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2 years ago

The theory of population growth based on geometric and arithmetic progressions is the

1 answer:

6 0

The theory of population growth based on geometric and arithmetic progressions is the Malthusian theory.

To add, in his 1798 work, An Essay on the Principle of Population, Malthus examined the relationship between population growth and resources and developed the Malthusian theory of population growth.

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Square efgh has been reflected across the x axis and then reflected across the y axis which of the following transformations wou

tigry1 [53]

An 180-degreee rotation would return the square to its original position.

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3 years ago

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The graph below represents which system of inequalities?

mamaluj [8]

The graph below represents y < 2 over 3x − 2 | y > 2x + 2 system of inequalities. The answer is letter C. The rest of the choices do not answer teh qustion above

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3 years ago

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please help me The question involves multiplying two complex numbers, then turning it into an a+bi equation (pictures included)

Sloan [31]

Answer:

(a, b) = (0, -15)

Step-by-step explanation:

In "cis" form the product of two complex numbers is the product of their magnitudes at the angle that is the sum of their angles. I find this the easiest way to multiply complex numbers.

z1 × z2 = (3 cis π)(5 cis π/2)

= (3·5) cis (π +π/2)

= 15 cis 3π/2

Of course, "cis" is short for "cosine + i·sine", so you have ...

z1 × z2 = 15 cis 3π/2 = 15(cos(3π/2) +i·sin(3π/2))

= 15(0 +i·(-1))

= 0 -15i

(a, b) = (0, -15)

8 0

3 years ago

Find f'(x) and state the domain of f': f(x) = In (2x^2+1)

-Dominant- [34]

Answer:

$f'(x) = \frac{4x}{2x^2+1}$

Domain: All Real Numbers

General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x)

Calculus

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Chain Rule: $\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Derivative: $\frac{d}{dx} [ln(u)] = \frac{u'}{u}$

Step-by-step explanation:

Step 1: Define

f(x) = ln(2x² + 1)

Step 2: Differentiate

Derivative ln(u) [Chain Rule/Basic Power]: $f'(x) = \frac{1}{2x^2+1} \cdot 2 \cdot 2x^{2-1}$
Simplify: $f'(x) = \frac{1}{2x^2+1} \cdot 4x$
Multiply: $f'(x) = \frac{4x}{2x^2+1}$

Step 3: Domain

We know that we would have issues in the denominator when we have a rational expression. However, we can see that the denominator would never equal 0.

Therefore, our domain would be all real numbers.

We can also graph the differential function to analyze the domain.

5 0

2 years ago

HELP ASAP!!! 40 POINTS

ICE Princess25 [194]

Using derivatives, it is found that the x-values in which the slope belong to the interval (-1,1) are in the following interval:

(-15,-10).

<h3>What is the slope of the tangent line to a function f(x) at point x = x0?</h3>

It is given by the derivative at x = x0, that is:

$m = f^{\prime}(x_0)$ .

In this problem, the function is:

$f(x) = 0.2x^2 + 5x - 12$

Hence the derivative is:

$f^{\prime}(x) = 0.4x + 5$

For a slope of -1, we have that:

0.4x + 5 = -1

0.4x = -6

x = -15.

For a slope of 1, we have that:

0.4x + 5 = 1.

0.4x = -4

x = -10

Hence the interval is:

(-15,-10).

More can be learned about derivatives and tangent lines at brainly.com/question/8174665

#SPJ1

8 0

1 year ago