## Second order half life

Input interpretation |
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second | order | elements | half-life |

Result |

second | order | 50 hours |

Category: Coordinate Geometry

Input interpretation |
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second | order | elements | half-life |

Result |

second | order | 50 hours |

Input interpretation |
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117 minutes |

Comparison as half‐life |

~~ 23 × half-life of uranium-241 (~~ 300 s ) |

Offsets from current time |

117 minutes from now | 6:08 am HKT | Friday, July 21, 2017 117 minutes before now | 2:14 am HKT | Friday, July 21, 2017 |

Interpretations |

time |

Input |
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13×5 |

Result |

65 |

Number name |

sixty-five |

Input interpretation |
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polar curves | area enclosed |

Result |

bifoliate | A = (pi a^2)/(2 sqrt(2)) bifolium | A = (pi a^2)/2 cardioid | A = (3 pi a^2)/2 cycloid of Ceva | A = 3 pi a^2 circle | A = pi a^2 circle parallel curve | A = pi (a + k)^2 cranioid | A = 1/2 pi (a^2 + 4 b c F_1(1/2;-1/2, -1/2;1;p, q) – b^2 (p – 2) – c^2 (q – 2)) folium of Descartes | A = (3 a^2)/2 fourth heart curve | A = 1/420 (-196 sqrt(5) 6^(3/4) tan^(-1)(root of 6 x^4 – 25 near x = -1.42872 + 1) + 2400 2F1(1, 1, 5/4, 24/49) + 2555 – 1176 log(6) + 98 sqrt(5) 6^(3/4) log(12 + 5 sqrt(6) – 2 sqrt(5) 6^(3/4)) – 98 sqrt(5) 6^(3/4) log(12 + 5 sqrt(6) + 2 sqrt(5) 6^(3/4)) + 196 sqrt(5) 6^(3/4) tan^(-1)(1 + sqrt(5)/6^(1/4))) – (5 pi^(3/2) (25 2F1(3/4, 1, 1/2, 49/24) + 38 2F1(3/4, 1, 9/4, -25/24)))/(96 sqrt(2) Gamma(5/4) Gamma(9/4)) + (6 – (21 – 7 i)/(sqrt(5) 6^(1/4))) pi hippopede curve | A = 2 pi (2 a – b) |

Input interpretation |
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parametric plane curves | area enclosed |

Result |

astroid | A = (3 pi a^2)/8 astroid pedal curve | A = -1/8 pi (a^2 + 4 (x_0^2 + y_0^2)) bifoliate | A = (pi a^2)/(2 sqrt(2)) bifolium | A = (pi a^2)/2 cardioid | A = (3 pi a^2)/2 cycloid of Ceva | A = 3 pi a^2 circle | A = pi a^2 circle parallel curve | A = pi (a + k)^2 cranioid | A = 1/2 pi (a^2 + 4 b c F_1(1/2;-1/2, -1/2;1;p, q) – b^2 (p – 2) – c^2 (q – 2)) cycloid | A = 3 pi a^2 |

Input |
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y = sqrt(x) |

Geometric figure |

parabola |

Plots |

Root |

x = 0 |

Properties as a real function |

Derivative |

(d)/(dx)(sqrt(x)) = 1/(2 sqrt(x)) |

Implicit derivatives |

Global minimum |

min{sqrt(x)} = 0 at x = 0 |

Input |
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x + y = 1 |

Geometric figure |

line |

Implicit plot |

Alternate forms |

Real solution |

y = 1 – x |

Solution |

y = 1 – x |

Input interpretation |
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plot | x^2 – y^2 = 1 |

Implicit plot |

Geometric figure |

hyperbola |