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Lilit [14]
3 years ago
13

Find the first three iterates of the function f(z) = z2 + c with a value of c = 2 - 3i and an initial value of z0 = 1 + 2i.

Mathematics
1 answer:
Artist 52 [7]3 years ago
3 0

Answer:

C

Step-by-step explanation:

We have: (I rewrote the function)

f(z_n)={z_{n-1}} ^2+c

Given that:

\displaystyle c=2-3i \text{ and } z_0 = 1 + 2 i

The first iterate will be:

\displaystyle \begin{aligned} f(z_1)&=(z_0)^2+c \\ &=(1+2i)^2+(2-3i) \\ &= (1+4i+4i^2)+(2-3i) \\ &=1+4i-4+2-3i \\ &=-1+i \end{aligned}

The second iterate will be:

\begin{aligned}f(z_2) &=(z_1)^2+c\\ &=(-1+i)^2+(2-3i) \\&= (1-2i+i^2)+(2-3i) \\&=1-2i-1+2-3i \\&=2-5i \end{aligned}

And the third iterate will be:

\begin{aligned} f(z_3)&=(z_2)^2+c\\ &=(2-5i)^2+(2-3i) \\ &=(4-20i+25i^2)+(2-3i) \\ &=4-20i-25+2-3i \\ &=-19-23i \end{aligned}

Hence, our answer is C.

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Sonja [21]

Answer:

Z= 75*6 -250=200

So then the correct answer is B. $200.

Step-by-step explanation:

Notation

Let X be the average contribution size before John makes his contribution.

Let Y be the total contribution size before John makes his contribution.

Let Z be John's contribution.

We know that for this case $ 75 represent the original average amount before the contribution with 50% increase so we can set up the following equation in order to find the original average amount

1.5 X = 75

And solvong for X we got:

X = \frac{75}{1.5}= 50

Now we can find the total contribution before the donation with the following proportion:

\frac{50}{1}= \frac{Y}{5}

Y = 250

And then with the formula of average taking in count the 6 values we can find the size of donation Z like this:

\frac{Y+Z}{6}= 75

\frac{250+Z}{6}= 75

Z= 75*6 -250=200

So then the correct answer is B. $200.

5 0
3 years ago
Solve This Using The Quadratic Formula: 3x^2+9x-6=0
aivan3 [116]
<h3>Therefore either  x = \frac{-3+\sqrt{17}}{2}    or,  x = \frac{-3-\sqrt{17}}{2}</h3>

Step-by-step explanation:

3x^2 +9x -6=0                                x = \frac{-b\pm\sqrt{b^2- 4ac} }{2a}

\Leftrightarrow x = \frac{-9\pm\sqrt{9^2- 4.3(-6)} }{2.3}                     here a = 3 ,b = 9 and c= -6

\Leftrightarrow x = \frac{-9\pm\sqrt{153} }{6}

\Leftrightarrow x = \frac{3(-3\pm\sqrt{17}) }{6}

\Leftrightarrow x = \frac{-3\pm\sqrt{17}}{2}

Therefore either  x = \frac{-3+\sqrt{17}}{2}    or,  x = \frac{-3-\sqrt{17}}{2}

4 0
3 years ago
You have 3.4 gigabytes available on your tablet. A song is about 0.004 gigabytes. How many songs can you download into your tabl
Leokris [45]

Answer:

850

Step-by-step explanation:

what you need to do is divide 3.4 by .004. and since they are both in the same unit, theres no need to convert.

7 0
3 years ago
Which linear inequality is represented by the graph? y &gt; Two-thirdsx – One-fifth y ≥ Three-halvesx + One-fifth y ≤ Two-thirds
Marta_Voda [28]

Answer:

y > 2/3x - 1/5

y ≥ 3/2x + 1/5

y ≤ 2/3x + 1/5

y < 3/2x - 1/5

(Assume that the question want you to draw a graph)

Remember:

> or < is a dotted line

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3 0
3 years ago
Read 3 more answers
-2(8+8x)+7x=-7x+2(x-8)
Inessa [10]

x=0 .

−2(8+8x)+7x=−7x+2(x−8)

Step 1: Simplify both sides of the equation.

−2(8+8x)+7x=−7x+2(x−8)

(−2)(8)+(−2)(8x)+7x=−7x+(2)(x)+(2)(−8)(Distribute)

−16+−16x+7x=−7x+2x+−16

(−16x+7x)+(−16)=(−7x+2x)+(−16)(Combine Like Terms)

−9x+−16=−5x+−16

−9x−16=−5x−16

Step 2: Add 5x to both sides.

−9x−16+5x=−5x−16+5x

−4x−16=−16

Step 3: Add 16 to both sides.

−4x−16+16=−16+16

−4x=0

Step 4: Divide both sides by -4.

−4x /−4 = 0 /−4

x=0


7 0
3 years ago
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