4
D)6 AND -6
Answer:
A
Step-by-step explanation:
Given
x² = 16 ( take the square root of both sides )
[tex]\sqrt{x^2}[/tex] = ± [tex]\sqrt{16}[/tex] ← note plus or minus sign
x = ± 4
Since 4² = 4 × 4 = 16 and
(- 4)² = - 4 × - 4 = 16
A circular pool has a radius of 10 feet. What is the areaof the surface of the water in the pool? Use 3.14 for π.
Answer:
314ft²
Step-by-step explanation:
A = πr²
A= π10²
A=100π
A=100*3.14
A=314
Hope this helps :)
Final answer:
To calculate the area of the circular pool's surface, use the formula A = πr² with π approximated as 3.14 and the given radius of 10 feet. The area is 314 square feet, as the calculation yields A = 3.14 × 100, which does not need adjustment for significant figures.
Explanation:
To find the area of the surface of the water in the circular pool with a radius of 10 feet, we use the formula for the area of a circle, which is A = πr². Let's use the given value for pi (π) as 3.14 and the radius (r) is 10 feet. So the calculation is A = 3.14 × (10 feet)².
Now, squaring the radius, we get (10 feet)² = 100 feet². Next, we multiply this by our value for pi, resulting in A = 3.14 × 100 feet² = 314 feet². Therefore, the area of the surface of the water in the pool is 314 square feet.
Recalling significant figures, since our given radius was precise to two significant figures, our final answer should also reflect two significant figures. However, since all the numbers in 314 are significant, there is no need for adjustments in this case, and the result remains 314 square feet.
5 cups of grape juice to 2 cups of apple juice
Electricity City increases the price of televisions by 25%. If a television now sells for
$425, what was the original price?
Answer:
340
Step-by-step explanation:
As it was increased by 25%, $425 is 125% of the original price, so we can get back to 100% by dividing 425 by 5 [85], so 85 is 25% of the price. We can now get the original price by subtracting 85 from 425 (or you could multiply 85 by 4) which is 340
You can check this answer by multiplying 340 by 1.25
If the answer is 425, then it is correct, else, not. [it is]
+10+10+10+10+10 cuz iam bored still answer it
Answer: 50 or 10/10
Step-by-step explanation:
1+1+1+1+1= 5 then just make it like this 10+10=20+10=30+10=40+10=50
+10+10+10+10+10 cuz iam bored still answer it
Someone pls help it’s due later
Answer:
5.)Z=7
Check:
6.) False
True
Step-by-step explanation:
5z-10=25
5z-10+10=25+10
5z=35
5z/5=35/5
z=7
Check:
5(7)-10=25
35-20=25
25=25
(Love your profile picture)
Answer:
5) 7
6a) no
6b) yes
Step-by-step explanation:
5)
add 10 to both sides then divide by 5 to isolate the Z
6a) the actual answer is 4F + 12
you don't add 4 you multiply
6b) That is the answer
You see which number is the greatest common factor (GCF)
Please Help...
A research group is trying to determine the correlation between the number of hours spent
studying and the number of hours sleeping. Use the data shown on the graph to compute
the correlation coefficient.
A) r = 1 C) r = − 1
B) r = 0.5 D) r = −0.5
Answer:
C) r = − 1Step-by-step explanation:
In the graph, you can observe that all five points are perfectly lined up on a straight line, which is decreasing, because each points is lower than the previous one.
This situation represents a coefficient of correlation of -1, which means there's a strong negative correlation between variable.
Once again, graphically, this strong negative correlation can be deduct from the behaviour of the data, which is clearly decreasing with a straight line behaviour. In other words, the line that best fits is almost unique.
Therefore, the right answer is C.
Answer: C
Step-by-step explanation: did usa test prep
after taking math online . what would you say are some pross (good) and cons (bad) about taking classes . online? what would make it better?
Answer:
Cons: Could be harder, Difficult to solve, hard to see problems online, Things to help: Post assignments in portions Pros: hand wont hurt if writing, Wont loose paper if it’s on paper
Step-by-step explanation:
After taking online classes, there are some pros and cons. The positive side of taking online classes are that you learn at a much faster rate, you have more choices and flexibilty with your education, and you're able to do it wherever you want with the comfort of your home. The negative side of taking online classes are that it's very expensive to take online classes, there's a higher chance of the student cheating instead of learning the lesson, and the lack of self-motivation, the increase in work can be stressful!
(This is in my own words, so I hope this helps!)
An item has a listed price of $35.If the sale tax rate is 5%, how much is the sales tax (in dollars)
The tax is 5% of 35 so we have to find out what 5% of 35 is. To do so, divide 5 by 100, then multiply the quotient by 35.
5% ⇒ 0.05
35 × 0.05 = 1.75
Answer:The sales tax is $1.75.
