convert [tex]\sqrt3 + i[/tex] to polar form
Answers
[tex]a~~\pm~~bi\implies r[\cos(\theta ) \pm i\sin(\theta )] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \sqrt{3}~~ + ~~i\implies \stackrel{x}{\sqrt{3}}~~ + ~~\stackrel{y}{1} i\qquad \qquad \begin{cases} r=\sqrt{x^2+y^2}\\\\ \theta =\tan^{-1}\left( \frac{y}{x} \right) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]r=\sqrt{(\sqrt{3})^2+(1)^2}\implies r=\sqrt{3+1}\implies r=2 \\\\\\ \theta =\tan^{-1}\left( \cfrac{1}{\sqrt{3}} \right)\implies \theta =\cfrac{\pi }{6} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 2\left[\cos\left( \frac{\pi }{6} \right)~~ + ~~i\sin\left( \frac{\pi }{6} \right) \right]~\hfill[/tex]
Check the picture below.
![Convert [tex]\sqrt3 + I[/tex] To Polar Form](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/dbZUKpDh2knxfM8fneU0ICHKYsl0R2PH.png)
Related Questions
Find the degree of this polynomial. 19x^9-2x^6+9x^5
Answers
Answer:
Step-by-step explanation:
The degree of a polynomial is the variable (in this case 1 variable) raised to the highest power.
Look at the first term: 19x^9
The variable is x
The highest power is 9
So the answer is 9.
Si en total tiene 250 monedas que suman $42.50 ,Cuántas monedas de 25 centavos tiene en su alcancía?
Answers
Answer:
65 alojamiento
Step-by-step explanation:
I don't know how to do this (don't mind the 21)
Answers
Answer:
The definition of alternate interior angles is that those two angles are the same.
Therefore because they are the same you can set them equal to eachother
3x + 24 = 78 is true
3x = 54
x = 18
Just know the definitions, for instance 3 and 4 are the same, 2 and 5 are the same, 1 and 6 are the same
What in the cinnamon toast crunch is 2+ x= 1
Answers
Answer:
x = -1
Step-by-step explanation:
Please help I'll mark brainliest
Answers
Answer:
The final answer is 16.
Gd luck with your work! :)
Answer:
Step-by-step explanation:
Find the area of the shaded region.
Answers
Nancy put new insulation in her attic and discovered that her heating bill for December decreased from $160 to $100. What is the percent decrease?
The amount of decrease is ______?
Answers
Answer:
37.5% decrease
Step-by-step explanation:
To find a relative percentage you generally follow the rule of part divided by whole.
$100 / $160 = .625 (62.5%)
So $100 is 62.5% of $160
To find the decrease we need to subtract 62.5% from 100%
100 - 62.5 = 37.5
Which product range generated the most profit over all???
Answers
Answer:
Blue label
Step-by-step explanation:
All that matters here is # of bottles sold * profit per bottle.
If you multiply these 2 values for each row you will see the blue label has the highest amount of profit.
Among all the product ranges blue label generated the most profit of $5625.
What is profit?Profit is basically the difference between the total revenue and the total cost of the product.
Profit=Total Revenue- Total cost.
How to calculate profit?We know that Average profit= total profit/ number of units.
So the profit will be as average profits* number of units.
So the profit of product ranges will be =average profit * number of bottles.
Profit of red label=1.12*3000
=$3360
Profit of black label=1.5*2000
=$3000.
Profit of gold label=2.75*1000
=$2750
Profit of white label=1.20*2750
=$3300
Profit of blue label=2.25*2500
=$5625.
Hence among all the product ranges blue label has generated maximum profit.
Learn more about profit at https://brainly.com/question/1078746
#SPJ2
Two number cubes whose sides are numbered 1 through 6 are rolled on a table. The two numbers showing are added. If you repeat this process 300 times, how many times would you expect the two cubes to add to exactly 7? ASAP
Answers
Answer:
50 times.
Step-by-step explanation:
When the 2 number cubes are rolled once:
The possible outcomes for a total of 7 are:
1 and 6
6 and 1
2 and 5
5 and 2
3 and 4
4 and 3
= 6 outcomes.
The total of all possible outcomes = 6 * 6 = 36.
So Prob( total of 7 in one throw of teh 2 cubes) = 6/36 = 1/6.
For 300 throws you would expect the total of 7 to occur
1/6 * 300 = 50.
