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3 years ago

The volume of a cube whose edge is 3x, is

Mathematics

1 answer:

diamong [38]3 years ago

6 0

Answer:

$27 { x}^{3}$

Step-by-step explanation:

s represents one side of the cube

Volume of cube= (s)^3

= (3x)^3

= 27x^3

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For the composite function, identify an inside function and an outside function and write the derivative with respect to x of th

alexira [117]

Answer:

The inner function is $h(x)=4x^2 + 8$ and the outer function is $g(x)=3x^5$ .

The derivative of the function is $\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4$ .

Step-by-step explanation:

A composite function can be written as $g(h(x))$ , where $h$ and $g$ are basic functions.

For the function $f(x)=3(4x^2+8)^5$ .

The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.

Here, we have $4x^2+8$ inside parentheses. So $h(x)=4x^2 + 8$ is the inner function and the outer function is $g(x)=3x^5$ .

The chain rule says:

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

It tells us how to differentiate composite functions.

The function $f(x)=3(4x^2+8)^5$ is the composition, $g(h(x))$ , of

outside function: $g(x)=3x^5$

inside function: $h(x)=4x^2 + 8$

The derivative of this is computed as

$\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=3\frac{d}{dx}\left(\left(4x^2+8\right)^5\right)\\\\\mathrm{Apply\:the\:chain\:rule}:\quad \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}\\f=u^5,\:\:u=\left(4x^2+8\right)\\\\3\frac{d}{du}\left(u^5\right)\frac{d}{dx}\left(4x^2+8\right)\\\\3\cdot \:5\left(4x^2+8\right)^4\cdot \:8x\\\\120x\left(4x^2+8\right)^4$

The derivative of the function is $\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4$ .

3 0

3 years ago

How do you write 0.0036 in scientific notation

Diano4ka-milaya [45]

3.6 * 10^(-3) is the scientific notation

5 0

3 years ago

Read 2 more answers

Explain why the function of f(x)=4x^2+8x is neither even or odd

myrzilka [38]

Answer:

By putting x = -x in f(x) i.e. f(-x) we didn't get f(x) or -f(x) so, the function is neither even nor odd.

Step-by-step explanation:

We need to explain why the function of $f(x)=4x^2+8x$ is neither even or odd

First we will understand, when the function is even and odd

Even function:

A function is even if f(-x) = f(x)

Odd function:

A function is odd if f(-x) = -f(x)

So, if we get the above result by putting x = -x, then we can say that the function is even or odd.

If we don't get any of the above results then the function is neither even nor odd.

So, for the given function: $f(x)=4x^2+8x$

Put x = -x

$f(x)=4x^2+8x\\Put x=-x\\f(-x)=4(-x)^2+8(-x)\\f(-x)=4x^2-8x$

So, by putting x=-x in f(x) i.e. f(-x) we didn't get f(x) or -f(x) so, the function is neither even nor odd.

6 0

3 years ago

If anybody now this pls help my homework due TOMORROW

Nezavi [6.7K]

Answer:

Part A: D. $y = (x + 1)(x+3)\\$

Part B: C. $3x(x-3) = 0\\$

Step-by-step explanation:

For part A) we just have to plug in 0 for x and solve for y until we find the equation that says 3 is the value for y when x is 0. For purposes of speeding up the process the correct answer is D. I will show how to check for it now.

The equation: $y = (x + 1)(x+3)$

Now plug in 0 for x.

$y = (0 + 1)(0+3)\\$

Now solve.

y = (1)(3)

y = 3

This proves that this is the correct answer.

For part B) we just have to plug in the give values for x separately and check for each value of x that it equals 0. For the purpose of speeding up the process the correct answer is C. I will show how to check for it now.

The equation: $3x(x-3) = 0$