Polar form of complex numbers is z=a+bi is
z = r(cosθ + i sinθ) . So, first find the absolute value of r and then argument θ. Polar form of given expression are
a) 7(√3/2 + i/2 )
b) 7(√3/2 - i/2)
c) 14(√3/2 + i/2)
d) 14(√3/2 - i/2)
The polar form of complex numbers is a different way of representing complex numbers than the orthogonal form. Complex numbers are usually represented in the form z = x+iy. where "i" is an imaginary number. But in polar form, complex numbers are represented as a combination of modulus and argument.
Problems Algebra Convert to polar form
a) 7(cos(30°) + i sin(30°))
we simplify each term.
The exact value of cos(30°) = √3/2
=> 7((√3/2) + i sin(30°))
The exact value of sin(30°) = 1/2
=> 7(√3/2 + i/2 )
Combine all values we get, 7(√3/2 + i/2 )
7(cos(330°) + i sin(330°))
Using quadrant system
b) cos(330°) = cos(360°- 30°) = cos 30° = √3/2
sin(330°) = sin(360°- 30°) = - sin 30° = -1/2
so, 7 ((√3/2) + i(-1/2))
= 7√3/2 - 7i/2 = 7(√3/2 - i/2)
c) 14(cos(30°) + i sin(30°))
= 14 ((√3/2) + i (1/2)) = 14√3/2 + 14i/2=14(√3/2 - i/2)
d) 14(cos(330°) + i sin(330°))
= 14 (√3/2) + 14i(-1/2) = 14√3/2 - 14i/2
= 14(√3/2 - i/2)
To learn more about polar form of complex , refer:
https://brainly.com/question/21655497
#SPJ4
Answer:
14(cos(330o) + i sin(330o))
Step-by-step explanation:
A weather forecaster says that the temperature is changing at a rate of -8° per hour. At this rate, how long will it take for the temperature change to be -24°? It will take _____ hours for the change in temperature to be -24
The transition to -24 degrees will take three hours .The balance between energy coming into and going out of the planet's system determines its temperature.
What influences how the temperature fluctuates?The balance between energy coming into and going out of the planet's system determines its temperature. The Earth warms up when incoming solar energy is absorbed by the Earth system. Earth does not warm as a result of solar energy being reflected back into space. Earth cools as energy that has been absorbed is ejected back into space.Since 1880, the Earth's average temperature has increased by 0.14° F (0.08° C) every decade; however, since 1981, the pace of warming has increased by 0.32° F (0.18° C) per decade, or more than twice as fast. Using NOAA's temperature data, 2021 ranked as the sixth-warmest year ever.Explanation:
-8% / -24 = 3.
The transition to -24 degrees will take three hours.
To learn more about Temperature refer to:
https://brainly.com/question/25677592
#SPJ1
How do you write 204,000,000 in scientific notation?
Answer:2.04.10/8
Step-by-step explanation:
Response:
2.04.10/8
Step by step explanation:
1. Write the number as a decimal
Plus Icon
204000000.0
2. Convert it to a new number between 1 and 10
Plus Icon
We move the decimal point so that 204000000.0 becomes a new number between 1 and 10. Since our number is greater than 10, we move the decimal point to the left. Remove trailing zeros. Keep count of amounts times we move the decimal point.
204000000.0 -> 2.04
Our new number is 2.04. We have moved the decimal point 8 times.
3. Define the power of 10
Plus Icon
Since our original number was greater than 10, the exponent of 10 is positive. Remember that we moved the decimal point 8 times, so the exponent is positive 8:
4.End result
Plus Icon
what is s for the following function
Answer:
S = 3
S = 5
S = 7
S = 9
Step-by-step explanation:
t = 3s + 2
when t = 11
11 = 3s + 2
11 – 2 = 3s
9 = 3s
s = 3
t = 3s + 2
when t = 17
17 = 3s + 2
17 – 2 = 3s
15 = 3s
s = 5
t = 3s + 2
when t = 23
23 = 3s + 2
23 – 2 = 3s
21 = 3s
s = 7
t = 3s + 2
when t = 29
29 = 3s + 2
29 – 2 = 3s
27 = 3s
s = 9
I HOPE ALL THIS HELPS
RATE AS BRAINLIEST PLS
the questionnaire is a carefully constructed measurement instrument. group of answer choices true false
Yes, its true that the questionnaire is very carefully constructed by an individual to provide the measurement instrument.
