What comes next in this pattern? 7/2, 6/3, 5/4, ... 4/9 4/7 4/5
1 answer:
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Using the product rule, we have
so that
The equation of the tangent line to <em>W(x)</em> at <em>x</em> = 7 has all the information we need to determine <em>m'</em> (7).
When <em>x</em> = 7, the tangent line intersects with the graph of <em>W(x)</em>, and
<em>y</em> = 4.5 + 2 (7 - 7) ==> <em>y</em> = 4.5
means that this intersection occurs at the point (7, 4.5), and this in turn means <em>W</em> (7) = 4.5.
The slope of this tangent line is 2, so <em>W'</em> (7) = 2.
Then
According to the information given in the exercise, the following expression represents the area of the rectangular garden:
And the following expression represents the combined area of the walkway around the rectangular garden and the area of the garden:
You can identify that the word "combined" indicates that that expression was obtained by adding both areas.
Knowing the above, you can set up the following equation:
Where "A" is the area of the walkway around the rectangular garden.
Solving for "A", you get the following expression:
The answer is: