Answer:
(Choice D)
Step-by-step explanation:
You first need to solve the following inequality in order to get the actual answer and find the actual graph:
-Subtract to both sides:
-Divide both sides by :
The number line graphed:
Let x=small rugs and y=medium rugs. It takes 8 hours to dye a small rug, so you would write 8x. It takes 12 hours to dye a small rug, so you would write 12y. Those two would need to be added together. The dyer needs to dye at least 22 rugs in 240 hours, so you would need a less than or = to sign.
I'm not sure which choice has the line beneath, indicating that the sign is a "less than or equal to" sign, but the answer is gonna be either C or D.
8x+12y≤240, or 12y+8x<span>≤240</span>
<h3>Answer:</h3>
<h3>Explanation:</h3>
It can work well to consider the function in parts. Define the following:
... a(x) = (1/2)ln(x^2+3)
... b(x) = x(4x^2-1)^3
Then the derivatives of these are ...
... a'(x) = (1/2)·1/(x^2 +3)·2x = x/(x^2+3)
... b'(x) = (4x^2 -1)^3 + 3x(4x^2 -1)^2·8x = (4x^2 -1)^2·(4x^2 -1 +24x^2)
... = (4x^2 -1)^2·(28x^2 -1)
___
<em>Putting the parts together</em>
f(x) = a(x)/b(x)
f'(x) = (b(x)a'(x) -a(x)b'(x))/b(x)^2 . . . . . rule for quotient of functions
Substituting values, we have
... f'(x) = (x(4x^2 -1)^3·x/(x^2 +3) -(1/2)ln(x^2 +3)·(4x^2 -1)^2·(28x^2 -1)) / (x(4x^2 -1)^3)^2
We can cancel (4x^2 -1)^2 from numerator and denominator. We can also eliminate fractions (1/2, 1/(x^2+3)). Then we have ...
... f'(x) = 2x^2(4x^2 -1) -(x^2 +3)ln(x^2 +3)·(28x^2 -1)/(2x^2·(x^2 +3)(4x^2 -1)^4))
Simplifying a bit, this becomes ...
... f'(x) = (8x^4 -2x^2 -ln(x^2 +3)·(28x^4 +83x^2 -3))/(2x^2·(x^2 +3)(4x^2 -1)^4))
Answer:
See attached figure with table filled in.
Step-by-step explanation:
Answer:
<em>Here</em><em>,</em>
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<em>if</em><em> </em><em>f</em><em>(</em><em>x</em><em>)</em><em>=</em><em>11</em>
<em>we</em><em> </em><em>know</em><em> </em><em>that</em><em>,</em>
<em>o</em><em>r</em><em>,</em><em>11</em><em>=</em><em>2x</em><em>+</em><em>3</em><em>(</em><em>x-3</em><em>)</em>
<em>o</em><em>r</em><em>,</em><em>11</em><em>=</em><em>2x</em><em>+</em><em>3x-9</em>
<em>o</em><em>r</em><em>,</em><em>11</em><em>+</em><em>9</em><em>=</em><em>5x</em>
<em>o</em><em>r</em><em>,</em><em>20</em><em>=</em><em>5x</em>
<em>T</em><em>h</em><em>e</em><em>r</em><em>e</em><em>f</em><em>o</em><em>r</em><em>e</em><em>,</em><em>x</em><em>=</em><em>4</em>