A questionnaire is a studies device which includes a sequence of questions for the motive of amassing facts from respondents. Questionnaires may be concept of as a form of written interview. A questionnaire is a listing of questions or gadgets used to collect facts from respondents approximately their attitudes, experiences, or opinions.
Questionnaires may be used to acquire quantitative and/or qualitative facts. Questionnaires are generally utilized in marketplace studies in addition to withinside the social and fitness sciences. Questionnaires are typically taken into consideration to be excessive in reliability. This is due to the fact it's miles feasible to invite a uniform set of questions. Any troubles withinside the layout of the survey may be ironed out after a pilot study. The greater closed questions used, the greater dependable the studies.
To learn more about questionnaire, refer: brainly.com/question/25685309
#SPJ4
Write a pseudocode algorithm which inputs numeric scores and outputs the average score. The end of the data is signalled by a user input of -1.
Programming or the process of writing algorithms both involve pseudocode. A technique that aids the programmer in defining an algorithm's implementation is pseudocode.
The algorithms are described using pseudocodes in pseudocode algorithms because it is simpler for everyone to understand the pseudo-codes, regardless of programming experience or familiarity with a different programming language.
do{
input=take input
}
While(input not equal to -1)
{
Store in an array for every input
Like append the new input to an array
}
After loop terminates
Take the average of the array
By traversing through all elements of an array and store in a variable
The sum divided by the length of the array gives the average
IN C language:
#include<stdio.h>
Int main(){
Int input,i=0,sum,avg,are[1000];
Do{
Scanf(“%d”,&input);
}
While(input !=0)
{
arre[i]=input;
i=i+1;
}
Sum=sum(arre[]);
Avg=sum/len(arre);
Printf(“%d”,Avg);
Return 0;
}
To know more about average scores visit: brainly.com/question/28993111
#SPJ4
Let
f(x)=12−x
f^-1(x)=
The inverse for f(x) = 12 - x is f^-1(x) = -x + 12
Define Inverse Function
An inverse function or an anti function is defined as a function, which can reverse into another function.
The given equation is ,
f(x) = 12 - x
We can also write like this,
y = 12 - x
Now, for the inverse just swap x and y like this
x = 12 - y
x - 12 = - y
y = -x + 12
Now, we know
y = f^-1(x) = -x + 12
Hence, f^-1(x) = -x + 12
To read more about Inverse Function
https://brainly.com/question/132832
#SPJ1
group of scandinavians consists of 5 swedes, 6 finns, and 7 norwegians. they are seated at random around a table. compute the following probabilities: (a) that all swedes sit together, (b) that all swedes and all the finns sit together, and (c) that all the norwegians, all the swedes, and all the finns sit together.
For the following data of group of Scandinavians consisting of Swedes, Finns and Norwegians the probability for the following parts will be:
By using the formula, Circular permutation = (n-1)
Total permutations = 18 - 1 = 17
(a) all the swedes sit together
Total permutations where all the swedes sit together
= 13 x 5
all swedes sitting on 5 consecutive seats so they can be arranged times and everyone including Norwegians as a group can be arranged in
Probability that all the swedes sit together = [tex]\frac{13 X 5}{17}[/tex]
(b) that all the Finns and all the Swedes sit together
Total permutations where all the Finns and all swedes sit together = 8 x 6 x 5
Probability that all the Finns and all swedes sit together = [tex]\frac{8 X 6 X 5}{17}[/tex]
(c) that all the Norwegians, Swedes, and Finns sit together.
Total permutations where all the Norwegians, Swedes, Finns sit together = (3-1)
So Probability that all the Norwegians, Swedes, Finns sit together = [tex]\frac{2 X 6 X 5 X 7}{17}[/tex]
To learn more about probability: https://brainly.com/question/13604758
#SPJ4
Please answer this question ty.
Answer:
u forgot the question...........
What is the solution to the following system of equations
7x+2y=24
8x+2y=30
The total surface area of this 3-D object is?
Write the Standard Form of the line with x-intercept of 3 and y-intercept of 4.
