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2 years ago

Compute each of the following sums and differences:

Mathematics

1 answer:

cluponka [151]2 years ago

7 0

Answer:

a) 7 + 5i

b) 1 + 24i

a) 34 + i

b) -156 + 12i

Step-by-step explanation:

a) (5 + 8i) + (2 - 3i)

Add real parts ⇒ 5 + 2 = 7

Add imaginary parts ⇒ 8i + -3i = 5i

∴ (5 + 8i) + (2 - 3I) = 7 + 5i

b) (-3 + 12i) + (4 + 12i)

Add real parts ⇒ -3 + 4 = 1

Add imaginary parts ⇒ 12i + 12i = 24i

∴ (-3 + 12i) + (4 + 12I) = 1 + 24i

Products:

a) (5 + 8i)(2 - 3i)

= 10 - 15i + 16i - 24i² ⇒ (i² = -1)

= 10 + i - 24(-1) = 10 + i + 24

= 34 + i

b) (-3 + 12i)(4 + 12i)

= -12 - 36i + 48i + 144i² ⇒ (i² = -1)

= -12 + 12i + 144(-1) = -12 + 12i - 144

= -156 + 12i

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Which of the following is the standard equation of the ellipse with vertices at (1,0) and (27,0) and an eccentricity of 5/13?

Dovator [93]

The equation of the elipse is given by:

$\frac{(x - 14)^2}{169} + \frac{y^2}{144} = 1$

The equation of an elipse of center $(x_0, y_0)$ is given by:

$\frac{(x - x_0)^2}{a^2} + \frac{(y - y_0)^2}{b^2} = 0$

Values a and b are found according to the vertices and the eccentricity.

It has vertices at (1,0) and (27,0), thus:

$x_0 = \frac{27 + 1}{2} = 14$

$y_0 = \frac{0 + 0}{2} = 0$

$a = \frac{27 - 1}{2} = 13$

$a^2 = 169$

It has eccentricity of $\frac{5}{13}$ , thus:

$\frac{5}{13} = \frac{c}{a}$

$\frac{5}{13} = \frac{c}{13}$

$c = 13$

Thus, b is given according to the following equation:

$c^2 = a^2 - b^2$

$b^2 = a^2 - c^2$

$b^2 = 169 - 25$

$b = \sqrt{144}$

$b = 12$

The equation of the elipse is:

$\frac{(x - 14)^2}{169} + \frac{y^2}{144} = 1$

A similar problem is given at brainly.com/question/21405803

3 0

2 years ago

a rabbit's fur grows at a rate of 5/2 per month. How many months will it take for the rabbit's fur to grow 15/4 inches

UkoKoshka [18]

The answer is 1.5 months

explanation:

5/2 = 2.5

15/4 = 3.75

2.5 per month

3.75 per x months

x = (3.75×1)/2.5

x = 3.75/2.5

x = 3/2 = 1.5 months

3 0

3 years ago

A class of 40 students elected a class president. There were 12 votes for Candidate A, and 18 votes for Candidate B.

Helen [10]

Hey there, Bulgogi!

The correct answer will be the first one since [I'm assuming] you know that to calculate the percentage of something, it's the amount of that something divided by the total amount but since only 30 students voted [12+18] multiplied by 100.

So, we are calculating the percentage on votes and 12 students voted for Candidate A so our Numerator will be 12 and our Denominator will be the total amount of student who voted, so 30 [or 12+18]

Once put into a fraction, we will get $\frac{12}{12+18}$ which would be equals to 2/5 or 0.4. Now we multiply by 100 and we get a total of 40% for Candidate A.

Thank you for using Brainly.
See you soon!

4 0

3 years ago

Solving the equation

liubo4ka [24]

Answer:

y = 5

Step-by-step explanation:

Step 1: Write equation

-(4y + 2) - (-3y - 6) = -1

Step 2: Solve for y

Distribute: -4y - 2 + 3y + 6 = -1
Combine like terms: -y + 4 = -1
Subtract 4 on both sides: -y = -5
Divide both sides by -1: y = 5

Step 3: Check

Plug in y to verify it's a solution.

-(4(5) + 2) - (-3(5) - 6) = -1

-(20 + 2) - (-15 - 6) = -1

-22 - (-21) = -1

-22 + 21 = -1

-1 = -1

7 0

2 years ago

You will use 220ft of fencing to fence a rectangular plot of land. The length is 20 more than the width. What are the dimensions

PSYCHO15rus [73]

Set up the following equations:

$L + W = 110$
$L - W = 20$

110 represents the lengths of the length and width of the triangle, as you'll divide total perimeter of the rectangle, 220, by 2 to find the individual lengths. 20 is the difference between the length and width.

We'll use elimination for this system of equations, as there are opposite coefficients for W in both equations. Combine the two equations:

$2L = 130$

Divide both sides by 2 to get L by itself:

$L = 65$

The length of the rectangle is 65 feet.

Plug this value into the second equation:

$65 - W = 20$

Add W to both sides:

$65 = 20 + W$

Subtract 20 from both sides:

$45 = W$

The width of the rectangle is 45 feet.

6 0

2 years ago