Answer:
Step-by-step explanation:
50 IS THE ANSWEr
CAN SOMEBODY SOLVE THE EQUATION
Answers
Answer:
s = 38.1 billion
Step-by-step explanation:
x = 22 (2020-1998)
s = 1.5 x 22 +5.1
s = 38.1 billion
Coach Jill brought 28 L of sports drink to the soccer game. She divided the sports frink equally between 7 coolers. How many mL of sports drink did coach jill put in each cooler?
Answers
Answer:
400ml
Step-by-step explanation:
1 cooler=28L÷7=4L
1L=100ml
4L=400ml(Ans)
Write an equation in slope-intercept form of the line shown.
An equation is
Answers
Answer:
y = - 1/2 x + 1
Step-by-step explanation:
Answer:
y = -1/2x + 1
Step-by-step explanation:
m, rise/run = (2 - 4)/(-2 + 6) = -2/4 = -1/2
b, y-intercept = (0, 1)
y = mx + b
y = -1/2x + 1
PLEASE HELP PLEASE PLEASE HELP PLEASE
Answers
Answer:
True
Step-by-step explanation:
like pirates, the stars were their navagation
a rectangular field is 50 M long and 30 M broad . find a perimeter b) the length of wire required to fence it thrice c)calculate area of a rectangular field
Answers
Answer: b) 160 c) 1500
Step-by-step explanation: b) 50 + 50 + 30 + 30 = 160 c) 50 x 30 = 1500
Step-by-step explanation:
[tex]length \: of \: a \: field \: = 50m[/tex]
[tex]breadth \: of \: a \: field \: = 30m[/tex]
[tex]Perimeter \: of \: a \: field \: = ? [/tex]
We know,
Perimeter ( p ) = 2 ( l + b )
= 2 ( 50m + 30m )
= 2 × 80 m
= 160 m
The length of a wire required to fence it thrice
= 3 × 160 m
= 480 m
Area ( A ) = l × b
= 50 × 30 m
[tex] = {1500m}^{2} [/tex]
A club swimming pool is 22 ft wide and 44 ft long. The club
members want an exposed aggregate border in a strip of
uniform width around the pool. They have enough material for
432 ft squared. How wide can the strip be?
Answers
Answer:
968 is what they need and no they do not enough material
Step-by-step explanation:
What I always do on these questions is length times width and they need 536 more material
Help help help help math
Answers
Answer:
Step-by-step explanation:
2x+y
=2(2)+1
=4+1
=5
Answer:
5
Step-by-step explanation:
Sub x=2, y = 1
2(x) + y = 5
2(2) + 1 = 5
hellllllllllllllp please
Answers
Answer:
The hieght should be 3 cm
Step-by-step explanation:
We can put it into an equation form:
6⋅2⋅x=36
Then solve from there!
Hope this helps!!
Answer:
Yo I was going to answer this question but I assume there is a mistake I think your teacher meant the length of the box is 6cm if not the answer is 6 cm high if so and there's a mistake then the answer is 3 cm high.
Step-by-step explanation:
PLSSSS HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
There are 8 possible spaces that the spinner can land on. Of those, the options are 0, 1, 2, or 3.
There is one space that has 0 in it = 1 / 8 = 0.125
There are two spaces that have 1 in them = 2 / 8 = 0.25
There is one space that has 2 in it = 1 / 8 = 0.125
There are four spaces that have 3 in them = 4 / 8 = 0.5
Hope this helps!
Which statement is true about every exterior angle of any quadrilateral inscribed in a circle?
The measure of an exterior angle is equal to the measure of the nonadjacent interior angle.
The measure of an exterior angle is equal to the measure of an adjacent interior angle.
The measure of an exterior angle is equal to the average of the measures of the two adjacent interior angles.
The measure of an exterior angle is equal to the difference of the measures of the two adjacent interior angles.
Answers
Answer:
A
Step-by-step explanation:
In an inscribed quadrilateral, opposite angles are supplementary.
An exterior angle of a quadrilateral is supplementary to the adjacent interior angle.
Since the exterior angle is supplementary to both the adjacent interior angle and to the opposite interior angle, the exterior angle and the opposite interior angle are congruent.
