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2 years ago

Suppose that 40 deer are introduced in a protected wilderness area. The population of the herd

Mathematics

1 answer:

Scorpion4ik [409]2 years ago

8 0

The horizontal asymptote of the function is the minimum number of deer in the area.

The equation of horizontal asymptote is: $\mathbf{y = 40}$
The horizontal asymptote means that, the number of deer will never be less than 40

The equation is given as:

$\mathbf{f(x) = \frac{40 + 2x}{1 + 0.05x}}$

Expand the numerator

$\mathbf{f(x) = \frac{40(1 + 0.05x)}{1 + 0.05x}}$

Cancel out the common factor

$\mathbf{f(x) = 40}$

Hence, the equation of horizontal asymptote is:

$\mathbf{y = 40}$

The horizontal asymptote means that, the number of deer will never be less than 40

Read more about horizontal asymptotes at:

brainly.com/question/4084552

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What key features will all continuous exponential functions have?

Hoochie [10]

Answer:

The graph passes through the point (0,1)
The domain is all real numbers.
The range is y>0.
The graph is increasing.
The graph is asymptotic to the x-axis as x approaches negative infinity.
The graph increases without bound as x approaches positive infinity.
The graph is continuous.

7 0

2 years ago

Lorena is designing a rectangular patio in her garden. She has enough tiles to cover 324 square feet. She wants the length of th

IceJOKER [234]

Using the area of a rectangle, it is found that her patio should have a width of 12 feet and a length of 27 feet.

<h3>What is the area of a rectangle?</h3>

The area of a rectangle of length l and width w is given by:

A = lw.

In this problem:

She has enough tiles to cover 324 square feet, hence A = 324.

She wants the length of the patio to be 15 feet longer than the width, hence l = 15 + w.

Thus:

324 = w(15 + w)

w^2 + 15w - 324 = 0

w = -27 or w = 12.

We take the positive value, hence l = 15 + w = 15 + 12 = 27 feet.

The dimensions should be a width of 12 feet and a length of 27 feet.

You can learn more about the area of a rectangle at brainly.com/question/10489198

7 0

1 year ago

Graph the first six terms of a sequence where a1 = −10 and d = 3. (2 points)

liberstina [14]

It will be a1 times D

4 0

2 years ago

Read 2 more answers

Find an equation of the line. Write the equation using function notation.

Gemiola [76]

The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:

$y = -4x+9$

Step-by-step explanation:

Given equation of line is:

$4y=x-8$

We have to convert the given line in slope-intercept form to find the slope of the line

So,

Dividing both sides by 4

$\frac{4y}{4} =\frac{x-8}{4}\\y = \frac{1}{4}x-\frac{8}{4}\\y = \frac{1}{4}x-2$

Let m1 be the slope of given line

Then

$m_1 = \frac{1}{4}\\$

Let m2 be the slope of line perpendicular to given line

As we know that produt of slopes of two perpendicular lines is -1

$m_1.m_2 = -1\\\frac{1}{4} . m_2 = -1\\m_2 = -1*4\\m_2 = -4$

The slope intercept form of line is given by:

$y = m_2x+b$

Putting the value of slope

$y = -4x+b$

to find the value of b, putting (3,-3) in equation

$-3 = (-4)(3) + b\\-3 = -12 +b\\b = -3+12\\b = 9$

Putting the value of b in the equation

$y = -4x+9$

Hence,

The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:

$y = -4x+9$

Keywords: Equation of line, slope

Learn more about equation of line at:

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4 0

2 years ago

Please help ASAP Meteorologists are planning the location of a new weather station to cover Santa Cruz, Morgan Hill, and Gilroy,

Likurg_2 [28]

Answer:

(-1, -2.5)

Step-by-step explanation:

(3, 0) is the midpoint between (2, 2) and (4, -2)

(-5, -5) (3, 0) the midpoint between these two points is

(-5 + 3) / 2 = -1, (-5 + 0) / 2 = -2.5

4 0

2 years ago