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3 years ago

Hi, can anyone show me how to do this problem? 100 points for this. Thanks in advance

Mathematics

2 answers:

algol [13]3 years ago

7 0

Answer:

z^2 + (-1 + 5·i)·z + 14 - 7·i = 0

(1 + 2·i)^2 + (-1 + 5·i)·(1 + 2·i) + 14 - 7·i = 0

(1 + 4·i - 4) + (-1 - 2·i + 5·i - 10) + 14 - 7·i = 0

0 = 0 --> true

z^2 + (-1 + 5·i)·z + 14 - 7·i = 0

(1 - 2·i)^2 + (-1 + 5·i)·(1 - 2·i) + 14 - 7·i = 0

(1 - 4·i - 4) + (-1 + 2·i + 5·i + 10) + 14 - 7·i = 0

20 - 4·i = 0 --> false

White raven [17]3 years ago

3 0

z^2 + (-1 + 5·i)·z + 14 - 7·i = 0

1+2i is a root

z= 1+2i

z^2 = (1+2i) (1+2i)

= 1 +2i+2i +4i^2

= 1 +4i -4

= -3+4i

= (-1+5i) (1+2i)

-1+5i-2i+10i^2

-1+3i-10

-11+3i

z^2 + (-1 + 5·i)·z + 14 - 7·i = 0

-3+4i + -11+3i +14 - 7i

Combine like terms

-3-11 +14 +4i +3i-7i

So 1+2i is a root

1-2i is not a root

z= 1-2i

z^2 = (1-2i) (1-2i)

= 1 -2i-2i +4i^2

= 1 -4i -4

= -3-4i

= (-1+5i) (1-2i)

-1+5i+2i-10i^2

-1+7i+10

9+7i

z^2 + (-1 + 5·i)·z + 14 - 7·i = 0

-3-4i + 9+7i +14 - 7i

Combine like terms

-3+9 +14 -4i +7i-7i

20 -4i

So 1-2i is not a root

The complex conjugate being roots is only true for real coefficients

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Marty and Ethan both wrote a function, but in different ways.

marishachu [46]

Question:

Marty and Ethan both wrote a function, but in different ways.

Marty

y+3=1/3(x+9)

Ethan

x y

-4 9.2

-2 9.6

0 10

2 10.4

Whose function has the larger slope?

1. Marty’s with a slope of 2/3

2. Ethan’s with a slope of 2/5

3. Marty’s with a slope of 1/3

4. Ethan’s with a slope of 1/5

Answer:

Marty’s with a slope of 1/3 has the larger slope

Solution:

Given that Marty equation is:

$y + 3 = \frac{1}{3}(x+9)$

The point slope form is given as:

$y - y_1 = m(x-x_1)$

Where, "m" is the slope of line

On comapring both equations,

$m = \frac{1}{3}$

Ethan wrote a function:

Consider any two values from the table we have;

(0, 10) and (2, 10.4)

The slope is given by formula:

$m = \frac{y_2-y_1}{x_2-x_1}$

From above two points,

$(x_1, y_1) = (0, 10)\\\\(x_2, y_2) = (2, 10.4)$

Therefore,

$m = \frac{10.4-10}{2-0}\\\\m = \frac{0.4}{2} \\\\m = 0.2$

Thus we get,

$\text{Slope of Ethan} < \text{Slope of Marty}$

Therefore, Marty’s with a slope of 1/3 has the larger slope

4 0

3 years ago

Read 2 more answers

You are building a model of a square pyramid. The side length of the base of the model is 30 cm. The height is 21 cm. What is th

Shalnov [3]

Answer:

Step-by-step explanation:

find the area of the base (square)=900 sq. cm
find area of triangles=1260 sq. cm
total= 2160 sq. cm

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3 years ago

Find the circumference and area of a circle that has a radius of x+1

lbvjy [14]

Circumference: 2πr
Circumference: 2(3.14)(x + 1)
Circumference: 6.28(x + 1)
Circumference: 6.28(x) + 6.28(1)
Circumference: 6.28x + 6.28

Area: πr²
Area: 3.14(x + 1)²
Area: 3.14(x +1)(x + 1)
Area: 3.14(x(x + 1) + 1(x + 1))
Area: 3.14(x(x) + x(1) + 1(x) 1(1))
Area: 3.14(x² + x + x + 1)
Area: 3.14(x² + 2x + 1)
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6 0

3 years ago

Mrs. Bautista invested Php2700.00 part at 8% and the rest at 11% .How musch did she invest at each rate if her total annual inco

Margarita [4]

Answer:

The answer to the question is

She invested

Php2700.00 at 8 % and

Php 20,400.00 at 11 %

Step-by-step explanation:

To solve the question we note that

Simple interest is given by $\frac{P*R*T}{100}$ where

P= Principal, R = Rate and T = Time

If we call the first part P₁, T₁, and R₁ and the second part

P₂, T₂, and R₂

Then ${P_1*(1+R_1*T_1}) +{P_*(1+R_2*T_2}) = 2460.00$

= 2700×0.08×1 + P₂×0.11×1 = 2460 which gives

2244÷0.11 = P₂ or P₂ = Php 20,400.00

That is she invested

Php2700.00 at 8 % and

Php 20,400.00 at 11 %

5 0

3 years ago

Find the missing values assuming continuously compounded interest. (Round your answers to two decimal places.)

alexdok [17]

Answer:

Step-by-step explanation:

Using the compound interest formula to calculate the amount compounded after 10years.

$A = P(1+r)^{nt}$

P = principal = $2000

r = rate (in %) = 5.6%

t = time (in years) = 10years

n = 1year = time used in compounding

$A = 2000(1+0.056)^{10} \\A = 2000(1.056)^{10}\\A = 2000*1.7244046\\A = 3448.81 (to\ 2dp)$

Amount compounded after 10 years is $3448.81

4 0

3 years ago