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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)

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Answer:

14(cos(330o) + i sin(330o))

Step-by-step explanation:

Answer:

I  added a picture, hope this helps!

Step-by-step explanation:

Let me know if you need to show work

Answer:D

Step-by-step explanation: 610/488= 1.25 or 5/4

The solution to each of the system of equations is given as follows:

11. (1,-1).

13. (-6,-5).

15. (-4,3).

For item 11, the system is given as follows:

The variable x can be isolated as follows:

Then the solution for y is given as follows:

y + 6  = 3 - 2y

3y = -3

y = -1.

Then the solution for x is of:

5x = -1 + 6

5x = 5

x = 1.

Following the same procedure, in item 13, we have that:

Hence the solution for x is of:

6x + 21 = 4x + 9

2x = -12

x = -6.

The solution for y is of:

3y = 4(-6) + 9

3y = -15

y = -5.

For item 15, we have that:

Hence the solution for y is of:

5 - 3y = -6y + 14

3y = 9

y = 3.

Then the solution for x is of:

x = 5 - 3(3)

x = 5 - 9

x = -4.

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The equation part of the given word problem is x+y=52 and y=x+16.

a) Let x = number of green eyed dolls

And let y = number of blue-eyed dolls

Now we are told the following:

x+y=52 → eq1

and

y=x+16 → eq2

b) substitute y = x+16 from eq2 into eq1:

x+x+16 = 52 subtract 16 from each side

x+x+16-16 = 52-16 collect like terms

2x = 36 divide each side by 2

x = 18 → number of green-eyed dolls

substitute x = 18 into equation2

y = 18+16 =34 → number of blue-eyed dolls

18+34=52

52=52

and

18+16=34

34=34

THIS PROBLEM CAN ALSO BE SOLVED USING ONE EQUATION AND ONE UNKNOWN:

Let x = Number of green-eyed dolls

Then 52-x = Number of blue-eyed dolls

Now we are told that:

x+16 = 52-x add x to and subtract 16 from each side

x+x+16-16 = 52-16-x+x collect like terms

2x=36 → same as before

x = 18.

Hence, the equation part of the given word problem is x+y=52 and

y=x+16.

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Answer:

27,000 or D

Step-by-step explanation:

30 x 30 x 30 = the answer on edge <3 good luckkk

The mean of the squared deviations

What is Squared deviations?

The sum of all scores' squared deviations from the mean is lower than the sum of all scores' squared deviations from any other number. The least squares concept governs this.

What is Mean ?

The average of a group of values is referred to as the mean. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

The term "mean square" refers to the sample variance in the analysis of variance (ANOVA) table, which calculates the mean squared deviation.

The average of the deviations' squared

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Cost of another 3 panes of class is 7.95

Given, Number of panes of glass bought = 8

Cost of 8 panes of glass = $21.20

Number of broken panes of glass = 3

We must determine the price of three glass panes.

By unitary method, If 8 panes of glass costs $21.20 , then the cost of one pane of glass will be as follows,

Cost of one pane of glass = 21.20/8

                                            = $2.65

Therefore,  cost of  3 panes of glass it would be $2.65×3 = 7.95

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value. In essence, this method is used to find the value of a unit from the value of a multiple, and hence the value of a multiple.

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Answer:

x³ -6x² +11x-6

Step-by-step explanation:

as there are three zeros visible, we assume the function is cubic. It can be written in the form ax³ +bx²+cx +d. Another form of writing a function is by making the brackets (x-x0), where x0 is the zero of the function (the value of the function for x0 is equal zero):  a(x-1)(x-2)(x-3) (I assumed a is 1). By multiplying the brackets, you got the answer.

The derivative of 1/logx is With the chain rule.

1log(x)=log(x)−1 is ,= -1xlog(x)2 .

