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3 years ago

Simplify the following expression (1 + 4i) – (3 - 6i)

Mathematics

1 answer:

blagie [28]3 years ago

4 0

Answer:

10i - 2

Step-by-step explanation:

( 1 + 4i ) - ( 3 - 6i )

= 1 + 4i - 3 + 6i

= 1 - 3 + 4i + 6i

= - 2 + 10i

= 10i - 2

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alukav5142 [94]

Answer:

To the line

Step-by-step explanation:

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2 years ago

What are the domain and range of the exponential function below? <img src="https://tex.z-dn.net/?f=F%28x%29%20%3D%205%5

faust18 [17]

Answer:

Step-by-step explanation:

The domain is the set of x values for which the function is defined.

The range is the set of y values for which the function is defined.

Attached is the graph of the exponential function.

It is the basic graph of exponential function of y = 5^x which is shifted 6 units above (because of +6 at the end).

Looking at the graph, the domain is the set of all x values.

The range is anything above 6.

Correct answer is B.

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2 years ago

Rationalise the denominator.

grin007 [14]

Let's see what to do buddy...

_________________________________

To do this, we have to multiply the face and denominator of the fraction by the denominator conjunction, which is :

$(5 -\sqrt{2})$

°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°

Reminder :

$(a + b)(a - b) = {a}^{2} - {b}^{2} \\$

°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°

So we have :

$\frac{1}{ 5-\sqrt{2} } \times \frac{ 5+\sqrt{2} }{ 5 +\sqrt{2} } = \frac{1 \times ( 5 +\sqrt{2}) }{(5- \sqrt{2} )( 5 +\sqrt{2}) } = \\$

The other is in the photo.

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And we're done.

Thanks for watching buddy good luck.

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7 0

3 years ago

Suppose that contamination particle size (in micrometers) canbe modeled as

asambeis [7]

Answer:

c) 2

d) 0.96

Step-by-step explanation:

We are given the following in the question:

$f(x) = 2x^{-3}, x > 1\\~~~~~~~= 0, x \leq 1$

a) probability density function.

$\displaystyle\int^{\infty}_{\infty}f(x) dx = 1\\\\\displaystyle\int^{\infty}_{-\infty}2x^{-3}dx = 1\\\\\displaystyle\int^{\infty}_{1}2x^{-3}dx\\\\\Rightarrow \big[-x^{-2}\big]^{\infty}_1\\\\\Rightarrow -(0-1) = 1$

Thus, it is a probability density function.

b) cumulative distribution function.

$P(X$

c) mean of the distribution

$\mu = \displaystyle\int^{\infty}_{-\infty}xf(x) dx\\\\\mu = \int^{\infty}_12x^{-2}dx\\\\\mu = (-\frac{2}{x})^{\infty}_{1}\\\\\mu = 2$

d) probability that the size of random particle will be less than 5 micrometers

$P(X$

4 0

2 years ago

9/11 convert to decimal

Tasya [4]

The answer is 0.81 repeating

3 0

3 years ago