Answers
Answer:
The square roots of 49·i in ascending order are;
1) -7·(cos(45°) + i·sin(45°))
2) 7·(cos(45°) + i·sin(45°))
Step-by-step explanation:
The square root of complex numbers 49·i is found as follows;
x + y·i = r·(cosθ + i·sinθ)
Where;
r = √(x² + y²)
θ = arctan(y/x)
Therefore;
49·i = 0 + 49·i
Therefore, we have;
r = √(0² + 49²) = 49
θ = arctan(49/0) → 90°
Therefore, we have;
49·i = 49·(cos(90°) + i·sin(90°)
By De Moivre's formula, we have;
[tex]r \cdot (cos(\theta) + i \cdot sin(\theta) )^{\dfrac{1}{2}} = \pm \sqrt{r} \cdot \left (cos\left (\dfrac{\theta}{2} \right ) + i \cdot sin\left (\dfrac{\theta}{2} \right ) \right )[/tex]
Therefore;
√(49·i) = √(49·(cos(90°) + i·sin(90°)) = ± √49·(cos(90°/2) + i·sin(90°/2))
∴ √(49·i) = ± √49·(cos(90°/2) + i·sin(90°/2)) = ± 7·(cos(45°) + i·sin(45°))
√(49·i) = ± 7·(cos(45°) + i·sin(45°))
The square roots of 49·i in ascending order are;
√(49·i) = - 7·(cos(45°) + i·sin(45°)) and 7·(cos(45°) + i·sin(45°))
Related Questions
What is the solution to this system of linear equations?
Answers
Answer: To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect. The two lines intersect in (-3, -4) which is the solution to this system of equations.
Step-by-step explanation: hope this helps
Find the 50th term of the
sequence:
65536, 49152, 36864, 27648...
A) 0.0495
B) 0.066
C) 0.088
D) 0.117
Answers
Pls helpppppp for brainly
Answers
Answer:
[tex]\frac{6}{8}[/tex] or [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Convert the mixed numbers into improper fractions.
[tex]2\frac{3}{8}-1\frac{5}{8}=\frac{19}{8}-\frac{13}{8}[/tex]
Since the two fractions have the same denominator, just subtract the numerators.
[tex]\frac{19}{8}-\frac{13}{8}=\frac{6}{8}[/tex]
If required, rewrite the fraction in simplest form.
[tex]\frac{6}{8}=\frac{3}{4}[/tex]
How many whole numbers are there with not more than 4 digits IF YOU PUT A LINK OR UNHELPFUL ANSWER I WILL REPORT I WILL GIVE BRAINLIEST
Answers
Answer:
There are 9,999 positive whole numbers with 4 or less digits or less and one whole number which is neither positive nor negative.
This gives us 9,999+9,999+1 or 19,999 , whole numbers composed of 4 digits or less.
In 2016, the number of Internet users in the Middle East was about 1×108, and in Australia, it was about 3×107. Approximately how many times larger was the number of Internet users in the Middle East than in Australia in 2016?
0.03 times
0.3 times
3 times
30 times
Answers
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP MEEE PLSSSS
Answers
Answer:
d. 2x+3
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
Pls help asap thx
...
