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1 year ago

Which statement describes how the reasonable domain compares to the mathematical domain?

1 answer:

8 0

A statement which best describes how the reasonable domain compares to the mathematical domain is that: C. the mathematical domain includes all real numbers, while the reasonable domain includes only real numbers greater than 2.

<h3>What is a domain?</h3>

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values or numbers to a function and the domain of any graph comprises all the input numerical values or numbers which are primarily shown on the x-axis.

Next, we would evaluate the function which represents the perimeter of this rectangle by substituting the value of 2 as follows:

f(w) = 6w – 8

f(2) = 6(2) – 8

f(2) = 12 – 8

f(2) = 4.

For the length of this rectangle, we have:

Length = 2w - 4

Length = 2(2) - 4

Length = 4 - 4

Length = 0

Therefore, the width of this rectangle must be real numbers that are greater than 2.

Read more on domain here: brainly.com/question/17003159

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Complete Question:

A rectangle has a length that is equal to 4 less than twice the width. The function for the perimeter depending on the width can be expressed with the function f(w) = 6w – 8, where w is the width of the rectangle in centimeters.

Which statement describes how the reasonable domain compares to the mathematical domain?

Both the mathematical and reasonable domains include only positive real numbers.

Both the mathematical and reasonable domains include only positive whole numbers.

The mathematical domain includes all real numbers, while the reasonable domain includes only real numbers greater than 2.

The mathematical domain includes all real numbers, while the reasonable domain includes only whole numbers greater than 2.

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3 years ago

Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] $ y =

Advocard [28]

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The answer is " $\frac{5 e^{5\sqrt{x} }}{2\sqrt{x}}$ ".

Step-by-step explanation:

Given:

$y = e^{{\color{\red}5}\sqrt{x}}$

let

$\to t= 5\sqrt{x}\\\\\frac{dt}{dx}= 5 \frac{1}{2\sqrt{x}}\\\\\frac{dt}{dx}= \frac{5}{2\sqrt{x}}\\\\$

and

$\to y=e^t\\\\\to \frac{dy}{dt}=e^t\\$

$\to \frac{dy}{dt}=e^{5\sqrt{x} }\\$

So,

$\to \frac{dy}{dx}= \frac{dy}{dt} \times \frac{dt}{dx}$

$=e^{5\sqrt{x} }\times \frac{5}{2\sqrt{x}}\\\\= \frac{5 e^{5\sqrt{x} }}{2\sqrt{x}}$

$\to g(x) = 5\sqrt{x} \\\\\to f(x) = e^{(x)}\\\\$

Derivate:

$\to f''g' = \frac{e^{(5\sqrt{x})}5}{(2\sqrt{x})}$

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3 years ago

A) what is the simplified product of seven-fourths divided by eight-fifths as an improper fraction

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Answer:

First were going to put our numbers in perspective.

$\frac{7}{4}$ ÷ $\frac{8}{5}$

But to find the improper fraction, we have to cross multiply these numbers.

$\frac{7}{4}$ × $\frac{8}{5}$

7 x 5 = 35. 

4 x 8 = 32.

Now we have our improper fraction is $\frac{35}{32}$

To turn our improper fraction into a mixed number, we will use division.

We know that the 32 can only go into 35 one time. We also know that the bottom number always stays the same. So our equation will look somewhat like this.

$1\frac{?}{32}$

Now to fine the top number we will have to subtract 35 from 32 because we already know that 32 can go into 35 one time, so 35 - 32 = 3. So are mixed number will look like this.

$1\frac{3}{32}$