Answer:
Use a model to find the sum of two fractions with the same denominator
Add fractions with a common denominator without a model
Add fractions with a common denominator that contain a variable h
Step-by-step explanation:
h
Kusum bought 50 glasses for rs 1500 out of which 4 were broken if she sold the rest of the glasses for rs 35 each how many profit or loss percent did she bear
Answer:
7.3%
Step-by-step explanation:
Cost for 50 glasses = ₹1500 -----> Cost Price (C.P)
Cost per glass = 1500/50 = ₹30
Here, 4 glasses break. So, she now has
50-4 = 46 glasses
She sold 46 glasses for ₹35 each,
Money earned = 46x35 = ₹1610 -----> Selling Price (S.P)
Since S.P > C.P,
she made a profit = 1610-1500 = ₹110
Profit% = Profit/Cost Price x 100
= 110/1500 x 100
= 7.3%
lim 1+ x/1+√x^2+1x
x→-infinity
Answer:
1/2
Step-by-step explanation:
Find the following limit:
lim_(x->∞) (x + 1)/(1 x + sqrt(x)^2 + 1)
(x + 1)/(1 x + sqrt(x)^2 + 1) = (x + 1)/(2 x + 1):
lim_(x->∞) (x + 1)/(2 x + 1)
The leading term in the denominator of (x + 1)/(2 x + 1) is x. Divide the numerator and denominator by this:
lim_(x->∞) (1 + 1/x)/(2 + 1/x)
The expressions 1/x and 1/x both tend to zero as x approaches ∞:
Answer: 1/2
How many eighth notes equal a half note?
Answer:four eighth notes
Step-by-step explanation:
What is the equation of the line that passes through the point (6,2) and has a slope of 1/3 ?
The equation of the line passes through the point (6,2) and slope 1/3 is
X=3Y-3
Here the point is (6,2) and the slope is 1/3
Means,
x=6 y=2 and m=1/3
We know that the equation of a line is -
Y=mx+c
Putting these values in the above equation we get
⇒2=1/3×6+c
⇒2=6/3+c
⇒2=2+c
⇒c=1
Therefore we find that the intercept is 1
So after putting all these values in that equation y=mx+c we get
Y=1/3X+1
⇒X/3=Y-1
⇒X=3Y-3
The equation passes through the point (6,2) and the slope is 1/3 is x=3y-3
Learn more about the equation of a line:
https://brainly.com/question/13763238
One basketball costs $2 more than another. The sum of their costs is $146. How much does each basketball cost?
Answer:
$72 and $74
Step-by-step explanation:
Let the cheaper ball cost x.
x + x + 2 = 146
2x = 144
x = 72
x + 2 = 74
Answer: $72 and $74
I need help, thanks…
Answer:
1st and 4th are the right answers
Step-by-step explanation:
the rule for the sides of a triangle are that two of the side lengths need to be bigger than the third one. Because of this the 1st and 4th are the only ones that meet this expectation.
What is the length of AB
Answer: 11.5 maybe ? {sorry if its wrong]
Step-by-step explanation:
Elizabeth rents a home for $1,200 a month. The security deposit she paid is one months' rent. Renters insurance will cost $120 for the year. Elizabeth expects utilities to average $164 a month. What will be the total cost of renting the home for the first year (prior to any refund of her security deposit)? PLEASE SHOW WORK
Answer:
$17,688.00
Step-by-step explanation:
(1200 x 13) + 120 + (164 x 12)
17688
Can someone help, it is a proportion q
1) Is the triangle right angled?
8cm
16cm
18cm
Answer:
for right angle triangle ...by Pythagoras theorem
18^2 = 8^2 + 16^2
324 = 64 + 256
324 = 320
which is not true ....
hence not a right angle triangle
m×n , when m=13 and n=12
Answer:
156
Step-by-step explanation:
mxn
13x12= 156
......
PLS HELP!
Which of the following are square roots of the number below? Check all that
apply.
9
A. -3
B. 81
C. 3
D. 18
OE. -9 1/2
OF. 9 1/2
Answer:
A. -3 and C. 3
Step-by-step explanation:
The square root of 9 is ±3, which means that the square root can either be 3 or -3.
Verify that if Y has a beta distribution withα=β=1then Y has a uniform distribution over (0, 1). That is, the uniform distribution over the interval (0, 1) is a special case of a beta distribution.
The standard uniform distribution is a special case of the beta distribution when β = γ = 1.
A sort of probability distribution called the beta distribution encompasses all potential probabilities. With examples, let's go over its definition and formula. The Beta distribution is a continuous probability distribution that is defined by two positive parameters in probability and statistics. It is a kind of probability distribution that is used to depict the results or irrational behavior of percentages or proportions.
Let the random variable X ∼ beta(β, γ). The probability density function of X is mentioned in the picture given below which is the probability density function of a standard uniform random variable.