The by-product of logₐ x (log x with base a) is 1/(x ln a). Here, the thrilling issue is that we have "ln" withinside the by-product of "log x". Note that "ln" is referred to as the logarithm (or) it's miles a logarithm with base "e".

The by-product of 1/log x is -1/x(log x)^2. Note that 1/logx is the reciprocal of log.

[tex]With the chain rule. \\

1log(x)=log(x)−1 \\

So you follow the chain rule to the electricity after which to the log: \\

ddxlog(x)−1=−1⋅log(x) \\ \\−2⋅ddxlog(x)

\\ =−1log(x)21x

\\ =−1xlog(x)2 .[/tex]

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The ratio of basketballs to soccer balls is 2 : 1

The quantity which would be written first if basketballs to soccer balls is 2 : 1 is basketball

This refers to a number representing a comparison between two or more named things.

If the ratio of basketballs to soccer balls = 2 : 1

This means,

Basketball : soccer ball = 2 : 1

Therefore, Basketball is the quantity which would be written first because it comes first in the given expression.

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By using the given information we can prove that  m ∠ABC = m ∠EDC.

What are similar angles?

Polygons' corresponding sides and corresponding angles are compared as part of the geometric tests for congruence and similarity. With care taken to maintain the order of adjacency, each side and each angle in one polygon is paired with a side or angle in the other polygon in these tests.

Given:

m ∠1 = m ∠2

m ∠2 = m ∠4

We have to prove that m ∠ABC = m ∠EDC

Let, ∠ABC = ∠1 + ∠2

and  ∠EDC = ∠3 + ∠4

So, m ∠ABC = m ∠1 + m ∠2

and  m ∠EDC = m ∠3 + m ∠4

From the given information,

m ∠1 + m ∠2 = m ∠3 + m ∠4        (Since m ∠1 = m ∠3,  m ∠2 = m ∠4)

⇒ m ∠ABC = m ∠EDC

Hence, by using the given information we can prove that  

m ∠ABC = m ∠EDC.

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The variable y takes the value -7 when we have x = -3.

Here we have the linear equation:

y = x - 4

We want to find the value of x such that y = -7, to get that, we only need to replace the variable y by the number -7 in the linear equation above:

-7 = x - 4

Now we can solve the linear equation for x.

-7 = x - 4

-7 + 4 = x

-3 = x

That is the solution.

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Answer:

Therefore, the equation of the line that is parallel to the given line and passes through the point ( − 6 , 9 ) (−6,9) is y = 4x + 33.

Step-by-step explanation:

To find the equation of a line that is parallel to a given line and passes through a given point, you can use the point-slope form of a linear equation. The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

Where (x1, y1) is the point through which the line passes, and m is the slope of the line.

The slope of a line is given by the difference in the y-coordinates of two points on the line, divided by the difference in the x-coordinates of those points. The slope of a line is also the coefficient of the x-term in the standard form of a linear equation (y = mx + b).

In this case, the given line is x − 6y = −60 − 9x. To find the slope of this line, you can rearrange the equation to standard form:

x − 6y = −60 − 9x

−9x + x − 6y = −60

−8x − 6y = −60

y = 4x + 15

The slope of this line is m = 4.

To find the equation of a line parallel to this line that passes through the point ( − 6 , 9 ) (−6,9), you can use the point-slope form of a linear equation with (x1, y1) = ( − 6 , 9 ) (−6,9) and m = 4:

y - 9 = 4(x - (-6))

y - 9 = 4(x + 6)

y - 9 = 4x + 24

y = 4x + 33

If the raisin swells to twice its original size, relative to the water, the raisin must have been a)hypertonic solution. So, correct option is a.

Hypertonic alludes to an answer with higher osmotic strain than another arrangement. At the end of the day, a hypertonic arrangement is one in which there is a more noteworthy fixation or number of solute particles outside a layer than there are inside it.

Hence, correct option is a.

