answer these 2 question

The sum of given complex numbers in polar form as [tex]w+z=cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} )[/tex]

"The number of the type a + ib is called as complex number, where a, b are real numbers and [tex]i=\sqrt{-1}[/tex] "

"The polar form of a complex number z = x + iy is [tex]z=r(cos\theta+i~sin\theta)[/tex] where [tex]r=\sqrt{x^2+y^2}[/tex] and [tex]\theta=tan^{-1}({\frac{y}{x} })[/tex] "

For given question,

We have been given two complex numbers in polar form.

[tex]w=4(cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} ))~,z=3(cos(\frac{3\pi}{2} )+i~sin(\frac{3\pi}{2} ))[/tex]

The sum of given complex numbers would be,

[tex]w+z= 4(cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} ))+3(cos(\frac{3\pi}{2} )+i~sin(\frac{3\pi}{2} ))[/tex]

We know that

[tex]cos(\frac{\pi}{2} )=0\\\\sin(\frac{\pi}{2} )=1\\\\cos(\frac{3\pi}{2} )=0\\\\sin(\frac{\pi}{2} )=-1[/tex]

So, the sum of given complex numbers would be,

[tex]w+z\\\\= 4(cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} ))+3(cos(\frac{3\pi}{2} )+i~sin(\frac{3\pi}{2} ))\\\\=4(0+i(1))+3(0+i(-1))\\\\=4(i)+3(-i)\\\\=i\\\\=0+i[/tex]

We can write above sum of complex numbers in polar form as,

[tex]0+i=cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} )[/tex]

Therefore, the sum of given complex numbers in polar form as [tex]w+z=cos(\frac{\pi}{2} )+i~sin(\frac{\pi}{2} )[/tex]

Learn more about complex numbers here:

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Answer:

b on edge

Step-by-step explanation:

Answer:

Totals: 4.5% = 435$ 6% = 1452$, Monthly: 18$, 24$

Step-by-step explanation:

Answer:

See Explanation

Step-by-step explanation:

The options are missing. However, the question is still solvable.

Given

[tex]Work\ Hours = 1944[/tex]

[tex]Earnings = \$14[/tex] per hour

[tex]Estimated\ Earnings = \$28,000[/tex]

[tex]Sedan = \$25,750[/tex]

[tex]Convertible = \$27,990[/tex]

[tex]SUV = \$29,500[/tex]

First, we need to calculate her actual earnings.

This is calculated by multiplying the actual work hours (without approximation) by the earnings per hour

[tex]Total\ Earnings = 1944 * \$14[/tex]

[tex]Total\ Earnings = \$27,216[/tex]

Next, we compare this actual earnings to the amount of a Convertible

[tex]\$27216 < \$27,990[/tex]

Hence, Ashlee's conclusion is not logical because with her actual earnings, she cannot afford a Convertible

Answer:

see explanation

Step-by-step explanation:

A rational number Q can be expressed in the form

[tex]\frac{a}{b}[/tex] where a and b can take any integer value except b = 0

This is because it would lead to division by zero which is undefined.

Answer:

The answer is B

Step-by-step explanation:When you do 2 pages an hour, 2 hours is 4 pages, but you dont need an extra whole hour, instead just add a half which is why the answer is 2.5 hours.

Answer:

87.8

Step-by-step explanation:

I assume you know how to do this so I didn't show any steps. Have a nice night. :)

Answer

Quiz: Measures of Center

I got one wrong, so use at discretion

Step-by-step explanation: I took the test

1. 87.8

2. 6,060

3. 36

4. 312

5. 4.41 and 45.6

6. no mode

7. 0.236

8. 1,136

9. no mode

10. 33,745

Answer:

Yes, it is proportional

Step-by-step explanation:

the equation for the table is

x ÷ 28 = y

plug in the numbers for the variables

56 ÷ 28 = 2

84 ÷ 28 = 3

140 ÷ 28 = 5

Answer:

translate (x,y) (x-5,y+8)

Answer:

0.6666667

Step-by-step explanation:

1/3 of 2 is 0.6666667

Answer:

f(5) = 13

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = x² - 12

x = 5

Step 2: Evaluate

Answer:

13

Step-by-step explanation:

replace the x with 5.

5^2-12=

25-12=13

Answer:

66

Step-by-step explanation:

The sum of all of the angles in a triangle is 180. So all three angles would add up to 180:

(a + 21) + 57 + (a - 30) = 180

Combine like terms:

2a + 48 = 180

2a = 132

a = 66

Answer:

a+21+57+a-30=180(angle of triangle)

2a+48=180

2a=180-48

2a=132

a=132/2

a=66

then,a+21=66+21 =87

a-30=66-30 =36

Step-by-step explanation:

I think this is the answer

Answer:

4005 mètres de distance.