To know more about beta distribution visit: brainly.com/question/28932397
#SPJ4
a certain acid has a ka equal to 5.57 x 10-5. determine the pkb of its conjugate base (give your answer to two decimal places)
The pk[tex]_b[/tex] of given acid conjugate base is 9.74 if k[tex]_a[/tex] of the same acid is equal to 5.57×10⁻⁵
The Bronsted-Lowry corrosive base hypothesis incorporates the ideas of form acids and form bases. At the point when a corrosive separates into its particles in water, it loses a hydrogen particle. The species that is shaped is the corrosive's form base.
A more broad definition is that a form base is the base part, X-, of a couple of mixtures that change into one another by acquiring or losing a proton. The form base can acquire or retain a proton in a synthetic response. The form corrosive gives the proton or hydrogen in the response.
In a corrosive base response, the substance response is:
Corrosive + Base ⇌ Form Base + Form Corrosive
We know very well that from equilibrium state theories that pk[tex]_b[/tex] +pk[tex]_a[/tex] =14
where pk[tex]_a[/tex] = - log( k[tex]_a[/tex] )
So, we have k[tex]_a[/tex] =5.57×10⁻⁵
Taking log of k[tex]_a[/tex] ,we get
=>pk[tex]_a[/tex]= -log(5.57×10⁻⁵)
Using properties of logarithm, log(a × b)=log(a)+log(b)
=>pk[tex]_a[/tex]= -log(5.57) -log(10⁻⁵)
=>pk[tex]_a[/tex]= -0.745 +5
=>pk[tex]_a[/tex]=4.25
Therefore, from above written formula, we get
=>4.25+pk[tex]_b[/tex]=14
=>pk[tex]_b[/tex]=14-4.25
=>pk[tex]_b[/tex]=9.74
Hence, pk[tex]_b[/tex] value is 9.74
To know more about conjugate base, visit here:
https://brainly.com/question/12883745
#SPJ4
Work out the size of angle 0.
Give reasons for your answer.
Answer:
θ = 56°
Step-by-step explanation:
As OA and OB are both radii, triangle AOB is an isosceles triangle:
⇒ m∠ABO = m∠OAB = 48°
Interior angles of a triangle sum to 180°:
⇒ m∠ABO + m∠OAB + m∠AOB = 180°
⇒ 48° + 48° + m∠AOB = 180°
⇒ m∠AOB = 180° - 48° - 48°
⇒ m∠AOB = 84°
Angles on a straight line sum to 180°:
⇒ m∠AOB + m∠DOB = 180°
⇒ 84° + m∠DOB = 180°
⇒ m∠DOB = 180° - 84°
⇒ m∠DOB = 96°
The tangent of a circle is always perpendicular to the radius.
Therefore, tangent BC is perpendicular to radius OB, and tangent DE is perpendicular to radius OD, so:
m∠OBC = 90°m∠ODE = 90°OBCD is a quadrilateral.
The interior angles of a quadrilateral sum to 360°:
⇒ m∠OBC + m∠BCD + m∠CDO + m∠DOB = 360°
⇒ 90° + θ + 28° + 90° + 96° = 360°
⇒ θ + 304° = 360°
⇒ θ = 360° - 304°
⇒ θ = 56°
Is any additional information needed to show △≅△?
Answer:
No
Step-by-step explanation:
To prove 2 triangles an congruent we need three pieces of information
SSS or SAS or ASA or RHS
S - Side
A - Angle
R - Right angle
H - Hypotenuse
We have an angle side and another side
So these two triangles can be proved congruent by SAS
Hope this helped and have a good day
What is the solution?
Answer:
336.
Step-by-step explanation:
8P3 = 8! / (8 - 3)!
= 8*7*6*5*4*3*2*1 / 5*4*3*2*1
= 8*7*6
= 336
guse lagrange multipliers to find the maximum or minimum values of the function subject to the given constraint. (if an answer does not exist, enter dne.) f(x, y)
Therefore the maximum value of function f(x,y,z)=[tex]x^{2} y^{2} z^{2}[/tex] =1/27
And the minimum value is 0
What is function?function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable) (the dependent variable) (the dependent variable). Mathematics uses functions frequently, and functions are essential for specifying physical relationships in the sciences.