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(Complete question) is:

You are bored at a lunch meeting and surreptitiously place a raisin in your glass of iced tea. The raisin shrinks to half its original size. The raisin must have been a __?__ solution.

a)hypertonic

b)aquatonic

c)hypotonic

d)isotonic

Answer:

y-intercept: -1

Step-by-step explanation:

The equation is y = mx + b

In this case, the y-intercept is -1

-1 is an integer, so my answer is correct!

Answer:

Slope: 1/3, [tex]y[/tex]-intercept: -1

Step-by-step explanation:

The [tex]y[/tex]-intercept of the line with equation [tex]y=mx+b[/tex] is [tex]b[/tex]. The slope is [tex]m[/tex].

Answer:

y = 51.2

Step-by-step explanation:

y/32=16/10

First, we time 32 on both sides to get y alone

y = 32(16/10)

y = 32(1.6)

y = 51.2

Let's check:

51.2/32 =  16/10

1.6 = 1.6

The answer y = 51.2 is correct!

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We specify the one-way anova model in the model statement of proc glm is model response variable; (the grouping variable is only specified in the class statement.)

So option b. is the correct option of the given statement.

Information that needs to be accessed and changed by a computer program is stored in variables. In order to make our programs more understandable to ourselves and the reader, they also offer a mechanism to label data with a descriptive name.

Values can be stored in variables. In order to use a variable, we must first declare it so the program is aware of it and then assign it so the program is aware of the value we are storing in the variable.

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The number of people died from aids in U.S. in 2005 are 2,30,68,96,671

Given, diseases tend to spread according to the exponential growth model.

In the early days of aids, the growth factor (i.e. common ratio; growth multiplier) was around 1.9.

In 1983, about 1700 people in the U.S. died of aids.

we have to find the number of people died from aids in 2005.

Let the exponential function, be

P(x) = AB^x

where, A is the initial population of people died of aids in U.S.

B is the growth factor of aids in U.S.

as, B = 1.9

In 1983, x = 0

P(0) = AB^0

1700 = A

Now, P(x) = 1700(1.9)^x

and the number of years from 1983 to 2005 are, 22 years

The number of people died from aids in 2005 be,

P(22) = 1700(1.9)^22

P(22) = 2,30,68,96,671

So, 2,30,68,96,671 people died from aids in 2005.

Hence, 2,30,68,96,671 people died from aids in 2005.

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The minimal approximation error A-A 2achievable by a rank-1 approximation A to A is

||A - A1||₂=0 where A is 2×2 matrix.

We have given a matrix A as seen in above figure or A = [ 5 15 ; 6 18 ; -1 -3 ; -4 -12 ; 2 6]

note here that C₂= 3C₁

where Cᵢ --> iᵗʰ column

v = [ 5 ; 6 ; -1 ; -4 ; 2]

||v||² = 82 => ||v|| = √82

and A At v = 820 v

and A At = [ 82 246 ; 246 738]

AAt [1;3] = 820[1;3]

=> v1 = 1/√10(1,3)^t

Then the best rank of 1 approx

= √820 /√80√10 [ 5 ; 6 ; -1 ; -4 ; 2] [ 1 3]

= A

Since , the rank of matrix A is one so, the minimal approx. value is ||A - A1||2 = 0

Hence, the minimal Approx. ||A - A1||2 = 0 .

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Complete question:

Consider the matrix A: A = [5 15] 6 18 -1 -3 -4 -12 [26] What is the minimal approximation error A-A 2 achievable by a rank-1 approximation A to A? Hint: Can you determine this without explicitly calculating the SVD?

There are 195 natural numbers from 1 to 600

The term integer is referred as the combination of zero, natural numbers and their additive inverse

Here we need to find how many of the natural numbers from 1 to 600, inclusive, contain the digit 5 at least once.

