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Math Help - Function notation for an equation w/ 1 side equal to the greater of two expressions

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    Function notation for an equation w/ 1 side equal to the greater of two expressions

    Hello. Thank you in advance for any help you can offer. I'm working with afunction that relates flow and pressure. For simplicity, letís say the function is P = A Q^2, where P is pressure, Q is flow, and A isconstant. This equation accuratelydescribes the behavior of a system when Q exceeds a certain value. Below this threshold, P is constant. For the systems I am now contemplating, Iknow what the threshold value of P is, but I donít yet know A. So, right now, I donít know the value of Qthat corresponds to the known pressure threshold.
    Letís say that Iknow that P can never be less than 80 and through experiments I learn that A = 5. In this case, Iíll be able write: P = 80 when Q < 4; P = 5 Q^2 when Q > = 4. While this notation may not comply withapplicable math notation standards, a reader would probably get the gist of what Iímtrying to say. (By the way, I would liketo know the technically correct way to express this conditional if somebodywould kindly show me.)
    More immediately, I would liketo better understand the correct way to express the above equation when I donít yetknow A and the value of Q that corresponds to the known minimum threshold ofP. For example: I want to write an expressionthat says P is equal to the greater of these two values: 80 or A Q^2. What is the correct notation to express this?
    Thanks!
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    Re: Function notation for an equation w/ 1 side equal to the greater of two expressio

    Quote Originally Posted by Wayintense View Post
    Hello. Thank you in advance for any help you can offer. I'm working with afunction that relates flow and pressure. For simplicity, letís say the function is P = A Q^2, where P is pressure, Q is flow, and A isconstant. This equation accuratelydescribes the behavior of a system when Q exceeds a certain value. Below this threshold, P is constant. For the systems I am now contemplating, Iknow what the threshold value of P is, but I donít yet know A. So, right now, I donít know the value of Qthat corresponds to the known pressure threshold.
    Letís say that Iknow that P can never be less than 80 and through experiments I learn that A = 5. In this case, Iíll be able write: P = 80 when Q < 4; P = 5 Q^2 when Q > = 4. While this notation may not comply withapplicable math notation standards, a reader would probably get the gist of what Iímtrying to say. (By the way, I would liketo know the technically correct way to express this conditional if somebodywould kindly show me.)
    More immediately, I would liketo better understand the correct way to express the above equation when I donít yetknow A and the value of Q that corresponds to the known minimum threshold ofP. For example: I want to write an expressionthat says P is equal to the greater of these two values: 80 or A Q^2. What is the correct notation to express this?
    Thanks!
    Simple. P = max(80, AQ^2)

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    Re: Function notation for an equation w/ 1 side equal to the greater of two expressio

    Thank you Dan! Simple, elegant, and (sadly) completely out of mind until you pointed me in the right direction! Thanks again.
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