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tekilochka [14]
3 years ago
12

If (x+yi)(1-3i)=10 Then x+y=

Mathematics
1 answer:
Naily [24]3 years ago
7 0

Answer:

x + y = 4

Step-by-step explanation:

Given that, (x + iy)(1 - 3i) = 10, then we have to calculate x + y.

Now, (x + iy)(1 - 3i) = 10

⇒ x(1 - 3i) + iy(1 - 3i) = 10

⇒ x - 3xi + iy - 3yi² = 10

⇒ (x + 3y) + i(y - 3x) = 10

Now, comparing the real and imaginary part of both sides we get,

(x + 3y) = 10 ............. (1) and

y - 3x = 0

⇒ y = 3x ............... (2)

Solving equations (1) and (2) we get

x + 3(3x) = 10

⇒ x = 1

So, y = 3x = 3

Therefore, x + y = 1 + 3 = 4 (Answer)

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Write the equation of a circle with a center (-3,9) and a radius of 14
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Answer:

(x+3) + (y-9) = 14^2

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3 years ago
A cube has a volume of 64. What is the length of one side of the cube?
bearhunter [10]

Answer:

4

Step-by-step explanation:

The volume of a cube can be represented as s^3 = v, where s = side and v = volume. In this case, we're given the volume as 64, so s^3 = 64. To solve this problem, we first have to know what a cube root is.

What's a cube root?

  • The cube root of a number is the number you multiply by itself 3 times to get another number.
  • One common cube is 27, and the cube root of it is 3 because 3 x 3 x 3 = 27.

Given the information above, let's go in order with the list of cube roots to see which one has a cube of 64.

  • 1: 1 x 1 x 1 = 1.
  • 2: 2 x 2 x 2 = 8.
  • 3: 3 x 3 x 3 = 27.
  • 4: 4 x 4 x 4 = 64. (This is the cube root!)

We found the cube root of 64, or the side of the cube with a volume of 64. The side of the cube, therefore, is 4.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

3 0
2 years ago
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4 0
3 years ago
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Given the directrix of y = 6 and focus of (0, 4), which is the equation of the parabola?\
Yuliya22 [10]

Answer:

The directrix is y=6 and focus is (0,4)

The equation of the parabola is,

20-4y=x²

5 0
3 years ago
Find the distance between the points E(3, 7) and F(6, 5). The exact distance between the two points is .
S_A_V [24]

Answer:

\sqrt{13}

Step-by-step explanation:

The trick here is to know the distance formula (a formula that helps you find the distance between two points).

Distance formula: distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

But now that we know this, we can simply plug in our values and solve!

\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\sqrt{(6-3)^2+(5-7)^2}\\\sqrt{(3)^2+(-2)^2}\\\sqrt{9+4}\\\sqrt{13}

Now we can tell from our answer that the distance between both points is \sqrt{13}

7 0
3 years ago
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