While we looking, into the given range of numbers 100 integers from 500 - 599 contain at least one 5

And here we know that in each of the 499 integers

=> _5, _15, _25, _35, _ 45, _55 , _65, _ 75, _ 85 , _ 95

And we also know that in each hundred  from 1 to 499 contain at least one 5

Therefore, there are 5 sets of these = 5 * 10  =  50

So, in each hundred from 1 to 499 we have the  integers

Therefore, _5_   where the last digit is not a 5

So, we have 9 of these in every hundred

Then here we have  5 * 9  = 45 of these

=> 100 + 50 + 45  = 195

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The value of the product of the numbers 10 and 2/3 is less than 10. Then the correct option is C.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The numbers are given below.

10 and 2/3

The product of the numbers 10 and 2/3 will be given as,

⇒ 10 x 2 / 3

⇒ 20 / 3

⇒ 6.67

The value of the product of the numbers 10 and 2/3 is less than 10. Then the correct option is C.

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The answer is 240 sticky hands. This is because each sticky hand costs 2 tickets, so if she has 480 tickets, she can buy 240 sticky hands.

What is cost?

Cost is the amount of money that is required to purchase, use, or produce something. It is an economic measure of the value of goods, services, or resources. Cost is typically associated with the purchase of goods and services and can include both the monetary and non-monetary costs associated with the acquisition. For example, when buying a car, the cost is the money spent on the purchase plus any additional costs such as taxes, registration fees, and insurance. Non-monetary costs can include the time and effort invested in researching and shopping for the car, as well as the opportunity cost of not using the money for something else.

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We have a 1/6 chance of rolling doubles on the first roll. The odds of rolling a double on the second turn but not the first are (5/6) x (1/6) = 5/36.

So we have a total of 36 outcomes over here. So we have 36 possibilities, and if we simplify this, 6/36 is 1/6. So the chance of rolling doubles on two six-sided dice numbered 1 to 6 is 1/6.

The odds of rolling a double on the second turn but not the first are (5/6) x (1/6) = 5/36.

We'll now look at the chances of getting out of jail by rolling doubles. Because there are more possibilities to examine, this probability is significantly more complex to compute.

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The zeros of the expression 3x² + 5x - 2 are 1/3 and -2

A quadratic equation can simply be defined as an algebraic equation having the second degree of x.

From the information given, we have that;

3x² + 5x - 2

Equate the expression to zero

3x² + 5x - 2 = 0

Find the pair factors of -6 that sum up to + 5, we get;

+ 6 and -1

Substitute the values into the equation;

3x² + 6x - x - 2 = 0

Enclose in brackets

(3x² + 6x) - ( x - 2) = 0

Factor the common terms

3x( x + 2) - 1( x + 2)

Then,

3x - 1 = 0

x = 1/3

x +2 = 0

x = -2

Hence, the values are 1/3 and -2

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Answer:

volume = 960π m³ ; surface area = 368π m²

Step-by-step explanation:

base area = 8²π = 64π m²

base perimeter = 8 x 2 x π = 16π m

lateral area = 16π x 15 = 240π m²

surface area = 2 x 64π + 240π = 128π + 240π = 368π m²

Volume = 64π x 15 = 960π m³

Answer:

true i think

Step-by-step explanation:

The area of a triangle whose sides are 4.5 cm and 1 cm and perimeter 10.5 cm is 2.045 square cm

The area for the triangle whose perimeter and side is given is solved by the formula

A= √(s(s ﹣ a) (s ﹣ b) ( s ﹣ c))

where:

a, b, and c are the sides of the triangle

s = perimeter / 2

perimeter = a + b + c

10.5 = 4.5 + 1 + c

c = 10.5 - 5.5

c = 5

s = (a + b + c) /2

s = 10.5/2

s = 5.25

substituting for s a b and c

A= √(s(s ﹣ a) (s ﹣ b) ( s ﹣ c) )

A= √(5.25 (5.25 ﹣ 4.5) (5.25 ﹣ 1) (5.25 ﹣ 5) )

A = √4.18358

A = 2.045 square cm

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