Step-by-step explanation:

Graph the line.

y=-4x+4

Graph the line.

y=-4x+4Graph the line.

y=-4x+4Graph the line.

y=-4x+4Graph the line.

y=-4x+4Graph the line.

y=-4x+4

Answer:

slope is 4

Step-by-step explanation:

rise over run lol

You have 12 cookies left because C=300

Answer:

100 adult tickets and 140 student tickets

Step-by-step explanation:

Answer:

Sold student tickets: 130, sold adult tickets: 110

Step-by-step explanation:

Let s = number of student tickets sold,

Let a = number of adult tickets sold.

[tex]s = 20+a[/tex] (It is given that there were 20 more student tickets sold than adult tickets)

[tex]s+a=240[/tex] (It is given that the total tickets sold is 240)

[tex]20+a+a = 240[/tex]

[tex]2a=220[/tex]

[tex]a = 110[/tex]

We can use substitution to find the number of student tickets:

[tex]s+a = 240[/tex]

[tex]s + 110 = 240[/tex]

[tex]s = 130[/tex]

∴110 adult tickets and 130 student tickets were sold.

I hope this helps :)

Answer:

B. The function shown on the graph has a smaller rate of change and a lower starting point.

Step-by-step explanation:

✍️The function y = 6x - 1, has:

slope (m) = 6, and

Starting point/y-intercept (b) = -1

✍️Let's find the slope (m) and the starting point (y-intercept) of the function shown on the graph:

Using the points, (0, -6) and (2, 4),

Slope = [tex] m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 -(-6)}{2 - 0} = \frac{10}{2} = 5 [/tex]

Slope (m) = 5

The strating value is the value of y when x = 0. In order words, it is the point at which the line of the function intercepts the y-axis.

The y-axis is intercepted at y = -6.

Therefore, the starting value (b) = -6.

Therefore, the statement correctly compares the function shown on the graph above with the function y = 6x - 1 is:

B. The function shown on the graph has a smaller rate of change and a lower starting point.

Comparing their slopes, 5 is smaller than 6.

Comparing their starting points, -6 is lower than -1.

Answer:

B

Step-by-step explanation:

Correct on a p e x

The probability of getting 3 in 132 times is 22.

A probability is a number that reflects the chance or likelihood that a particular event will occur.

Given that, Paul rolls a fair dice 132 times.

The probability of getting 3 in one roll is 1/6

so now it is 132 rolls

so,

= 132/6

= 22

Hence, The probability of getting 3 in 132 times is 22

For more references on probability, click;

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Answer: [-4, 8]

Step-by-step explanation:

The range is the mimimum y-value, the highest y-value.

On the graph, the lowest y-value is -4 and the highest y-value is 8. Thus, when writing in the range form, the range would by [-4, 8].

The range would be in hard brackets because the range touches exactly the points of -4 and 8. If each point had an open circle, instead of a closed point, there would be soft brackets.

Answer:

Step-by-step explanation:

I take you mean that f(x) = 4x + 1. If it really is C leave a note below the question, and I'll come back if you post within the hour.

f(3) = 4*3 + 1

f(3) = 12 + 1

f(3) = 13

Answer:

x=35

Step-by-step explanation:

simple equstion x+40+3x=180 then subtract forty combine the two X's and divide by 180

Answer:

The answer  is

B. 20.75

Answer:b.20.75

Step-by-step explanation:

big brain knowledge

Answer:

that would be 3.5

Step-by-step explanation:

have a great day (:

Answer: 3 1/2

Step-by-step explanation: The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed. Therefore, a way to solve this problem is by multiplying (7/8 x 4/1) which will give us a final answer or result of 3.5 or 3 1/2.

Step-by-step explanation:

Length of rectangular park = 175 m

Breadth of rectangular park = 150 m

Perimeter of park = 2 x (length + breadth)

= 2 x (175 + 150)

= 2 x 325 = 650 m

Since, cost of fencing park per meter = = Rs. 12

Therefore, cost of fencing park of 600 m = 12 x 650 = Rs. 7,800

Square park=250m

Perimeter of the square park x 4

=250x4

=1000m

So, the cost of the fencing at the park would have a rate of 20 per m = 1000x20

=20000

Answer:

4 to the right and 3 upward

or 7 overall

Step-by-step explanation:

4-0=4

5-2=3

Answer:

90

Step-by-step explanation: