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Omni-MATH / A real number x is chosen uniformly at random from the interval (0,10). Compute the probability that √(x),√(x+7), and √(10−x) are the side lengths of a non-degenerate triangle.

Problem

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problem

A real number xx is chosen uniformly at random from the interval (0,10)(0,10). Compute the probability that x,x+7\sqrt{x}, \sqrt{x+7}, and 10−x\sqrt{10-x} are the side lengths of a non-degenerate triangle.
Plain-text mathematical notation (without MathML)
A real number x is chosen uniformly at random from the interval (0,10). Compute the probability that √(x),√(x+7), and √(10−x) are the side lengths of a non-degenerate triangle.
Original LaTeX notation
A real number $x$ is chosen uniformly at random from the interval $(0,10)$. Compute the probability that $\sqrt{x}, \sqrt{x+7}$, and $\sqrt{10-x}$ are the side lengths of a non-degenerate triangle.

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Source and history

task_id
16655a94-120b-5fdb-9afe-62bc52aa8bc2
task_key
test--16655a94-120b-5fdb-9afe-62bc52aa8bc2
task_revision_id
1
config / split
/ test

Official source

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