Math Homework-lamsey I Need You!

I have a math homework problem. It is as follows:

A rock is thrown into the air from a hole in the ground. The solution for the time it takes the rock to reach a certain distance is (y= -x^2+10x-16). X is the time and y stands for how high above the ground level the rock is. The questions I have to answer are as follows:

A) What is the rock's maximum height?
B ) How much time it took for the rock to reach it's maximum height?
C) How long does it take for it to hit the ground after it was thrown up?
D) How far down was the rock initially thrown from?

This is what I know so far:

The image is of a parabola, that looks like an upside down U. In order to find the turning point, you would use the formula x= -b/2a. That would give you the maximum time is took the rock to reach its peak height. If you were to substitute that number into the equation (y= -x^2+10x-16), that would give you the time it took to reach its maximum height. From there, you would substitute different numbers for X to get different numbers for Y. Can anyone guide me?? I also believe that the X part of the turning point is 5. Am i right???

This is one for Lamsey

Thanks for any help you guys might provide.

The answer is 42.

what is 42???

6*9 (base 13) according to my DM tutor

anybody- could ya help

A) will be where the maximum stationary point is. In other words, it'll be where dy/dx (differential of y in respect to x) will be zero. All you need is the y co-ordinate
B) will be the same as a, except it'll be the x co-ordinate
C) will be when y = 0 - Substitute 0 for y and find x for the answer
D) will be when x = 0 - Find f(x) when x = 0 Find y for the answer

Can't be bothered working them out but that's what you're supposed to do.

Co-Ordinate Geometry, Pure 1/2, English A-Level Mathematics :P

Technically you could in theory solve it in a mechanics sense as well, but that's for another day ;)

anybody???

is the x part of the turning point 5?

That is oh so rude ..... completely ignoring the fact othrs have tried to help .. and are probably right .. though I wouldn't have a dandy .. called being tired where we come from.

Quote:

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Originally posted by Illuminati@24 March 2004 - 19:14
A) will be where the maximum stationary point is.  In other words, it'll be where dy/dx (differential of y in respect to x) will be zero.  All you need is the y co-ordinate
B) will be the same as a, except it'll be the x co-ordinate
C) will be when y = 0 - Find x for the answer
D) will be when x = 0 - Find y for the answer

Can't be bothered working them out but that's what you're supposed to do. 

Co-Ordinate Geometry, Pure 1/2, English A-Level Mathematics :P

Technically you could in theory solve it in a mechanics sense as well, but that's for another day ;)

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WoW :w00t: :P

Quote:

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Originally posted by RGX@24 March 2004 - 23:56
The answer is 42.

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someone has been watching the hitchikers guide to the galaxy. :lol:

Actually, just for the hell of it - I will try to write both geometric & mechanic solutions to this tomorrow :D

Just not right now - I need sleep :frusty:

Quote:

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Originally posted by Illuminati@25 March 2004 - 00:14
A) will be where the maximum stationary point is. In other words, it'll be where dy/dx (differential of y in respect to x) will be zero. All you need is the y co-ordinate
B) will be the same as a, except it'll be the x co-ordinate
C) will be when y = 0 - Substitute 0 for y and find x for the answer
D) will be when x = 0 - Find f(x) when x = 0 Find y for the answer

Can't be bothered working them out but that's what you're supposed to do.

Co-Ordinate Geometry, Pure 1/2, English A-Level Mathematics :P

Technically you could in theory solve it in a mechanics sense as well, but that's for another day ;)

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What he said.

I will give you a hint: the derivative of the equation of that curve is

dy/dx = -2x + 10

Quote:

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Originally posted by 4play+25 March 2004 - 01:19--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td>QUOTE (4play @ 25 March 2004 - 01:19)</td></tr><tr><td id='QUOTE'> <!--QuoteBegin-RGX@24 March 2004 - 23:56
The answer is 42.

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someone has been watching the hitchikers guide to the galaxy. :lol: [/b][/quote]
Actually I read it when I was 10-12 :P

Quote:

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Originally posted by Lamsey@25 March 2004 - 00:21
What he said.

I will give you a hint: the derivative of the equation of that curve is

dy/dx = -2x + 10

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10 - 2x is surely a cleaner representation?

:rolleyes:

i know one way of doing it, the one my math teacher likes, and tat would be to first find the maximum (turning point) which i concluded to be x=5 and y= 59. This is the height. meaning, after 5 seconds, the height will be 59. is this right at least?? My math teacher told me that the next step is to take 4 number below 5 and 4 numbers above 5 and substitute them into the original equation. That will give different times and heights. Am i right?

Quote:

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Originally posted by 4th gen+25 March 2004 - 00:23--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td>QUOTE (4th gen @ 25 March 2004 - 00:23)</td></tr><tr><td id='QUOTE'> <!--QuoteBegin-Lamsey@25 March 2004 - 00:21
What he said.

I will give you a hint: the derivative of the equation of that curve is

dy/dx = -2x + 10

---

10 - 2x is surely a cleaner representation?

:rolleyes: [/b][/quote]
http://www.ebaumsworld.com/forumfun/whocares2.jpg

I think I see Dr. Bramley in the corner :huh:

for C, i got 2 answers. i got 8 and 2. which is right? which should i reject???