Two calc problems

  • Thread starter cscott
  • Start date
784
1
PV = C (Boyle's Law)

At a certain instant, the volume is 480 cm^3, the pressure is 160 kPa, and the pressure is increasing at a rate of 15 kPa/min. At what rate is the volume decreasing at this instant?

----

Find the equations of both lines that pass through the point (2, 3) and are tangent to the parabola y = x^2 + x.



I don't really know where to start with these...
 

benorin

Homework Helper
1,057
7
[tex]PV=C\Rightarrow\frac{d}{dt}(PV)=\frac{d}{dt}C\Rightarrow \frac{dP}{dt}V+P\frac{dV}{dt}=0[/tex]

then plug-in the known values of P,V, and dP/dt to solve for dV/dt.
 

HallsofIvy

Science Advisor
41,618
821
Any line through (2, 3) can be written as y= m(x- 2)+ 3 for some m.

If (x,y) is a point where that line intersects the parabola y= x2+ x, then we must have m(x-2)+ 3= x2+ x. If, in addition, the line is tangent to the parabola there, we must have
m= 2x+ 1. Solve those two equations for x and m.

I've edited this: before I had m= 2x- 1. Obviously, the derivative of x2+ x is 2x+ 1, not 2x- 1.
 
Last edited by a moderator:
784
1
Thank you.
 

Want to reply to this thread?

"Two calc problems" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Top Threads

Top