Can anyone help??

numberconfused

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Oct 8, 2012
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1. The following models thre height of any object over time projected upward with an initial velocity of v, from its height k, but not to objects under populsion
h(t)=-16t^(2)+vt+k (t is time in any time increment)
A member of a local rotary club launches a rocket from a large field. At the moment its fuel is exhausted the rocket has a velocityof 225 feet per second and an altitude of 544 feet.
a.) write the function that models the height of the rocket.
b.)How high is the rocket at time equal to zero and explain why if the rocket took off from the ground that the height of the rocket at time equal to zero is not zero feet?
c.)How high is the rocket after 4 seconds and after 13 seconds? Explain what your answer reveals about the rocket trajectory.
d.) How long will it take for the rocket to reach its maximum height and what is that maximum height?
e.)How long will it take for the rocket to land on the ground?


2. when the drug acetaminophen used for pain relief is taken orally the concentration of the drug in the patients bloodstream after t minutes is given by A(t)=26.6t-0.35t^(2) where 0≤t≤80 and the concentration A(t) is measured in grams per liter(g/L). Likewise when the drug Ibroporphen is taken orally the concetration of the drug in the patients bloodstream after t minutes is given by the function
I(t)=21.7t-0.48t^(2), where 0≤t≤60 and the concentration I(t) is measured in g/L
a.)When is the maximum of each concentration reached, and what is the maximums concetration for each other?
b.)At what time will the drug concentration leave the patients bloodstream?
c.) Since both drugs are used for pain relief, there must be advantages and disadvantages to both types of drugs. Describe what these advantages and disadvantages are for both drugs with support from the data. Why would you use one drug versus the other (and vise-versa).

If anyone can help, even with only part of any of the problems, I'd be really really grateful! Thank you!
 
1. The following models thre height of any object over time projected upward with an initial velocity of v, from its height k, but not to objects under populsion
h(t)=-16t^(2)+vt+k (t is time in any time increment)
A member of a local rotary club launches a rocket from a large field. At the moment its fuel is exhausted the rocket has a velocityof 225 feet per second and an altitude of 544 feet.
a.) write the function that models the height of the rocket.
b.)How high is the rocket at time equal to zero and explain why if the rocket took off from the ground that the height of the rocket at time equal to zero is not zero feet?
c.)How high is the rocket after 4 seconds and after 13 seconds? Explain what your answer reveals about the rocket trajectory.
d.) How long will it take for the rocket to reach its maximum height and what is that maximum height?
e.)How long will it take for the rocket to land on the ground?


2. when the drug acetaminophen used for pain relief is taken orally the concentration of the drug in the patients bloodstream after t minutes is given by A(t)=26.6t-0.35t^(2) where 0≤t≤80 and the concentration A(t) is measured in grams per liter(g/L). Likewise when the drug Ibroporphen is taken orally the concetration of the drug in the patients bloodstream after t minutes is given by the function
I(t)=21.7t-0.48t^(2), where 0≤t≤60 and the concentration I(t) is measured in g/L
a.)When is the maximum of each concentration reached, and what is the maximums concetration for each other?
b.)At what time will the drug concentration leave the patients bloodstream?
c.) Since both drugs are used for pain relief, there must be advantages and disadvantages to both types of drugs. Describe what these advantages and disadvantages are for both drugs with support from the data. Why would you use one drug versus the other (and vise-versa).

If anyone can help, even with only part of any of the problems, I'd be really really grateful! Thank you!

For problem 1, they have given you the initial velocity and height to use in the equation; just plug them in. v = 225 and k = 544. That's your equation. Graph it. It's an inverted parabola, right? The vertex of the parabola shows the peak height the rocket reaches. When the rocket drops to the ground, its height , h = 0. On your graph, that would be an x-intercept.

If you graph it and study the graph, that should help you answer all your questions.
 
1. The following models thre height of any object over time projected upward with an initial velocity of v, from its height k, but not to objects under populsion
h(t)=-16t^(2)+vt+k (t is time in any time increment)
A member of a local rotary club launches a rocket from a large field. At the moment its fuel is exhausted the rocket has a velocityof 225 feet per second and an altitude of 544 feet.
a.) write the function that models the height of the rocket.
The height of the rocket after the fuel is exhausted is given by the formula above. IF you take t= 0 at the moment the fuel is exhausted, "v" is 225 and "k" is 544.

b.)How high is the rocket at time equal to zero and explain why if the rocket took off from the ground that the height of the rocket at time equal to zero is not zero feet?
As I said above.

c.)How high is the rocket after 4 seconds and after 13 seconds? Explain what your answer reveals about the rocket trajectory.
Find -16t^2+ 225t+ 544 when t= 4 and when t= 13. What do those tell you?

d.) How long will it take for the rocket to reach its maximum height and what is that maximum height?
The simplest way to find the "maximum" for a quadratic is to complete the square. if h= -(x- a)^2+ b, the h(a)= b while any other value is b minus something.

e.)How long will it take for the rocket to land on the ground?
Since "on the ground" means h= 0, solve the equation -16t^2+ 225t+ 544= 0


2. when the drug acetaminophen used for pain relief is taken orally the concentration of the drug in the patients bloodstream after t minutes is given by A(t)=26.6t-0.35t^(2) where 0≤t≤80 and the concentration A(t) is measured in grams per liter(g/L). Likewise when the drug Ibroporphen is taken orally the concetration of the drug in the patients bloodstream after t minutes is given by the function
I(t)=21.7t-0.48t^(2), where 0≤t≤60 and the concentration I(t) is measured in g/L
a.)When is the maximum of each concentration reached, and what is the maximums concetration for each other?
Again, complete the square to determine the maximum values.

b.)At what time will the drug concentration leave the patients bloodstream?
I don't now what "drug concentration leave the patients bloodstream" means! If it means the concentration is 0, solve the equations 26.6t- 0.35t^2= 0 and 21.7t- 0.48t^2= 0.

c.) Since both drugs are used for pain relief, there must be advantages and disadvantages to both types of drugs. Describe what these advantages and disadvantages are for both drugs with support from the data. Why would you use one drug versus the other (and vise-versa).
Since the only "data" you have is maximum concentrations and time there is drug in the bloodstream. How would those be good or bad?

If anyone can help, even with only part of any of the problems, I'd be really really grateful! Thank you!
 
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