I hope this helps :)
Find the indicated side of the triangle a= I'll mark you brainliest for the correct answer
Answer:
[tex] a = 17 \sqrt{2}[/tex]
Step-by-step explanation:
[tex] \sin \: 45 \degree = \frac{17}{a} \\ \frac{1}{ \sqrt{2} } = \frac{17}{a} \\ a = 17 \sqrt{2} \\ [/tex]
To find the length of side a in a right triangle, we can use the Pythagorean theorem.
Explanation:To find the length of the side a, we can use the Pythagorean theorem. In a right triangle, the Pythagorean theorem states that the square of the length of the hypotenuse (h) is equal to the sum of the squares of the lengths of the other two sides (a and b). So, we have a² + b² = h². Rearranging the equation, we can solve for side a: a = sqrt(h² - b²). Plugging in the known values, we can calculate the value of side a.
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URGENT Matina drove from her home to school at 40 mph and was 10 minutes late. The next day she drove at 60 mph and was 10 minutes early. How far is Matina’s school from her home.
answer-----
777x4
explanarion
berisycg awinsub egfsbcysdgbcwstgh 7qagoihbsbwesdfzy v
3/4+4/5+5/6=?
WHAT IS THE ANSWER I NEED IT ASAP PLEASE!!
Answer:
143 /60
Step-by-step explanation:
Explain why you cannot use y = mx + b to find the equation of a vertical line.
Answer:
because the slope would be 1/0 which is undefined
Step-by-step explanation:
Answer:
Because a vertical line has an undefined slope. If you were to use rise over run you get any number over 0 (ex. 7/0). You cannot divide any number by zero which means you will get an undefined answer.
A sign is in the shape of a triangle. It has a base of 12 inches and an area of 120 square inches. What is the height of the sign?
Answer:
The height is 20
Step-by-step explanation:
This is because 120= .5x12
which equals 120= 6. Of course this is not equal so we do 120/6= 20.
Now if we insert 20 to check .5x12x20= 20 which makes the statement true
Answer: 20
Step-by-step explanation: 120 divided by 3 = 40 half of 40 is 20
what fraction is equivalent to 2 over negative 3
Answer:
-2/3 or negative two thirds. Other examples of -2/3 could be -4/6, -8/12, and -10/15.
Step-by-step explanation:
To get equivalent fractions, just multiply the numerator and denominator by the same number.
What do we use to determine the order of operations
Answer:
PEMDAS determines order of operations
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Answer:
so I use pemdas which is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Step-by-step explanation:
You might remember this as "Please excuse my dear Aunt Sally.) This means that you should do what is possible within parentheses first, then exponents, then multiplication and division (from left to right), and then addition and subtraction (from left to right).
find the exact length of the third side
Answer: 3 times the square root of 5! (Or the square root of 45 if you don’t want to simplify)
Step-by-step explanation:
First, you would need to use the Pythagorean Theorum, a^2 + b^2 = c^2, since it is a right triangle.
So in this case,
6^2 + 3^2 = c^2
This simplfys to:
36 + 9 = c^2
45 = c^2
Now you have to take out the square in the c. What you do to one side, you have to do to the other, so you have to put 45 in a square root. This simplies to 3 times the square root of 5.
n+6 (10n+7)= simply expression
Answer:
The correct answer is 61n+42
Which inequalities are true? Check all that apply.
(pic attached)
Answer:
first, last and 4th one
Answer:
1st
3rd
5th
Step-by-step explanation:
Cylinder A has radius r and height h as shown in the diagram. Cylinder B has radius 4r and height 4h. How many times greater is the surface area of Cylinder B than the surface area of Cylinder A?
Pls help WILL GIVE BRAINLIEST
Answer:
16 times
Step-by-step explanation:
Since the sides are in the same ratio, i.e
1 : 4
The cylinders are similar
(Ratio of sides)² = Ratio of areas
4² = 16
Step-by-step explanation:
Step 1: Make a ratio of the sides
Side of Cylinder A : Side of Cylinder B
1 : 4
Step 2: Find the ratio of the area
[tex]1 : 4[/tex] ← Ratio of Side
[tex](1)^2 : (4)^2[/tex] ← Ratio of Area
[tex]1 : 16[/tex] ← Ratio of Area
Answer: The area of Cylinder B is 16 times greater than Cylinder A
Guysss I need help ASAPPPP I need to get this done todayyy :(((
Answer:
see below
Step-by-step explanation:
t = 7m
Let m = 6
t = 7*6 = 42
Let m = 8
t = 7*8
t = 56
Answer:
For this, all you have to do is multiply each number on the left by 7.
T = 7m
M= 6 x 7
T = 42
M = 8 x 7
T = 56.