# Thread: Three tiny questions

1. ## 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!

2. Originally Posted by Open that Hampster!
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) $\displaystyle F\propto r^4$ so what can you deduce from here ? when r is 1.01 times , what would happen to F

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