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3 years ago

Which of the following is the conjugate of 10 – 3i?

Mathematics

2 answers:

wariber [46]3 years ago

7 0

10 + 3i ...........................

ipn [44]3 years ago

3 0

we know that

The conjugate of a complex number is the number with equal real part and imaginary part equal in magnitude but opposite in sign

In this problem we have

$10-3i$

the conjugate is equal to--------> $10+3i$

therefore

the answer is the option

10+3i

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Pyramid A has a triangular base where each side measures 4 units and a volume of 36 cubic units. Pyramid B has the same height,

omeli [17]

Answer:

The volume of pyramid B is 81 cubic units

Step-by-step explanation:

Given

Pyramid A

$s = 4$ -- base sides

$V = 36$ -- Volume

Pyramid B

$s = 6$ --- base sides

Required

Determine the volume of pyramid B [Missing from the question]

From the question, we understand that both pyramids are equilateral triangular pyramids.

The volume is calculated as:

$V = \frac{1}{3} * B * h$

Where B represents the area of the base equilateral triangle, and it is calculated as:

$B = \frac{1}{2} * s^2 * sin(60)$

Where s represents the side lengths

First, we calculate the height of pyramid A

For Pyramid A, the base area is:

$B = \frac{1}{2} * s^2 * sin(60)$

$B = \frac{1}{2} * 4^2 * \frac{\sqrt 3}{2}$

$B = \frac{1}{2} * 16 * \frac{\sqrt 3}{2}$

$B = 4\sqrt 3$

The height is calculated from:

$V = \frac{1}{3} * B * h$

This gives:

$36 = \frac{1}{3} * 4\sqrt 3 * h$

Make h the subject

$h = \frac{3 * 36}{4\sqrt 3}$

$h = \frac{3 * 9}{\sqrt 3}$

$h = \frac{27}{\sqrt 3}$

To calculate the volume of pyramid B, we make use of:

$V = \frac{1}{3} * B * h$

Since the heights of both pyramids are the same, we can make use of:

$h = \frac{27}{\sqrt 3}$

The base area B, is then calculated as:

$B = \frac{1}{2} * s^2 * sin(60)$

Where

$s = 6$

So:

$B = \frac{1}{2} * 6^2 * sin(60)$

$B = \frac{1}{2} * 36 * \frac{\sqrt 3}{2}$

$B = 9\sqrt 3$

So:

$V = \frac{1}{3} * B * h$

Where

$B = 9\sqrt 3$ and $h = \frac{27}{\sqrt 3}$

$V = \frac{1}{3} * 9\sqrt 3 * \frac{27}{\sqrt 3}$

$V = \frac{1}{3} * 9 * 27$

$V = 81$

6 0

3 years ago

Read 2 more answers

Calculate the distance between each given pair of points. Round your answer to the nearest tenth, if necessary.

Ksju [112]

The answer is 5

Here are the steps:

First off, we will be using the distance formula of
$d=\sqrt{(x_ {2}- x_{2}) ^{2}+( y_{2}- y_{1})^2 }$

So we have the ordered pairs of (3,1) and (6,5)

Once you plug them into the formula it should look like this:
$d= \sqrt{(6-3)^2+(5-1)^2}$

Now we do the math inside the parenthesis and end up with:
$d=\sqrt{3^2+4^2}$

Then you multiply by the power and simplify to get:
$d=\sqrt{25}$

And the $\sqrt{25}$ =5

So your answer is 5

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3 years ago

Question 1

gulaghasi [49]

Answer:

Step-by-step explanation:

A function is where each input has a single output.

(A) There can be a different amount of students in a class (e.g. 21 or 22) that have the same class length

(B) There can be multiple things that Mike can order with $1

(D) There can be multiple students have the same GPA

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3 years ago

Graph the system of equations.

Marat540 [252]

You can soustracte the first or the second one

and y cancel

x = 6

now you put 6 in x
you can take the first or the second one

6 - y = -2
6 - y = -2
y = -8

8 0

3 years ago

Please help me I’m struggling

zhannawk [14.2K]

Answer:

-2\3

Step-by-step explanation:

3 0

3 years ago