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3 years ago

Which of the following expressions is the conjugate of a complex number with 2 as the real part and 3i as the imaginary part?

2 answers:

4 0

The complex number is represented as 2 + 3i. The conjugate of the complex number is the number with equal real part and imaginary part equal in magnitude but opposite in sign. Therefore, the correct answer is option B. The conjugate of the complex number is 2 − 3i.

luda_lava [24]3 years ago

4 0

Answer:

The conjugate of the complex number is 2 − 3i.

Step-by-step explanation:

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ANSWER ASAP TEST IN ONLY 45 MINUTES

melomori [17]

Answer:

-2x-15

Step-by-step explanation:

7 0

2 years ago

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A geologist had two rocks on a scale that weighed 2 1/2 lbs together. Rock A was 1/7 of the total weight. How much did Rock A we

GenaCL600 [577]

The total weight is 2 1/2 lbs

Rock A is 1/7 of the total weight....so it is 1/7 of 2 1/2 lbs..." of " means multiply

1/7 * 2 1/2 =
1/7 * 5/2 =
5/14 lbs <==

7 0

3 years ago

If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f at (2, 4, 0) in the direction

valentina_108 [34]

Answer:

a) $\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$ .

b) $Du_{f}(2,4,0) = -\frac{8}{\sqrt{11}}$

Step-by-step explanation:

Given a function $f(x,y,z)$ , this function has the following gradient:

$\nabla f(x,y,z) = f_{x}(x,y,z)\mathbf{i} + f_{y}(x,y,z)\mathbf{j} + f_{z}(x,y,z)\mathbf{k}$ .

(a) find the gradient of f

We have that $f(x,y,z) = x\sin{yz}$ . So

$f_{x}(x,y,z) = \sin{yz}$

$f_{y}(x,y,z) = xz\cos{yz}$

$f_{z}(x,y,z) = xy \cos{yz}$ .

$\nabla f(x,y,z) = f_{x}(x,y,z)\mathbf{i} + f_{y}(x,y,z)\mathbf{j} + f_{z}(x,y,z)\mathbf{k}$ .

$\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$

(b) find the directional derivative of f at (2, 4, 0) in the direction of v = i + 3j − k.

The directional derivate is the scalar product between the gradient at (2,4,0) and the unit vector of v.

We have that:

$\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$

$\nabla f(2,4,0) = \sin{0}\mathbf{i} + 0\cos{0}\mathbf{j} + 8 \cos{0}\mathbf{k}$ .

$\nabla f(2,4,0) = 0i+0j+8k=(0,0,8)$

The vector is $v = i + 3j - k = (1,3,-1)$

To use v as an unitary vector, we divide each component of v by the norm of v.

$|v| = \sqrt{1^{2} + 3^{2} + (-1)^{2}} = \sqrt{11}$

$v_{u} = (\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}})$

Now, we can calculate the scalar product that is the directional derivative.

$Du_{f}(2,4,0) = (0,0,8).(\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}}) = -\frac{8}{\sqrt{11}}$

6 0

3 years ago

The difference between two integers is 32.The ratio of these integers is 1:3.Find these integers

shutvik [7]

Answer:

16 and 48

Step-by-step explanation:

let the 2 integers be x and 3x ← ratio 1 : 3

Then

3x - x = 32 ← difference between the integers

2x = 32 ( divide both sides by 2 )

x = 16

and 3x = 3 × 16 = 48

Since magnitude of difference is 32

We can also express the difference as

x - 3x = 32

- 2x = 32 ( divide both sides by - 2 )

x = - 16

and 3x = 3 × - 16 = - 48

The 2 integers are 16 and 48 or - 16 and - 48

7 0

3 years ago

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Colin surveyed 12 teachers at school to determine how much each person budgets for lunch. He records his results in the table. W

zmey [24]

Answer:

As mean and median are equal, so the data will be in normal distribution in shape of a symmetrical "bell curve".

Step-by-step explanation:

The given data: 10 5 8 10 12 6 8 10 15 6 12 18

Mean is the simple average of all data. As, there are total 12 data, so the Mean will be: $\frac{10+5+8+10+12+6+8+10+15+6+12+18}{12}= \frac{120}{12}=10$

For finding the Median, first we need to rearrange the data according to the numerical order and then identify the middle value. So........

5 6 6 8 8 10 10 10 12 12 15 18

Here the middle values are 10 and 10. So, the median will be the average of those two middle values.

Thus, Median $=\frac{10+10}{2}=\frac{20}{2}=10$

We can see that, the relationship between the mean and the median is "they are equal". So, the data will be in normal distribution and the shape will be symmetrical "bell curve".

8 0

2 years ago

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