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Word Problem

J

jeffeh

Banned
I'm scrambling to get this assignment done and would be really greatful if someone could take some time to try and solve these problems.

#1

A triangle has a base of (4-x)cm and a height of (2x+3)cm
a. what is the maximim area of the triangle to the nearest tenth
b. what value of x will produce that maximum area?

#2

If a bullet is fired vertically with an initial speed of 100m/s, its height h, is metres, after time t, in seconds, is given by h=100t-5t^2.
a. what maximum height will the bullet reach?
b. how long is it in the air (assuming it falls back to the ground?

Thank you very much
 
#1 Calculate the area of the triangle in terms of X. Find the max of it by using derivatives. And as an extra bonus you can use the 2nd derivative to make sure that it's a max and not a min.

#2 Same deal.
 
Originally posted by: jeffeh
I'm scrambling to get this assignment done and would be really greatful if someone could take some time to try and solve these problems.

#1

A triangle has a base of (4-x)cm and a height of (2x+3)cm
a. what is the maximim area of the triangle to the nearest tenth
b. what value of x will produce that maximum area?

#2

If a bullet is fired vertically with an initial speed of 100m/s, its height h, is metres, after time t, in seconds, is given by h=100t-5t^2.
a. what maximum height will the bullet reach?
b. how long is it in the air (assuming it falls back to the ground?

Thank you very much
Click to expand...

1) How do you find the area of a triangle?

2) How do you find the maximum of a function? You need to take derivatives...
 
any chance that one of you could figure the problem out?
trying to work on other questions, damn I hate this lol
 
Originally posted by: jeffeh
any chance that one of you could figure the problem out?
trying to work on other questions, damn I hate this lol
Click to expand...

No. You work on your own questions.

Edit: If you're not going to make an attempt at it, I'm not either.
 
Originally posted by: hypn0tik
Originally posted by: jeffeh
any chance that one of you could figure the problem out?
trying to work on other questions, damn I hate this lol
Click to expand...

No. You work on your own questions.

Edit: If you're not going to make an attempt at it, I'm not either.
Click to expand...

Ditto
 
Originally posted by: jeffeh
any chance that one of you could figure the problem out?
trying to work on other questions, damn I hate this lol
Click to expand...

Asking for help on your homework is one thing, asking someone to do it for you is :thumbsdown: :roll:
 
I tried to find the answer for the triangle but came up with a answer that im sure is incorrect

-x^2 + 4x - 5/4
 
Originally posted by: jeffeh
I tried to find the answer for the triangle but came up with a answer that im sure is incorrect

-x^2 + 4x - 5/4
Click to expand...

Double check your multiplication. After fixing it, do you know how to find minimum/maximums using derivatives?
 
Originally posted by: TuxDave
#1 Calculate the area of the triangle in terms of X. Find the max of it by using derivatives. And as an extra bonus you can use the 2nd derivative to make sure that it's a max and not a min.

#2 Same deal.
Click to expand...

/thread
 
care to explain, is there another way to do this because i couldn't see her giving us a question that we need to use something we havnt learnt to solve
 
Originally posted by: TuxDave
#1 Calculate the area of the triangle in terms of X. Find the max of it by using derivatives. And as an extra bonus you can use the 2nd derivative to make sure that it's a max and not a min.

#2 Same deal.
Click to expand...

#2 - Gotta do earth rotation, air pressure, wind, humidity, etc. Now if you vacuum your living room and do it in there, that is a different story. Let me know how it comes out.

 
Originally posted by: jeffeh
hmm derivitives, can't say I recognize that :s
Click to expand...

Then you're screwed. Nobody can learn what a derivative is in one night and fully learn how to apply it in real-world problems. Give up and get some sleep.

/thread
 
Originally posted by: Condor
Originally posted by: TuxDave
#1 Calculate the area of the triangle in terms of X. Find the max of it by using derivatives. And as an extra bonus you can use the 2nd derivative to make sure that it's a max and not a min.

#2 Same deal.
Click to expand...

#2 - Gotta do earth rotation, air pressure, wind, humidity, etc. Now if you vacuum your living room and do it in there, that is a different story. Let me know how it comes out.
Click to expand...

They gave you the equation. Besides, you stand no chance with analytical methods if you want that degree of accuracy and variable inclusion.
 
Originally posted by: kevinthenerd
Originally posted by: jeffeh
hmm derivitives, can't say I recognize that :s
Click to expand...

Then you're screwed. Nobody can learn what a derivative is in one night and fully learn how to apply it in real-world problems. Give up and get some sleep.

/thread
Click to expand...


Agreed if it is a class where you are supposed to know Derivatives give up now and goto bed. But he mnight not be in calc and this could be some other problem.
 
Originally posted by: jeffeh
I'm scrambling to get this assignment done and would be really greatful if someone could take some time to try and solve these problems.

#1

A triangle has a base of (4-x)cm and a height of (2x+3)cm
a. what is the maximim area of the triangle to the nearest tenth
b. what value of x will produce that maximum area?

#2

If a bullet is fired vertically with an initial speed of 100m/s, its height h, is metres, after time t, in seconds, is given by h=100t-5t^2.
a. what maximum height will the bullet reach?
b. how long is it in the air (assuming it falls back to the ground?

Thank you very much
Click to expand...

Ok, I'll help you cheat, but when you're competing with someone for a job one day, don't blame me if you never learn it.

1.

Area = (-x+4)(2x+3) = -2x^2 +5x + 12
Derivative with respect to x = -4x + 5
Maximum at dA/dx = 0
-4x + 5 = 0
x = 1.2
Max area = (4-1.2) * (2.4+3) = 2.8*5.4 = 15.12

2.
h = 100t - 5t^2
dh/dt = 100 - 10t

Max height when dh/dt = 0
t = 10
h = 1000-500 = 500

time in air = t*2 = 20 seconds


Edit: Did it all in my head with one exception for a quick Google calculation of 2.8*5.4. Check my math.
 
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