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3 years ago

This question is really hard for me.Please answer.

Mathematics

1 answer:

GarryVolchara [31]3 years ago

4 0

The correct answer is 13

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How do I determine z ∈ C:

saw5 [17]

Simplify the coefficient of z on the left side. We do this by rationalizing the denominators and multiplying them by their complex conjugates:

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3-2i}{1+i}\cdot\dfrac{1-i}{1-i} - \dfrac{5+3i}{1+2i}\cdot\dfrac{1-2i}{1-2i}$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{(3-2i)(1-i)}{1-i^2} - \dfrac{(5+3i)(1-2i)}{1-(2i)^2}$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3 - 2i - 3i + 2i^2}{1-(-1)} - \dfrac{5 + 3i - 10i - 6i^2}{1-4(-1)}$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3 - 5i + 2(-1)}2 - \dfrac{5 - 7i - 6(-1)}5$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{1 - 5i}2 - \dfrac{11 - 7i}5$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{1 - 5i}2\cdot\dfrac55 - \dfrac{11 - 7i}5\cdot\dfrac22$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{5 - 25i - 22 + 14i}{10}$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = -\dfrac{17 + 11i}{10}$

So, the equation is simplified to

$-\dfrac{17+11i}{10} z = \dfrac12 - \dfrac{2i}5$

Let's combine the fractions on the right side:

$\dfrac12 - \dfrac{2i}5 = \dfrac12\cdot\dfrac55 - \dfrac{2i}5\cdot\dfrac22$

$\dfrac12 - \dfrac{2i}5 = \dfrac{5-4i}{10}$

Then

$-\dfrac{17+11i}{10} z = \dfrac{5-4i}{10}$

reduces to

$-(17+11i) z = 5-4i$

Multiply both sides by -1/(17 + 11i) :

$\dfrac{-(17+11i)}{-(17+11i)} z = \dfrac{5-4i}{-(17+11i)}$

$z = -\dfrac{5-4i}{17+11i}$

Finally, simplify the right side:

$-\dfrac{5-4i}{17+11i} = -\dfrac{5-4i}{17+11i} \cdot \dfrac{17-11i}{17-11i}$

$-\dfrac{5-4i}{17+11i} = -\dfrac{(5-4i)(17-11i)}{17^2-(11i)^2}$

$-\dfrac{5-4i}{17+11i} = -\dfrac{85 - 68i - 55i + 44i^2}{289-121(-1)}$

$-\dfrac{5-4i}{17+11i} = -\dfrac{85 - 68i - 55i + 44(-1)}{410}$

$-\dfrac{5-4i}{17+11i} = -\dfrac{41 - 123i}{410}$

$-\dfrac{5-4i}{17+11i} = -\dfrac{41 - 41\cdot3i}{410}$

$-\dfrac{5-4i}{17+11i} = -\dfrac{1 - 3i}{10}$

So, the solution to the equation is

$z = -\dfrac{1-3i}{10} = \boxed{-\dfrac1{10} + \dfrac3{10}i}$

4 0

3 years ago

Find the measure of each marked angle.

Tatiana [17]

Answer:

x degrees = 50 degrees.

x + 50 degrees = 50 + 50 = 100 degrees

(180 - 3x) degrees = (180 - 3*50) = 30 degrees.

Step-by-step explanation:

In a triangle, the sum of all inside angles must be 180 degrees.

In this question:

The inside angles are: x, x + 50 and 180 - 3x.

Then

x + x + 50 + 180 - 3x = 180

2x - 3x = -50

x = 50

x degrees = 50 degrees.

x + 50 degrees = 50 + 50 = 100 degrees

(180 - 3x) degrees = (180 - 3*50) = 30 degrees.

6 0

4 years ago

The minute hand of a clock is 8 inches long. How far does the tip of the minute hand move in 30 minutes? How far does it move in

Brrunno [24]

Answer:

In 30 minutes:

The minute hand moves a distance of 25.13 inches

In 20 minutes:

The minute hand moves a distance of 16.76 inches

Step-by-step explanation:

When 60 minutes are completed, the minute hand of the relog makes a complete revolution. The distance s that the minute hand travels when making a complete revolution is:

$s = 2\pi r$ Where r is the radius of the circumference, and in this case, the radius of the minute hand.

So:

$s = 16 \pi$

s = 50.27 inches.

In 30 minutes (which is half of 60) the minute hand covers only half a revolution. Then the distance traveled in 30 minutes is $\frac{1}{2}(s) = 25.13$ inches

In 20 minutes (which is one third of 60) the minute hand only travels a third of a complete revolution. Then the distance traveled in 20 minutes is $\frac{1}{3}(s) = 16.76$ inches

3 0

3 years ago

To finance her community college education, Sarah takes out a loan for $4300. After a year Sarah decides to pay off the inter

VashaNatasha [74]

Answer:

301

Step-by-step explanation:

4300*.07=301

8 0

3 years ago

Read 2 more answers

Please help me! Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 f

blsea [12.9K]

Answer:

Step-by-step explanation:

This is an incomplete problem. Other data were not given.

Given:

Profit of every sandwich = $2

Profit of every wrap = $3

x = sandwich

y = wrap

Last month: 2x + 3y = 1,470

Next month: 2x + 3y = 1,593

Based on the given equation:

Both still have the same profit. $2 for sandwiches and $3 for wraps.

The only reason why there is a difference in the total amount is the change in the number of sandwich or wrap sold in a given month.

Since, next month's total sale is higher than last month's total sale, it is safe to assume that the sale of sandwich or wrap is higher than last month's sale.

4 0

3 years ago