For the rational function f(x)=x-2/3x^2+x-2, fill in the points on the graph at the function value f(x)=2.
1 answer:
Answer:
(-2/3, 2), (1/2, 2)
Step-by-step explanation:
A graphing calculator can show you those points: (-2/3, 2), (1/2, 2).
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Put the given value in the equation and solve for x.
2 = f(x)
2 = (x -2)/(3x^2 +x -2)
2(3x^2 +x -2) -(x -2) = 0 . . . . . multiply by the denominator; put in standard form
6x^2 +x -2 = 0 . . . . . collect terms
(3x +2)(2x -1) = 0 . . . factor
Solutions are values of x that make the factors zero:
x = -2/3, x = 1/2
Then the points on the graph are (-2/3, 2) and (1/2, 2).
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Answer:
- angles: 31.42°, 31.42°, 117.16°
- legs: 23.79 m
Step-by-step explanation:
The base angles can be found from the definition of the tangent function:
tan(base angle) = height/(half-base length)
base angle = arctan(12.4/20.3) ≈ 31.418°
Then the apex angle is double the complement of this:
apex angle = 2(90° -31.418°) ≈ 117.164°
The base angles are 31.42°, and the apex angle is 117.16°.
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The leg lengths can be computed from the Pythagorean theorem applied to the altitude and the half-base length.
leg length = √(12.4² +20.3²) = √565.85 ≈ 23.789 . . . . meters
The length of the legs is about 23.79 m.
