A rectangle has height of 3,27 meters and a base measuring 1.29 meters as shown which of the following is closest to x the lengt
1 answer:
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Answer:
- relative minimum -6√3 at x = -√3
- relative maximum 6√3 at x = √3
- decreasing on x < -√3 and x > √3
- increasing on -√3 < x < √3
- see below for a graph
Step-by-step explanation:
I find it convenient to draw the graph first when looking for relative extrema.
The function can be differentiated to get ...
f'(x) = -3x^2 +9
This is zero when ...
-3x^2 +9 = 0
x^2 = 3
x = ±√3 . . . . . x-values of relative extrema
Then the extreme values are ...
f(±√3) = x(9 -x^2) = (±√3)(9 -3) = ±6√3
The lower extreme (minimum) corresponds to the lower value of x (-√3), so the extrema are ...
(x, y) = (-√3, -6√3) and (√3, 6√3)
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Since the leading coefficient is negative and the degree is odd, the function is decreasing for values of x below the minimum and above the maximum. It is increasing for values of x between the minimum and the maximum.
decreasing: x < -√3, and √3 < x
increasing: -√3 < x < √3
Answers:
A. B 1/3 represents the area of triangle B
B. Triangle B area = 21/2 m² or 10 1/2 m² or 10.5 m²
Step-by-step explanation:
<em>Ok, we have two triangles measured in square meters (m²)</em>
∆ a = 1/3 b and ∆ b = 3 1/2
<em>Since these two areas have something in common (symbol a) we can consider they are almost the same, so we put them like this:</em>
∆ a => <u>1/3 b = 3 1/2</u> <= ∆ b
<em>Now that we know we can move some values. first we are gonna multiply the mixed fraction (3 1/2) to make it a regular fraction. As 3 is a whole, we can also write it on the following way:</em>
<em>We add these fractions:</em>
<em>The equation with this part solved is:</em>
<em>Since the </em><em>1/3 </em><em>is multiplying, it goes to the other side dividing the number on the right:</em>
<em></em>
<em>And then, we can solve the rest by inverting the second fraction () and multiplying it by the first one:</em>
<em></em>
<em></em>
<em>And that's it. Let me know if you have any doubts :D</em>