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Cake day: July 5th, 2023

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  • No, copilot solve this test

    Answer:

    To solve the expression ( e{\int_01 x^2+x+1 , dx} ), we first need to calculate the integral of ( x^2+x+1 ) from 0 to 1.

    The integral of ( x^2+x+1 ) is: [ \int x^2+x+1 , dx = \frac{x^3}{3} + \frac{x^2}{2} + x + C ]

    Evaluating this from 0 to 1 gives us: [ \left[ \frac{x^3}{3} + \frac{x^2}{2} + x \right]_0^1 = \left( \frac{1}{3} + \frac{1}{2} + 1 \right) - \left( 0 + 0 + 0 \right) = \frac{11}{6} ]

    Now, we raise ( e ) to the power of this result: [ e^{\frac{11}{6}} ]

    This is the solution to the given expression. If you need a numerical approximation, ( e^{\frac{11}{6}} ) is approximately 4.953.



  • fascinating range

    Stove (while being used): 200°C to 300°C when in use.

    Core of the Earth: In general, temperatures range from about 4,400°C (7,952°F) to about 6,000°C (10,800°F)

    Surface of the Sun: approximately 5,500°C (9,800°F)

    Core of the Sun: The Sun’s core is where nuclear fusion occurs, converting hydrogen into helium. The temperature at the Sun’s core is an astonishing 27 million°C (15 million°F) It’s the hottest part of our solar system.

    Random Examples:

    • Lightning Bolt: A lightning bolt can reach temperatures of 30,000°C (54,000°F) during discharge.
    • Lava Flow: Molten lava from a volcanic eruption can range from 700°C to 1,200°C (1,292°F to 2,192°F).
    • Spacecraft Reentry: During reentry into Earth’s atmosphere, spacecraft experience temperatures of about 1,650°C (3,002°F).
    • Boiling Water: Boiling water on your stove reaches 100°C (212°F) at sea level.
    • Liquid Nitrogen: Liquid nitrogen, used in cryogenics, is extremely cold at around -196°C (-321°F).
    • Absolute Zero: The theoretical lowest temperature, known as absolute zero, is -273.15°C (-459.67°F).