Answer: A
mollie wants to measure the capacity of the kitchen sink she has a 1 L container and a 10 mL container which should she use
Answers
Answer:
1 L
Step-by-step explanation:
Kitchen sinks are pretty large in terms of volume in Liters
use the 1 L container
Find the value of x
A. 4
B. 10
C. 17
D. 25
Answers
Answer:
X can be any of those numbers depending on which equation it is in
Step-by-step explanation:
The function h(t) = -2(t - 3)2 + 23 represents the height, in feet, t seconds after a volleyball is
served. Which of the following statements are correct? Select all that apply.
The volleyball reached its maximum height at 3 seconds.
The maximum height of the volleyball wag 23 feet.
If the volleyball is not returned by the opposing team, it will hit the ground in 5.5 seconds.
The graph that models the volleyball's height over time is exponential.
The volleyball was served from a height of 5 feet.
Answers
Answer:
1,2, and 5
Step-by-step explanation:
The statements about the function that are correct are:
The volleyball reached its maximum height at 3 seconds.
The maximum height of the volleyball was 23 feet.
We have,
The function h(t) = -2(t - 3)2 + 23 represents the height, in feet, t seconds after a volleyball is served.
Let's analyze each statement:
The volleyball reached its maximum height at 3 seconds.
This statement is correct.
The function h(t) is a quadratic function, and its graph is a parabola that opens downwards.
The vertex of the parabola represents the maximum height of the volleyball.
In this case, the vertex occurs when t = 3 seconds.
The maximum height of the volleyball was 23 feet.
This statement is also correct.
We can see from the function that the maximum height occurs at t = 3 seconds, and substituting t = 3 into the function gives:
h(3) = -2(3 - 3)2 + 23 = 23 feet.
If the volleyball is not returned by the opposing team, it will hit the ground in 5.5 seconds.
This statement is incorrect.
To find when the volleyball hits the ground, we need to find when h(t) = 0. Solving -2(t - 3)2 + 23 = 0 gives t = 3 ± √(23/2).
Since the vertex is at t = 3 seconds, the volleyball will hit the ground at the same height it was served, which is h(0) = -2(0 - 3)2 + 23 = 5 feet.
So the time it takes for the volleyball to hit the ground is when h(t) = 0, which occurs at t = 3 ± √(23/2), not 5.5 seconds.
The graph that models the volleyball's height over time is exponential.
This statement is incorrect.
The function h(t) is a quadratic function, not an exponential function.
The volleyball was served from a height of 5 feet.
This statement is also incorrect.
The function h(t) gives the height of the volleyball above the ground, not above the height it was served.
However, we can see from the function that h(0) = -2(0 - 3)2 + 23 = 5 feet, so the volleyball was served from a height of 5 feet above the ground.
Thus,
The statements about the function that are correct are:
The volleyball reached its maximum height at 3 seconds.
The maximum height of the volleyball was 23 feet.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ7
PLEASE HELP ASAPP!!! (NO LINKS) WILL GIVE BRAINLIEST
Find the number of solutions of
the
equation 6x^2 + 6x + 3 = 0 by
using the discriminant.
(1 solution, 2 solutions, or no
real solutions)
Answers
Answer:
No real solutions
Step-by-step explanation:
Discriminant
[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real solutions}[/tex]
[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real solution}[/tex]
[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real solutions}[/tex]
Given equation: [tex]6x^2+6x+3=0[/tex]
[tex]\implies a=6, \quad b=6, \quad c=3[/tex]
Inputting these values into the discriminant:
[tex]\implies (6)^2-4(6)(3)=-36 < 0\implies \textsf{no real solutions}[/tex]
According to the Mars company, packages of milk chocolate M&Ms contain 20% orange candies. Find the probability that in a random sample of 100 M&M candies, there are between 18% and 22% orange candies.
Answers
Using the normal distribution, it is found that there is a 0.383 = 38.3% probability that the sample proportion is between 18% and 22%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].In this problem, the proportion and the sample size are of p = 0.2 and n = 100, respectively, hence:
[tex]\mu = p = 0.2[/tex]
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.2(0.8)}{100}} = 0.04[/tex]
The probability that in a random sample of 100 M&M candies, there are between 18% and 22% orange candies is the p-value of Z when X = 0.22 subtracted by the p-value of Z when X = 0.18, hence:
X = 0.22:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.22 - 0.2}{0.04}[/tex]
Z = 0.5
Z = 0.5 has a p-value of 0.6915.
X = 0.18:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.18 - 0.2}{0.04}[/tex]
Z = -0.5
Z = -0.5 has a p-value of 0.3085.
