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3 years ago

Consider Z1= 4-4 radical 3i and Z2= -16 i. What is Z1-Z2?

Mathematics

1 answer:

goldfiish [28.3K]3 years ago

8 0

Answer:

Option (3)

Step-by-step explanation:

$Z_1=4-4\sqrt{3}i$

$Z_2=-16i$

$Z_1-Z_2=(4-4\sqrt{3}i)-(-16i)$

$=4-4\sqrt{3}i+16i$

$=4-(4\sqrt{3}i-16i)$

$=4-4(\sqrt{3}-4)i$

Therefore, Option (3) will be the correct option.

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What is the Length of this line

baherus [9]

Answer:

I can't see that very good, but I counted 8 units.

Step-by-step explanation:

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3 years ago

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Find the distance between the points <br> (-8,-6) and (4, 10)

never [62]

Answer:

d=20

Step-by-step explanation:

To find the distance between 2 points we use the distance formula

d = √(x2 - x1)²+(y2 - y1)²

The given points are (x1= -8, y1 = -6) and (x2 = 4, y2 = 10).

Substitute the given points into the distance formula.

d = √(4 + 8)²+(10 +6)²

d = √144+252

d= √400

d = 20

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3 years ago

F(x)=6x-18 sub in f(x/3), f(x)/3

arlik [135]

These are two separate problems: in the first we will have to substitute in a new value for x into the original equation and in the second we will manipulate the preexisting equation for f(x).

To begin, we will sub in f(x/3). To do this, we will substitute each variable x in the equation (in this case there is only one) with x/3, and then simplify the resulting equation.

f(x) = 6x - 18

f(x/3) = 6(x/3) - 18

To simplify, we should distribute the 6 on the right side of the equation.

f(x/3) = 6x/3 - 18

Now, we can divide the first term on the right side to finalize our simplification.

f(x/3) = 2x -18

Secondly, we are asked to find f(x)/3. To do this, we will take our original value for f(x), and then simplify divide that entire function by 3.

f(x) = 6x - 18

f(x)/3 = (6x-18)/3

This means that we must divide each term of the binomial by 3, so we are really computing

f(x)/3 = 6x/3 - 18/3

We can simplify by dividing both of the terms.

f(x)/3 = 2x - 6

Therefore, your answer is that f(x/3) = 2x - 18, but f(x)/3 = 2x - 6. It is important to recognize that these are two similar, yet different, answers.

Hope this helps!

8 0

3 years ago

A chemical plant has an emergency alarm system. When an emergency situation exists, the alarm sounds with probability 0.95. When

Lapatulllka [165]

Answer:

6.56% probability that a real emergency situation exists.

Step-by-step explanation:

We have these following probabilities:

A 0.4% probability that a real emergency situation exists.

A 99.6% probability that a real emergency situation does not exist.

If an emergency situation exists, a 95% probability that the alarm sounds.

If an emergency situation does not exist, a 2% probability that the alarm sounds.

The problem can be formulated as the following question:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

$P = \frac{P(B).P(A/B)}{P(A)}$

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

In this problem:

What is the probability of a real emergency situation existing, given that the alarm has sounded.

P(B) is the probability of there being a real emergency situation. So $P(B) = 0.004$ .

P(A/B) is the probability of the alarm sounding when there is a real emergency situation. So P(A/B) = 0.95.

P(A) is the probability of the alarm sounding. This is 95% of 0.4%(real emergency situation) and 2% of 99.6%(no real emergency situation). So

P(A) = 0.95*0.04 + 0.02*0.996 = 0.05792

Given that the alarm has just sounded, what is the probability that a real emergency situation exists?

$P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.004*0.95}{0.05792} = 0.0656$

6.56% probability that a real emergency situation exists.

6 0

3 years ago

Need answer fast as possible

k0ka [10]

Answer:15

Step-by-step explanation:

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3 years ago

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