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Thread: Three tiny questions

  1. #1
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    Three tiny questions

    Hi all,

    I've gotten somewhere on two of these, but I'm stuck on all three

    1) If a stone is thrown vertically upward from the surface of the moon with a velocity of 6 m/s, its height (in meters) after t seconds is h = 6t - 0.83t^2. (Round the answers to two decimal places.)

    Part 1: What is the velocity of the stone after 3 s?
    I did this, I differentiated and solved.

    Part 2 has me confused, though.

    (b) What is the velocity of the stone after it has risen 8 m?

    Plugging 8 in for h and solving seems like a really messy solution. Am I mistaken here?

    2) When blood flows along a blood vessel, the flux F (the volume of blood per unit time that flows past a given point) is proportional to the fourth power of the radius R of the blood vessel. F = kR^4

    How will a 1% increase in the radius affect the flow of blood?

    I substituted some values into the function above and got ~10 but I'm assuming that was incorrect. Do I need to derive it and then take the change in R into F'?

    3) y = (2ln(x))/x

    Find the tangent line at (1,0) and (exp,2/exp)

    I know that I need to differentiate to get the tangent line and then solve for the slope and plug it into point slope equation, but I keep getting the wrong derivative on that one, so any help would be nice.

    Thanks!
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  2. #2
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    Quote Originally Posted by Open that Hampster! View Post
    Hi all,

    I've gotten somewhere on two of these, but I'm stuck on all three

    1) If a stone is thrown vertically upward from the surface of the moon with a velocity of 6 m/s, its height (in meters) after t seconds is h = 6t - 0.83t^2. (Round the answers to two decimal places.)

    Part 1: What is the velocity of the stone after 3 s?
    I did this, I differentiated and solved.

    Part 2 has me confused, though.

    (b) What is the velocity of the stone after it has risen 8 m?

    Plugging 8 in for h and solving seems like a really messy solution. Am I mistaken here?

    2) When blood flows along a blood vessel, the flux F (the volume of blood per unit time that flows past a given point) is proportional to the fourth power of the radius R of the blood vessel. F = kR^4

    How will a 1% increase in the radius affect the flow of blood?

    I substituted some values into the function above and got ~10 but I'm assuming that was incorrect. Do I need to derive it and then take the change in R into F'?

    3) y = (2ln(x))/x

    Find the tangent line at (1,0) and (exp,2/exp)

    I know that I need to differentiate to get the tangent line and then solve for the slope and plug it into point slope equation, but I keep getting the wrong derivative on that one, so any help would be nice.

    Thanks!
    HI

    (1b) Plug 8 into h to find the time when this occurs . Then plug the t you found here into dh/dt .

    (2) F\propto r^4 so what can you deduce from here ? when r is 1.01 times , what would happen to F

    (3) did u get y'(x)=\frac{2(\log(x)-1)}{x^2} ?
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