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Old 12-7-2006, 07:51 PM   #1
Windscarredfaith
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Default 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. <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.
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Old 12-7-2006, 08:22 PM   #2
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Default 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

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Old 12-7-2006, 08:23 PM   #3
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Default Re: Calculus Help

Lol, yeah... those are the questions I got.. ^^"
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Old 12-7-2006, 08:32 PM   #4
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Default 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.
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(12:31:27 AM) jwcgator2: I got it! I'll write an auto-procrastination program!
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Old 12-7-2006, 08:33 PM   #5
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Default 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
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Old 12-7-2006, 08:34 PM   #6
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Default Re: Calculus Help

Tried the answers. Both wrong. =/
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Old 12-7-2006, 08:35 PM   #7
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Default Re: Calculus Help

The slope on that should be 2/9 not 9/2.
=> h'(x) = 2/9
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Quote:
Originally Posted by jwcgator
(12:31:27 AM) jwcgator2: I got it! I'll write an auto-procrastination program!
(12:31:33 AM) jwcgator2: meh, i'll make it later
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Old 12-7-2006, 08:37 PM   #8
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Default Re: Calculus Help

3a is -205 but I got that doing it in my head so it's probably wrong.
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Old 12-7-2006, 08:37 PM   #9
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Default Re: Calculus Help

Yeah. That one is right. <-- to what itmorr said

And, disregard 3, my submissions are gone.
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Old 12-7-2006, 08:39 PM   #10
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Default 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
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Old 12-7-2006, 08:40 PM   #11
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Default 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.
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Old 12-7-2006, 08:40 PM   #12
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Default Re: Calculus Help

Nope.... Lol. Sorry. ^^"
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Old 12-7-2006, 08:42 PM   #13
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Default 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.
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Old 12-7-2006, 08:43 PM   #14
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Default Re: Calculus Help

Lol. Thanks for that. I got 1/2 credit. xD

-- Edit

YAY! #6 is right. ^^
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Old 12-7-2006, 08:48 PM   #15
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Default 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
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Quote:
Originally Posted by jwcgator
(12:31:27 AM) jwcgator2: I got it! I'll write an auto-procrastination program!
(12:31:33 AM) jwcgator2: meh, i'll make it later
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Old 12-7-2006, 08:52 PM   #16
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Default Re: Calculus Help

Thanks for the explanations, itmorr. I'll definitely try to teach myself now since our teacher doesn't. =/
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Old 12-7-2006, 08:53 PM   #17
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Default 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.
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Old 12-7-2006, 08:53 PM   #18
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Default Re: Calculus Help

How the hell is #6 a Calculus question? That's Algebra II at worst.
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Old 12-7-2006, 08:56 PM   #19
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Default Re: Calculus Help

Quote:
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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
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Old 12-7-2006, 08:58 PM   #20
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Default Re: Calculus Help

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