Here,
The function is given as:
f(x,y,z)=[tex]x^{2} y^{2} z^{2}[/tex]
[tex]x^{2} +y^{2}+ z^{2}[/tex]=1
=>[tex]x^{2} +y^{2}+ z^{2}[/tex]-1=0
Using Lagrange multiplies, we have:
L(x,y,z,λ)=f(x,y,z) +λ(0)
Substitute f(x,y,z)=[tex]x^{2} y^{2} z^{2}[/tex] and [tex]x^{2} +y^{2}+ z^{2}[/tex]-1=0
Differentiate
L(x)=[tex]2xy^{2} z^{2}[/tex]+2λx
L(y)=[tex]2yx^{2} z^{2}[/tex]+2λy
L(z)=[tex]2zx^{2} y^{2}[/tex]+2λz
L(λ)=[tex]x^{2} +y^{2}+ z^{2}[/tex]-1
Equating to 0
[tex]2xy^{2} z^{2}[/tex]+2λx =0
[tex]2yx^{2} z^{2}[/tex]+2λy = 0
[tex]2zx^{2} y^{2}[/tex]+2λz = 0
[tex]x^{2} +y^{2}+ z^{2}[/tex]-1 = 0
Factorize the above expressions
[tex]2xy^{2} z^{2}[/tex]+2λx =0
2x([tex]y^{2} z^{2}[/tex]+λ)=0
2x=0 and ([tex]y^{2} z^{2}[/tex]+λ)=0
x=0 and [tex]y^{2} z^{2}[/tex]= -λ
[tex]2yx^{2} z^{2}[/tex]+2λy = 0
2y([tex]x^{2} z^{2}[/tex]+λ)=0
2y=0 and ([tex]x^{2} z^{2}[/tex]+λ)=0
y=0 and [tex]x^{2} z^{2}[/tex]= -λ
[tex]2zx^{2} y^{2}[/tex]+2λz = 0
2z([tex]y^{2} x^{2}[/tex]+λ)=0
2z=0 and ([tex]x^{2} y^{2}[/tex]+λ)=0
z=0 and [tex]x^{2} y^{2}[/tex]= -λ
So we have ,
x=0 and [tex]y^{2} z^{2}[/tex]= -λ
y=0 and [tex]x^{2} z^{2}[/tex]= -λ
z=0 and [tex]x^{2} y^{2}[/tex]= -λ
The above expression becomes
x=y=z=0
This means that,
[tex]x^{2} +y^{2}+ z^{2}[/tex]=1
[tex]x^{2} +x^{2}+ x^{2} =1 \\3x^{2 } =1[/tex]
x= ±1/[tex]\sqrt{3}[/tex]
So,
y= ±1/[tex]\sqrt{3}[/tex]
z= ±1/[tex]\sqrt{3}[/tex]
The critic points are
x=y=z=±1/[tex]\sqrt{3}[/tex]
x=y=z=0
Therefore the maximum value of function f(x,y,z)=[tex]x^{2} y^{2} z^{2}[/tex] =1/27
And the minimum value is 0
To know more about function , visit
https://brainly.com/question/12426369
#SPJ4
This design began from the construction of a regular hexagon.
Select all true statements about quadrilateral JKLO.
1.) When JKLO is reflected across segment OA, JKLO is taken to HGLO. So, quadrilateral JKLO is congruent to quadrilateral HGLO.
2.) When JKLO is reflected across segment OJ, JKLO is taken to JIHO. So, quadrilateral JKLO is congruent to quadrilateral JIHO.
3.) When JKLO is reflected in any way, it will not produce another congruent quadrilateral in this figure. However, there is a way to translate JKLO to take it to another quadrilateral in this figure.
4.) When JKLO is reflected across segment OI, JKLO is taken to JIHO. So, quadrilateral JKLO is congruent to quadrilateral JIHO.
5.) When JKLO is reflected across segment OL, JKLO is taken to HGLO. So, quadrilateral JKLO is congruent to quadrilateral HGLO.
The statement 2) and 5) about the construction are correct.
What is construction?In geometry, the term "construction" refers to precisely drawing forms, angles, or lines. These structures simply require a pencil, compass, and straightedge (a ruler).
Given this, a design was created by building a standard hexagon.
The construction's real claims are as follows:
2) JKLO is taken to JIHO when it is mirrored across segment OJ. Therefore, quadrilateral JKLO and quadrilateral JIHO are congruent.
5) JKLO is transferred to HGLO when it is reflected over segment OL. Therefore, quadrilateral JKLO and quadrilateral HGLO are congruent.
Therefore, statement 2 and 5 about the structure are true.
For more information about constructions, visit;
brainly.com/question/8606089
#SPJ1