0.6915 - 0.3085 = 0.383.
0.383 = 38.3% probability that the sample proportion is between 18% and 22%.
To learn more about the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213
write a polynomial f(x) of lowest degree that satisfies the given conditions. Zeros: -4, multiplicity 1; 3 multiplicity 2; and f(0)=-108
Answers
Answer:
First start with the factors
(3x+5)(3x+5)(6x-1) The multiplicity of 2 means there are 2 of that same factor.
Next, figure out how to get it to go through the point (0,50) Plug in these points, solve for a
50=a(3(0)+5)(3(0)+5)(6(0)-1)
50=a(5)(5)(-1)
50=-25a Divide both sides by -25
-2=a Plug this in
y=-2(3x+5)(3x+5)(6x-1) Now multiply the factors out. Will start by FOILING the first 2 factors
y=-2(9x2+30x+25)(6x-1) Now multiply the remaining factors together
y=-2(54x3+180x2+150x-9x2-30x-25) Combine like terms
y=-2(54x3+171x2+120x-25) Distribute the -2
y=-108x3-342x2-240x+50
How do you simply a ratio? I have no clue how to do that.
Answers
The side lengths in yards of a triangle and a square are shown in the diagram. The perimeter of the triangle is equal to the perimeter of the square. What is the value of x?
Answers
The value of x given the perimeter of the square is 6.
What is the value of x?The first step is to determine the perimeter of the square.
Perimeter of the square = 4 x length
4 x 2.5x = 10x yards
The perimeter of the triangle is equal to the sum of the three side lengths
2x + 4x - 2 + 2x + 14 = 10x
Combine similar terms
14 - 2 = 10x - 2x - 4x - 2x
Add similar terms
12 = 2x
Divide both sies by 2
x = 6
To learn more about triangles, please check: https://brainly.com/question/22949981
Answer:
it is 6
Step-by-step explanation:
i did it in class and the teacher siad it ws right
1. Ms. Rowel would like to buy a house costing $190000. She is required to make a down payment equal
to 10% of the value of the house then borrow the balance from a bank that charges interest at an annual
rate of 4.2% compounded monthly. The bank loan has to be paid o§ with equal monthly payments,
(paid at the end of each month), in 30 years. Assume that she will get the loan at the beginning of a
month and start making monthly payments on the last day of each month until the loan is paid o§
Answers
Answer:
the monthly payment would be 836.22
Step-by-step explanation:
you would find the loan amount which is 190,000 -10% of 190,000 which is 190,000 - 19,000=171,000
then you put the numbers in on a calculator which im using a spreadsheets/ excel
you need to make sure that you divide 12 for the interest and multiply 12 to the 30 years to get the monthly value of them
20 60 100 140 180 120 What percent of the time did Main Street have 100 or more cars per hour?
Answers
The distribution of the cars is an illustration of percentages
The main street has 100 or more cars per hour for 66.7% of the time
How to determine the time percentage?The dataset is given as:
20 60 100 140 180 120
From the above dataset, we have:
100 or more cars = 4Total distribution of cars = 6The percentage is then calculated as:
Percentage= 4/6 * 100%
Evaluate the product
Percentage= 66.7%
Hence, the main street has 100 or more cars per hour for 66.7% of the time
Read more about percentages at:
https://brainly.com/question/11360390
Question 1
What is the coefficient of the variable in the expression 4 − 3x − 7 + 6?
−7
−3
4
6
Question 2
How many variable terms are in the expression 3x3y + 5x2 + y + 9? (Input a numeric value only.)
Numerical Answers Expected!
Answer for Blank 1:
Question 3
)
Which of the following best describes the expression 7x + 2y?
The sum of two products; there are two terms
The product of two sums; there are two terms
The sum of two products; there are four terms
The product of two sums; there are four terms
Question 4
What is the constant term in the expression 6x3y + 8x2 + 5x + 7? (Input a numeric value only.)
Numerical Answers Expected!
Answer for Blank 1:
Question 5
Which of the following best describes the expression 6(y + 3)?
The product of two constant factors six and three plus a variable
The sum of two constant factors six and three plus a variable
The product of a constant factor of six and a factor with the sum of two terms
The sum of a constant factor of three and a factor with the product of two terms
Question 6
Which expression shows a sum of four terms?
4 + x + 4 + x
x4
4(x + 4)
4x
Answers
Answer:
for 1 is -3
Step-by-step explanation:
