find the absolute maximum absolute minimum of the function F(x)=(x^2-12x+32)^(1/3) on the interval [3,10]
1 answer:
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Answer:
- minimum: -∛4 ≈ -1.58740
- maximum: ∛12 ≈ 2.28943
Step-by-step explanation:
The expression under the radical can be written in vertex form as ...
x^2 -12x +32 = (x -6)^2 -4
The function will be symmetrical about x=6. The minimum is at x=6 where we have ...
F(6) = ∛(-4)
The maximum is at the end of the interval farthest from the vertex, so is ...
F(10) = ∛((10 -6)² -4) = ∛12
The minimum is -∛4 ≈ -1.587; the maximum is ∛12 ≈ 2.289.
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Answer:
<em>x = 30.2 units</em>
Step-by-step explanation:
<u>Trigonometric Ratios</u>
The ratios of the sides of a right triangle are called trigonometric ratios.
Selecting any of the acute angles, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides and the hypotenuse.
The given right triangle has an angle of measure 51° and its adjacent leg has a measure of 19 units. It's required to calculate the hypotenuse of the triangle.
We use the cosine ratio to calculate x:
Solving for x:
x = 30.2 units