**Answer:**

carbon dioxide,oxygen,nitrogen

**Answer:**

75 thousand

**Step-by-step explanation:**

R = -x³ + 102x² + 1575x

To maximize R, find dR/dx and set to 0:

dR/dx = -3x² + 204x + 1575

0 = -3x² + 204x + 1575

0 = x² − 68x − 525

0 = (x + 7) (x − 75)

x = -7 or 75

Since x can't be negative, x = 75.

Therefore, the revenue is a maximum when 75 thousand units are produced.

The tangent line to <em>y</em> = <em>f(x)</em> at a point (<em>a</em>, <em>f(a)</em> ) has slope d<em>y</em>/d<em>x</em> at <em>x</em> = <em>a</em>. So first compute the derivative:

<em>y</em> = <em>x</em>² - 9<em>x</em> → d<em>y</em>/d<em>x</em> = 2<em>x</em> - 9

When <em>x</em> = 4, the function takes on a value of

<em>y</em> = 4² - 9•4 = -20

and the derivative is

d<em>y</em>/d<em>x</em> (4) = 2•4 - 9 = -1

Then use the point-slope formula to get the equation of the tangent line:

<em>y</em> - (-20) = -1 (<em>x</em> - 4)

<em>y</em> + 20 = -<em>x</em> + 4

**<em>y</em>**** = -****<em>x</em>**** - 24**

The normal line is perpendicular to the tangent, so its slope is -1/(-1) = 1. It passes through the same point, so its equation is

<em>y</em> - (-20) = 1 (<em>x</em> - 4)

<em>y</em> + 20 = <em>x</em> - 4

**<em>y</em>**** = ****<em>x</em>**** - 24**

$255 because you do 130% over 100% = x over 850, than you do 130 times 850 divided by 100 and you get 1105, than you do 1105 minus 850 and you get $255