Calculus Help ASAP (Due Tomorrow)

[buddy]

Hi Everybody! This is buddy's daughter. I'm a junior in high school. This year, I'm taking calculus and I'm having difficulty understanding some concepts. Anyways, some help w/ the following problems would be grately appreciated.

-The point P (.5, 2) lies on the curve y=1/x.
Using this slope: -4.0816, find an equation of the tangent line to the curve at P.


-If a ball is thrown into the air with a velocity of 40ft/s, its height after t seconds is given by y=40t-16t^2

(a) Find the average velocity for the time period beginning when t=2 and lasting

i - .5 s
ii - .1 s
iii - .05 s
iv - .01s

(b) Find the instantaneous velocity when t = 2.

(what is instantaneous velocity?)


Thanks!
-Buddy's Daughter

 

[BahamaMama]

since when is calculus offered in jr. high?

 

[BahamaMama]

oops, sorry...guess i should have taken READING... now see that says *JUNIOR IN HIGH SCHOOL*, and now it makes sense

and what you need is an all out page for that cutie KDad!!!!!!!!!!!!!!!!!!!!!!

 

[buddy]

I'm a junior in high school. It's not junior high school - I'm in the 11th grade.

 

[marine]

stand by, answer coming shortly. gonna work it out and figure out the best way to post it... maybe just scan it and email it to you.

 

[beantownjim]

HEY MARINE WHY DONT YOU BEND OVER AND IT WILL COME OUT QUICKER NOT THE ANSWER TO THE CALCULUS QUESTION BUT THE DILDO IN YOUR ARSE.MARINE CANT FIGURE OUT TICK TACK TOE NOW HE IS WORKING ON CALCULUS GOOD LUCK KID GETTING THE ANSWER.

 

[marine]

I aint gonna just give you the answer, but I will point you in the very good direction here, quite simply because its a pain to type in math formulas here.

Take your equation y=1/x
take the derivative of it.
find the following
y'=
y(x)=
y'(x) =
left side of the equation is y-y(x)

for all above notes, in this problem X=1/2 per point P
consult your text book for further info - right side will start y'(x)* (insert answer))

 

[marine]

for future calc homework, might wanna check this link and find similar problems to help guide you on your approach.

http://www.usna.edu/MathDept/website/oldexams.html

 

[marine]

This problem is ugly because you have to figure in the hieght the ball will reach before it starts to fall back down again. but in a nutshell.


instantaneous velocity is equal to delta y over delta t

dy/dt
change in y over change in time

do yourself up a table for this problem.

check this site for some additional insight
http://schutz.ucsc.edu/~josh/5A/book/notes/node14.html

 

[freelancc]

:look:

 

[marine]

so what if i have math pages bookmarked and still retain a lil info. Some chicks dig nerds.

 

[marine]

btw,
I have to say, for a HS junior class this is good stuff. Normally I cringe about what high school is teaching kids these days (or lack of material) but it seems like this math teacher aint lettin you guys slide.

 

[Nole]

Easy! The answer is 3.

Glad I could help.

nole

 

[KotysDad]

Buddy's daughter,

For the first problem, the answer is quite simple to show. You know the slope (m) of the line you want and a point P(x1, y1) on that line, therefore the equation of that line is

y - y1 = m(x - x1)

Use m = -4.0816 and P(.5,2)

y - 2 = -4.0816(x - .5)
y - 2 = -4.0816x + 2.0418
y = -4.0816x + 4.0418

I would be curious to know why your teacher is telling you the slope is -4.0816. If the curve really is y = 1/x, then the slope of the tangent line at (.5,2) is exactly -4. I wonder why he/she is giving you -4.0816.


Still working on the velocity problem.

 

[KotysDad]

Velocity problem answer........

y(t) = 40t - 16t^2 gives you the object displacement (distance) at time t.

average velocity = change in distance / chance in time

So, compute its distance or displacement at each time t first.

y(2) = 16
y(2.5) = 0
y(2.1) = 13.44
y(2.05) = 14.76
y(2.01) = 15.7584

The average velocity from:

2 to 2.5 = 0-16 / 2.5 - 2 = -16 / .5 = -32
2 to 2.1 = 13.44 - 16 / 2.1 - 2 = -2.56 / .1 = -25.6
2 to 2.05 = 14.76 - 16 / 2.05 - 2 = -1.24 / .05 = -24.8
2 to 2.01 = 15.7584 - 16 / 2.01 - 2 = -.2416 / .01 = -24.16

Notice how as the time interval shorten, the average velocity is tending towards a "limiting value". You could probably make an educated guess and say that as the time interval gets shorter, the average velocity is getting closer and closer to -24.

Well, as you shorten the time interval down to nothing, you are computing the instantaneous velocity at t=2.

If you take y(t) = 40t - 16t^2 and comput its "derivative" (now I am not sure if you learned this concept yet) you get a new function, v(t) = 40 - 32t.

If you compute v(2), you would get 40 - 32(2) = -24. This is a second way of computing the instantaneous velocity.

I am guessing you didnt learn how to compute derivatives yet, so you need to understand that the instantaneous velocity is the limiting value of the average velocity as you shrink the time interval down to 0. In your example, you can see how the average velocity is approaching -24.

Now, if you wanna know why it's a negative value, you have to think about the function itself. You are throwing a ball up, then it reaches it max height, them comes down. As the ball goes up, it has a positive velocity. At his max height, its velocity is 0. As it comes back down to earth, velocity is negative because the ball is not travelling in the opposite direction as it started.


Hope this helps. Let me know if you have any other problems during the semester. Hope I didnt get you the answers too late, but the Ravens were on MNF.

 

[marine]

teach a girl to do math and she will balance her husbands checkbook while she spends..

Just flat out give her the answers (KOTYSDAD) and she will never think twice about spending it all.

I would be curious to know why your teacher is telling you the slope is -4.0816. If the curve really is y = 1/x, then the slope of the tangent line at (.5,2) is exactly -4. I wonder why he/she is giving you -4.0816.
------fully agree with this Kotys, I dont get where that extra .0816 comes from
it just dont make sense. If you ignore the given slope you come up with
y-y(x) = y'(x)(x-x1)
or in plain terms
y-2 = -4(x-.5)
y=-4x +4

close enough really since it is a tangent line, but it seems like the teach is confusing the students. There really just is not a need to give the slope in the problem.

 

[HighRoller]

HEY MARINE WHY DONT YOU BEND OVER AND IT WILL COME OUT QUICKER NOT THE ANSWER TO THE CALCULUS QUESTION BUT THE DILDO IN YOUR ARSE.MARINE CANT FIGURE OUT TICK TACK TOE NOW HE IS WORKING ON CALCULUS GOOD LUCK KID GETTING THE ANSWER.

hey dumb ass YES you dumb ass seems to me Marine has not only posted the answers but isnt it sad your too stupid to understand calculus ! Why Jack puts up with your shit I will never know. But as you just proved you are one stupid MF.

 

[beantownjim]

HEY HIGHROLLER I DIDNT SEE YOUR NAME FIGURING OUT THE CALCULUS PROBLEM YOU ONLY APPEAR IN THIS THREAD WHEN IT HAS BEEN SOLVED.WHO THE F-CK ARE YOU HIGHROLLER EINSTEIN YOU DUMB F-CK.I DONT KNOW WHY JACK PUTS UP WITH YOU WHEN WAS THE LAST TIME YOU SAID ANYTHING ANYBODY CARED TO READ.GO F-CK YOURSELF HIGHROLLER :thefinger

HIGHROLLER ALWAYS SLEEP WITH YOUR HANDS ABOVE THE COVERS THIS WAY YOU WONT BE TEMPTED TO TOUCH YOUR WEINER

 

[Chanman]

take it easy beaner. here's a subtraction problem:

What's the difference between an Irsih Wedding and an Irish Funeral?
One less Drunk!

P.S.- I'm Irish too...we get around ya know :142squint

 

[marine]

Lowballer,

Words of wisdom to you....

Tis better to let people think you are:a raging lunatic, mildly retarded punk with a touch of passive/aggressive behavior,
than to post on this thread and remove all doubt.