Help me with these questions

Prestige Car Rentals charges $44 per day plus 6 cents per mile to rent a mid-sized vehicle. Gateway Auto charges $35 per day plu

Mama L [17]

Make two equations from the information. Then graph them and see where they intersect. The answer is 62 miles. Plug 62 back into both equations and they should both be the same number.

6 0

3 years ago

Read 2 more answers

a line passes through the points (14,5) and (19,15) determine and equation for a perpendicular line that passes through the poin

PSYCHO15rus [73]

The equation of the line thru <span> (14,5) and (19,15) is found as follows:

15-5 5
slope = m = ----------- = ------ = -1
19-14 5

Thus, the slope of any line perpendicular to this first line has the slope

m = -1/1 = -1.

Then, using the point-slope form, y-15 = -1(x-19), or y -15 = -x + 19, or
y= -x + 34 (answer)</span>

8 0

4 years ago

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

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