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dybincka [34]
3 years ago
7

Can someone help me do part two please? It’s very important send a picture or something. I don’t even care if you tell me the st

eps in word form. Please help

Mathematics
1 answer:
Nataly_w [17]3 years ago
4 0
<h3>Explanation:</h3>

1. "Create your own circle on a complex plane."

The equation of a circle in the complex plane can be written a number of ways. For center c (a complex number) and radius r (a positive real number), one formula is ...

  |z-c| = r

If we let c = 2+i and r = 5, the equation becomes ...

  |z -(2+i)| = 5

For z = x + yi and |z| = √(x² +y²), this equation is equivalent to the Cartesian coordinate equation ...

  (x -2)² +(y -1)² = 5²

__

2. "Choose two end points of a diameter to prove the diameter and radius of the circle."

We don't know what "prove the diameter and radius" means. We can show that the chosen end points z₁ and z₂ are 10 units apart, and their midpoint is the center of the circle c.

For the end points of a diameter, we choose ...

  • z₁ = 5 +5i
  • z₂ = -1 -3i

The distance between these is ...

  |z₂ -z₁| = |(-1-5) +(-3-5)i| = |-6 -8i|

  = √((-6)² +(-8)²) = √100

  |z₂ -z₁| = 10 . . . . . . the diameter of a circle of radius 5

The midpoint of these two point should be the center of the circle.

  (z₁ +z₂)/2 = ((5 -1) +(5 -3)i)/2 = (4 +2i)/2 = 2 +i

  (z₁ +z₂)/2 = c . . . . . the center of the circle is the midpoint of the diameter

__₁₂₃₄

3. "Show how to determine the center of the circle."

As with any circle, the center is the <em>midpoint of any diameter</em> (demonstrated in question 2). It is also the point of intersection of the perpendicular bisectors of any chords, and it is equidistant from any points on the circle.

Any of these relations can be used to find the circle center, depending on the information you start with.

As an example. we can choose another point we know to be on the circle:

  z₄ = 6-2i

Using this point and the z₁ and z₂ above, we can write three equations in the "unknown" circle center (a +bi):

  • |z₁ - (a+bi)| = r
  • |z₂ - (a+bi)| = r
  • |z₄ - (a+bi)| = r

Using the formula for the square of the magnitude of a complex number, this becomes ...

  (5-a)² +(5-b)² = r² = 25 -10a +a² +25 -10b +b²

  (-1-a)² +(-3-b)² = r² = 1 +2a +a² +9 +6b +b²

  (6-a)² +(-2-b)² = r² = 36 -12a +a² +4 +4b +b²

Subtracting the first two equations from the third gives two linear equations in a and b:

  11 -2a -21 +14b = 0

  35 -14a -5 -2b = 0

Rearranging these to standard form, we get

  a -7b = -5

  7a +b = 15

Solving these by your favorite method gives ...

  a +bi = 2 +i = c . . . . the center of the circle

__

4. "Choose two points, one on the circle and the other not on the circle. Show, mathematically, how to determine whether or not the point is on the circle."

The points we choose are ...

  • z₃ = 3 -2i
  • z₄ = 6 -2i

We can show whether or not these are on the circle by seeing if they satisfy the equation of the circle.

  |z -c| = 5

For z₃: |(3 -2i) -(2 +i)| = √((3-2)² +(-2-i)²) = √(1+9) = √10 ≠ 5 . . . NOT on circle

For z₄: |(6 -2i) -(2 +i)| = √((6 -2)² +(2 -i)²) = √(16 +9) = √25 = 5 . . . IS on circle

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2.) What value for c will make the expression a perfect square trinomial?
andre [41]

Answer : \frac{49}{4}

Given expression is x^2 - 7x + c

To make perfect square trinominal we use completing the square method

In completing the square method we add and subtract the half of square of coefficient of middle term

Here coefficient of middle term is -7

Half of -7 is \frac{-7}{2}

Square of \frac{-7}{2} is (\frac{-7}{2})^2 = \frac{49}{4}

So the expression becomes x^2 - 7x +  [tex] \frac{49}{4} that gives perfect square trinomial

Hence , the value of 'c' is \frac{49}{4}


6 0
3 years ago
Read 2 more answers
In New York a crowed subway has 375 passengers distributed between 5 cars. What is the unit rate for each subway car?
Andrews [41]
<h2>Answer:</h2><h2 /><h2>The unit rate is 75/1.</h2><h2 /><h2>Step-by-step explanation:</h2><h2 /><h2>To figure out this problem you have to divide. </h2><h2>375 divided by 5 is equal to 75. </h2><h2 /><h2>Therefore the unit rate is 75/1.</h2><h2 /><h2>Hope this helps and have a great day!!!</h2><h2 /><h2>:)</h2>
7 0
3 years ago
Please help thank you
Gemiola [76]
Question 1:

This is a 45-45-90 right triangle. If the leg length is x, then the hypotenuse length will be x \sqrt{2}.

The leg length of this 45-45-90 right triangle is 8. Multiply that with the square root of 2. You get 8 \sqrt{2}. Thus, the last choice is your answer.

Question 2:

This triangle can be identified as a 30-60-90 right triangle.
Let's say the smallest leg as a length of x.
Then, the longer leg will have a length of x \sqrt{3}.
Also, the hypotenuse will have a length of 2x

This triangle follows this format, making it a 30-60-90 right triangle. Thus, the angles are 30, 60, and 90.

Hope this helps! :)
5 0
3 years ago
Exhibit B: A restaurant has tracked the number of meals served at lunch over the last four weeks. The data shows little in terms
Mekhanik [1.2K]

Answer:

Option E is correct.

The expected number of meals expected to be served on Wednesday in week 5 = 74.2

Step-by-step Explanation:

We will use the data from the four weeks to obtain the fraction of total days that number of meals served at lunch on a Wednesday take and then subsequently check the expected number of meals served at lunch the next Wednesday.

Week

Day 1 2 3 4 | Total

Sunday 40 35 39 43 | 157

Monday 54 55 51 59 | 219

Tuesday 61 60 65 64 | 250

Wednesday 72 77 78 69 | 296

Thursday 89 80 81 79 | 329

Friday 91 90 99 95 | 375

Saturday 80 82 81 83 | 326

Total number of meals served at lunch over the 4 weeks = (157+219+250+296+329+375+326) = 1952

Total number of meals served at lunch on Wednesdays over the 4 weeks = 296

Fraction of total number of meals served at lunch over four weeks that were served on Wednesdays = (296/1952) = 0.1516393443

Total number of meals expected to be served in week 5 = 490

Number of meals expected to be served on Wednesday in week 5 = 0.1516393443 × 490 = 74.3

Checking the options,

74.3 ≈ 74.2

Hence, the expected number of meals expected to be served on Wednesday in week 5 = 74.2

Hope this Helps!!!

8 0
3 years ago
a hose fills a hot tub at a rate of 3.59 gallons per minute. how many hours will it take to fill a 309 gallon hot tub​
iris [78.8K]

Answer:

about 1.43 hours.

Step-by-step explanation:

You can use your original equation to find how many minutes it takes to fill up the 309 gallon hot tub.

3.59x=309

x= how many minutes it takes to fill up a certain gallon.

Divide both sides by 3.59 to isolate x and you get x=86.0724234.

That is how many minutes it takes.

The question asks for how many hours, so that divide 86.0724234 by 60 since there are 60 minutes in an hour, and you get 1.43454039 or 1.43 hours.

There is also another way which is called dimensional analysis, but I don't know if you guys learned that yet.

Hope my answer helps!

6 0
3 years ago
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