Answers
Answer:
70
Step-by-step explanation:
35 times 4 = 140. 210-140= 70
\frac{x-5}{x^4-2x^3}\cdot \frac{x^2-4}{x^2-3x-10} x 4 −2x 3 x−5 ⋅ x 2 −3x−10 x 2 −4
Answers
Answer:
[tex]\frac{x-5}{x^4-2x^3}\cdot \frac{x^2-4}{x^2-3x-10} = \frac{1}{x^3}[/tex]
Step-by-step explanation:
Given
[tex]\frac{x-5}{x^4-2x^3}\cdot \frac{x^2-4}{x^2-3x-10}[/tex]
Required
Solve
Express [tex]x^2-4[/tex] as difference of two squares
[tex]\frac{x-5}{x^4-2x^3}\cdot \frac{(x-2)(x+2)}{x^2-3x-10}[/tex]
Factorize [tex]x^4 - 2x^3[/tex]
[tex]\frac{x-5}{x^3(x-2)}\cdot \frac{(x-2)(x+2)}{x^2-3x-10}[/tex]
Cancel out x - 2
[tex]\frac{x-5}{x^3}\cdot \frac{x+2}{x^2-3x-10}[/tex]
Expand [tex]x^2 - 3x - 10[/tex]
[tex]\frac{x-5}{x^3}\cdot \frac{x+2}{x^2+2x-5x-10}[/tex]
Factorize:
[tex]\frac{x-5}{x^3}\cdot \frac{x+2}{x(x+2)-5(x+2)}[/tex]
Factor out x + 2
[tex]\frac{x-5}{x^3}\cdot \frac{x+2}{(x-5)(x+2)}[/tex]
Cancel out x - 5 and x + 2
[tex]\frac{1}{x^3}\cdot \frac{1}{1}[/tex]
[tex]\frac{1}{x^3}\cdot 1[/tex]
[tex]\frac{1}{x^3}[/tex]
Hence:
[tex]\frac{x-5}{x^4-2x^3}\cdot \frac{x^2-4}{x^2-3x-10} = \frac{1}{x^3}[/tex]
Tell whether the shaded figure is a reflection of the nonshaded figure
Answers
Answer:
1. isn't a reflection
2. is a reflection
3. is a reflection
Andrew has a monthly cell phone bill. He pays a
monthly fee and a cost per minute. The graph to the
right shows his
cost per month depending on the
minutes used. What is the monthly fee for Andrew's
phone bill?
A. $49
B. $120
C. $60
D. $72
Answers
Answer:
C, $60
Step-by-step explanation:
It is where the graph starts even with 0 minutes.
PLEASE HELPPP WILL GIVE BRAINLIEST!!!
Answers
Answer:
Step-by-step explanation:
where is the question?
There are 5 trucks for every 8 cars in a parking lot. If there are a total of 112 cars in the parking lot. How many trucks are there?
the
Answers
Answer:
There are 70 trucks
Step-by-step explanation:
trucks : cars:
5 8
Take 112 cars and divide by 8 cars
112/8 =14
We need to multiply each number by 14
trucks : cars:
5*14 8*14
70 112
There are 70 trucks
I need the answers pls
Answers
ffggddaafvvcgghv de ryhvg
Rewrite the expression by combining like terms. 3y + 5x2 + 10x + 2x2 + 15x – 3y
Answers
Answer:
7x²+ 25x
Step-by-step explanation:
PLEASE HELP ME!!! THANK YOU SO MUCH!
Answers
Answer: B / 2,6,10,14,18
Step-by-step explanation:
you were given the equation next input 1 for n.
Solve and a = 2
Then you input 2 for n. Solve and you get a =6.
Do this up until you get to 5.
Substitution.
-3x - 2y = -12
y = 5x - 7
Answers
Answer:
-3x-2(5x-7)=-12
-3x-10x+14=-12
-13x+14=-12
-13x=-16
x=2
Find each sum or difference. 31 - 42.9 =
Answers
Answer:
-11.9
Step-by-step explanation:
plz crown
Answer: 11.9
Step-by-step explanation: you have to subtract the 2 numbers
Evaluate the function at the given value if f(x)= 5x-7 find f(2)
Answers
Answer:
3
Step-by-step explanation:
f(x)=5x-7
for f(2) just put 2 in place of x
so,
f(2)=5(2)-7
f(2)=10-7
f(2)=3
please help me no files or links
Answers
Answer:
it's a yw
Step-by-step explanation:
What is the volume of a rectangular prism that has a length of 8 square inches, a width of 6 3/4 square inches, and a height of 5 1/4 square inches?
Answers
Given:
Let us consider,
Length of a rectangular prism = 8 inches
Width = [tex]6\dfrac{3}{4}[/tex] inches
Height = [tex]5\dfrac{1}{4}[/tex] inches
To find:
The volume of the rectangular prism.
Solution:
The volume of a rectangular prism is:
[tex]V=l\times w\times h[/tex]
Where, l is length, w is width and h is height.
Putting the given values, we get
[tex]V=8\times 6\dfrac{3}{4}\times 5\dfrac{1}{4}[/tex]
[tex]V=8\times \dfrac{27}{4}\times \dfrac{21}{4}[/tex]
[tex]V=\dfrac{567}{2}[/tex]
[tex]V=283.5[/tex]
Therefore, the volume of the rectangular prism is 283.5 cubic inches.
