Find the interval in which the function is positive x^2-x-6=y
2 answers:
9514 1404 393
Answer:
(-∞, -2) ∪ (3, ∞)
Step-by-step explanation:
The function can be factored as ...
(x +2)(x -3) = y
The leading coefficient is positive, so the parabola opens upward. It will be positive up to the left-most zero, and positive again to the right of the right-most zero. That is, the function is positive everywhere outside the interval [-2, 3], where it is not.
The function is positive on (-∞, -2) ∪ (3, ∞).
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A right triangle will be formed with 2.2 km as the hypotenuse, 0.5 degrees as the angle, and an unknown height (see attachment).
Recall the trigonmetric ratios sine, cosine, and tangent that can be used for right triangles.
Sin<span>θ = opposite side/hypotenuse
</span>Cos<span>θ = adjacent side/hypotenuse
</span>tan<span>θ = opposite side / adjacent side
</span>θ (theta) refers to the angle (not the right angle). In this case, θ is the given angle of 0.5°.
In this problem, you will use sine because there is a side opposite to the angle (the unknown side h) and the hypotenuse, and sine relates those two sides.
Let the variable h represent the unknown opposite side, the height.
sin(0.5°) = h / (2.2km)
h = (2.2km)sin(0.5<span>°)
h = 0.019 km
Hope I helped! If you have questions on any of the steps, please comment below.</span>
Recall the trigonmetric ratios sine, cosine, and tangent that can be used for right triangles.
Sin<span>θ = opposite side/hypotenuse
</span>Cos<span>θ = adjacent side/hypotenuse
</span>tan<span>θ = opposite side / adjacent side
</span>θ (theta) refers to the angle (not the right angle). In this case, θ is the given angle of 0.5°.
In this problem, you will use sine because there is a side opposite to the angle (the unknown side h) and the hypotenuse, and sine relates those two sides.
Let the variable h represent the unknown opposite side, the height.
sin(0.5°) = h / (2.2km)
h = (2.2km)sin(0.5<span>°)
h = 0.019 km
Hope I helped! If you have questions on any of the steps, please comment below.</span>