# diferentiation

### #1neep

Showing Improvement

• Members
• 34 posts
• Gender:Male

Posted 08 October 2008 - 07:11 PM

need help with 2 questions from TeeJay Notes.
Here are the two questions
1. If P=(2m+3)^4 find dm/dt when m=1 given that dp/dt = 2
2. A spherical balloon is inflated so that its volume increases at a constant rate of 200cm^3/second. find the rate increase of the surface area of the balloon when the radius is 100cm.

Thanks for any help in a advance.

### #2Marcus

Site Swot

• Members
• 147 posts
• Location:Aberdeen
• Interests:Guitar - Passed my grade 6 :D :D<br />Write computer programs - won Heriot-Watt programming challenge 2006 and 2007 :D<br />
• Gender:Male

Posted 09 October 2008 - 03:36 PM

Question 1

For this question you need to know that

you probably found this in the parametric equations topic
rearrange

(you can kinda treat them as fractions...though they most definately are not)

now you find

now =
so

substitute in m and we get

and solve

Question 2 -- the way I did this is quite complex...so there is probably an easier way :S :S

now for this you need two equations:
equation for surface area and the equation for volume

you may notice now if you differentiate volume you get surface area so
we are also told that we could also work out from surface area equation (which is 4 times circumference nice that they are all related )

What we are being asked for is

so we have to make some sort of equation out of all this so (notice the dr and dV 'cancel out')

so
now r=100

and

then finally substitute them all in

couple of REALLY horrible questions there...I hope I haven't made any mistakes...but point out anything you don't understand
=-=-=Marcus=-=-=

#### 1 user(s) are reading this topic

0 members, 1 guests, 0 anonymous users
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}