Find the area of each sector. Round your answer to nearest tenth
Answers
Answer:
area of 150° segment = 188.5 km²
Step-by-step explanation:
area of full circle = πr² = (3.14)(12²) = 452.16 km²
area of segment = (150°/360°)(452.16) = 188.5 km²
the area of each sector is C
a company wants to rent a tent that had a height of at least 10 feet for an outdoor show. should they rent the tent show at the right? explain.
Answers
Related diagram is attached below :
Answer:
No
Step-by-step explanation:
The height, h of the tent attached below can be obtained using Pythagoras rule, as the shape forms a right angle triangle.
Length of base , = 24 / 2 = 12 feets
Hypotenus = 15 feets
The height, h = √(hypotenus² - Base²)
h = √15² - 12²
h = √225 -144
h = √81
h = 9 feet
Tent shouldn't be rented as it is below 10 feets
Find the volume to the nearest millimeter of a cylinder that is 45 millimeters tall and has a diameter of 26 millimeters. Use 3.14 for pie.
Answers
Answer:
Volume = π • r² • height
Volume = 3.14 • 13² • 45
Volume = 23,879.7 cubic millimeters
Volume = 23,880 cubic millimeters (to nearest millimeter)
Step-by-step explanation:
Using the formula below, calculate the z-score for the listed data points. z-score: zx = x − μ σ z1 = z5 = z6.5 =
Answers
Answer:
z1 = -1.95
z5 = 0.05
z6.5 = 0.8
Step-by-step explanation:
The value of the z score for a mean of 4 and standard deviation is 1.
What is Z score?The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (x - μ)/σ
Where x is the raw score, μ is the mean and σ is the standard deviation.
Let us assume that μ = 4, σ = 2, hence for x = 6:
z = (6 - 4) / 2 = 1
The value of the z score for a mean of 4 and standard deviation is 1.
Find out more on Z score at: https://brainly.com/question/25638875
PLEASE HELP ME 20 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
by using formula (a+b)^2=a^2+2ab+b^2
in these two we have to just open the formula
(3x+2y)^2
=(3x)^2+2(3x)(2y)+(2y)^2
=9x^2+12xy+4y^2
(3y+2x)^2
=(3y)^2+2(3y)(2x)+(2x)^2
=9y^2+12xy+4x^2
Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms.
6c^2+ 2c^4 - c
Answers
Answer:
Standard form: 2c^4 + 6c^2 - c
Degree: 4th
Leading coefficient: 2
Classification: Trinomial
Step-by-step explanation:
In standard form, you have to put the term with the highest exponent first.
With finding the degree, you just look at the highest exponent and that's the degree. 4 is the highest exponent, so it is to the 4th degree.
The leading coefficient is the number attached to the highest exponent. 4 is the highest and the number attached to it is 2.
Classification goes by how many terms there are. Since there are 3, it's trinomial. Tri as in three.
find the surface area! correct gets brainliest!
Answers
Answer:
where is the picture i cant see anything except find the surface area! correct gets brainliest!
Step-by-step explanation:
A triangle with side lengths of 21, 17, and 18 is classified as acute, obtuse, right, or equiangular?
Answers
Answer:
Acute
Step-by-step explanation:
and angle lower than 90 is acute exactly 90 is an right angle from 90 to 180 obtuse 180 to 360 reflex angle and equalateral is 60 degrees on each angle
can someone please help me with this question?
Answers
Answer: 1404
Step-by-step explanation:
V=πr^2h
(3)(6)^2(13)
(3)(36)(13)=1404
4/9
A bag contains 4 apples, 6 pears and 8
oranges. What is the probability of
picking an orange? (in simplest form)
Using the question above, what is the
COMPLEMENT of picking an orange from
the bag?
Answers
Answer:
The probability of picking an orange is 8/18, or 4/9.
8/18 of the fruits are oranges, so 10/18 of the fruits are not oranges. The complement of picking an orange is 10/18 or 5/9.
Step-by-step explanation:
There are 4 apples, 6 pears, and 8 oranges. That adds up to 18 fruits. 8 of those are oranges, so the probability of picking an orange is 8/18, or 4/9 simplified.
The complement means all outcomes that are NOT the favorable outcome, or in this case, all outcomes that are not oranges. There are 8 oranges out of 18, so there are 10 fruits that are not oranges. This makes the complement 10/18, or 5/9 simplified.
Answ2/6 or 33% chance of getting an apple, 3/24 or 13% of getting a pear and 13/24 or 54% chance of getting an orange hope that helps.er:
Step-by-step explanation:
