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Windscarredfaith 12-7-2006 07:51 PM

Calculus Help
 
THIS THREAD IS USELESS NOW UNLESS YOU SOMEHOW HAVE THE SAME QUESTIONS AS THESE.
I thank all the people who attempted and took time to help me out. :D <33 You guys are the best. ^^

---
M'kay. So my teacher Mr. Furry (his real name, I'm not kidding) just gave my class and I some questions that we didn't even learn. =/ It's due tonight at 11:55 PM EST... so, if you have some time (or if you are extremely bored), please help! I have NO idea how to do these. Lol. Any help is appreciated. (I'm in high school, btw.) Thanks in advance.

Here are the questions that I don't know how to do:

1. The area of a square with sides of length s is given by A = s2. Find the rate of change of the area with respect to s when s = 5 meters.
Answer is in meters^2. And it is not 25.

2. Consider the following function.
f(t) = 6t^2 - 4
(a) Find the average rate of change of the function below over the interval [5, 5.1].
Answer is not the average of the numbers plugged in...
(b) Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval.
Answer will have one at t=5 and another with t=5.1

3. Use the position function -16t^2 + vot + so for free-falling objects.
(a) A ball is thrown straight down from the top of a 240 foot building with an inital velocity of -25 feet per second. What is its velocity after 5 seconds?
Answer is in ft/sec.
(b) What is its velocity after falling 103 feet?
Answer is also in ft/sec.

4. Find k such that the line y = 5x + 6 is tangent to the graph of the function below. y=k*sqrt(x)
Answer is what k equals.

5. The tangent line to the graph of y = h(x) at the point (-7, 6) that passes through the point (2, 8). Find the following values.
(a) h(-7)
(b) h '(-7)

6. (Use the position function -4.9t^2 + vot + so for free-falling objects.) To estimate the height of a building, a stone is dropped from the top of the building into a pool of water at ground level. How high is the building if the splash is seen 5.2 seconds after the stone is dropped?

-- Edit

Answer for 1 is 10.

-- Edit #2

Answer is 60.6, 60, and 61.2 respectfully.

-- Edit #3

Disregard #3. I maxed out my submissions for the question. xD
3a was -185 though.

-- Edit #4
Answer is 11. I BSed that one.

-- Edit #5
Answer to part 2 is 2/9. Maxed out submissions for part 1, so disregard this question now.
And... YAY ONLY #6 LEFT!

-- Edit #6
Answer is 132.496. :D

GuidoHunter 12-7-2006 08:22 PM

Re: Calculus Help
 
1. dA/ds = 2s. dA/ds|s=5 = 2(5) = 10, though I don't see how it can be in m^2

2. df/dt = 12t. df/dt|t=5 = 60. df/dt|t=5.1 = 61.2 Average = 60.6

3. s = -16t^2 + vot + so
v = -32t + vo
v|vo=-25, t=5 = -160 - 25 = -180

(b) s = -16t^2 + vot + so
137 = -16t^2 - 25t + 240

EDIT: d'oh about 3

--Guido

http://andy.mikee385.com

Windscarredfaith 12-7-2006 08:23 PM

Re: Calculus Help
 
Lol, yeah... those are the questions I got.. ^^"

itmorr 12-7-2006 08:32 PM

Re: Calculus Help
 
On #5, find the y=mx+b for the tangent line. Slope is the difference in y over difference in x. Substitute an x and y pair in to find b. Then with h(x), plug the x value into your new mx+b to find y.

Doug31 12-7-2006 08:33 PM

Re: Calculus Help
 
Here's what I got for 5, haven't done the others yet.

5. tangent line -> y=9/2x +1, so h(7)=9/2(7) +1 = 22.5, and h'(7)=9/2

Windscarredfaith 12-7-2006 08:34 PM

Re: Calculus Help
 
Tried the answers. Both wrong. =/

itmorr 12-7-2006 08:35 PM

Re: Calculus Help
 
The slope on that should be 2/9 not 9/2.
=> h'(x) = 2/9

talisman 12-7-2006 08:37 PM

Re: Calculus Help
 
3a is -205 but I got that doing it in my head so it's probably wrong.

Windscarredfaith 12-7-2006 08:37 PM

Re: Calculus Help
 
Yeah. That one is right. <-- to what itmorr said

And, disregard 3, my submissions are gone.

Doug31 12-7-2006 08:39 PM

Re: Calculus Help
 
Okay, here's another, although very confusing of a way of doing it, but I think it's the right answer.
6. x=xo +vot +1/2at^2, so x-xo=1/2*4.9*5.2^2=66.248meters

talisman 12-7-2006 08:40 PM

Re: Calculus Help
 
well 6 is easy just move the h sub zero over to the left side and plug in the 5.2 and I think that will do it.

Windscarredfaith 12-7-2006 08:40 PM

Re: Calculus Help
 
Nope.... Lol. Sorry. ^^"

Doug31 12-7-2006 08:42 PM

Re: Calculus Help
 
Tried 5 again.

5. tangent line -> y=2/9x +68/9, so h(7)=2/9(7) +68/9 = 89/9, and h'(7)=2/9
Even though you're done with that now.

Edit, okay, so my answer for 6 was wrong, because the -4.9 already had the 1/2 in it, so I now think it's 132.496meters.

Windscarredfaith 12-7-2006 08:43 PM

Re: Calculus Help
 
Lol. Thanks for that. I got 1/2 credit. xD

-- Edit

YAY! #6 is right. ^^

itmorr 12-7-2006 08:48 PM

Re: Calculus Help
 
Does this work on the one you BS'd as 11?
y=k*sqrt(x) curve
y = 5x + 6 tangent to curve
5x + 6 = k*sqrt(x)
5x + 6 over sqrt(x) = k

Windscarredfaith 12-7-2006 08:52 PM

Re: Calculus Help
 
Thanks for the explanations, itmorr. I'll definitely try to teach myself now since our teacher doesn't. =/

Doug31 12-7-2006 08:53 PM

Re: Calculus Help
 
This isn't useless unless someone has the same questions as these, people can use this to find out how to do similar problems.:) I'm glad I could help.

Kilgamayan 12-7-2006 08:53 PM

Re: Calculus Help
 
How the hell is #6 a Calculus question? That's Algebra II at worst.

Windscarredfaith 12-7-2006 08:56 PM

Re: Calculus Help
 
Quote:

Originally Posted by Kilgamayan (Post 1026717)
How the hell is #6 a Calculus question? That's Algebra II at worst.

^^" I dunno. Lol. Maybe because it's high school Calculus?? It's a senior course, but I'm taking it as a Junior because I skipped a level. I feel left out there. xD

Kilgamayan 12-7-2006 08:58 PM

Re: Calculus Help
 
I did partial fractions in high school calc. That's not an excuse. >_>


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