Group+A+Period+8

Welcome Group A Period 8! You are to complete problems 1, 7 and 13. Each member must contribute. Feel free to use the discussion board to bounce ideas off one another.

This is a link to Patrick JMT's explanation of derivatives- http://www.youtube.com/watch?v=dQw4w9WgXcQ

1.) 1. A = (Pi)(r)^2 2. Take the derivative to get your answer 3. dA/dt = 2(Pi)(r)(dr/dt)

(dA/dt) - Rate of change of the area at that time interval. (dr/dt) - Rate of change of radius at that time interval.


 * 7.) //Changing Voltage.// The voltage V 9volts), current I (amperes), and resistance R (ohms) of an electric circuit like the one shown here are related by the equation V=IR. Suppose that V is increasing at the rate of 1 volt/sec while I is decreasing at the rate of 1/3 amp/sec. Let t denote time in sec.**

dV/dT= 1 volt/sec (increasing = positive) dI/dT=-1/3 amp/sec (decreasing = negative sign) dV/dT= I(dR/dT)+R(dI/dT) (*Remember original equation V=IR. Therefore, plug in derivatives) V=12 volts and I=2 amp. (We have to get the 12 volts from the 2 amp multiplied by the R (rate)). 12 volts= 2 amp x R (R now equals 6 ohms(from question)) (Now plug in everything back into the equation in (c)) (Remember solving for rate at which R is changing) 1 volt/sec= 2 amp (dR/dT) + 6 ohms (-1/3 amp/sec) 3 volt/sec= 2 amp (dR/dT) dR/dT= 3/2 ohms/sec
 * a) What is the value of dV/dT?**
 * b) What is the value of dI/ dT?**
 * c) Write and equation that relates dR/dT to dV/dT and dI/dT.**
 * d) //Writing to Learn.//** Find the rate at which R is changing when V=12 volts and I=2 amp. Is R increasing, or decreasing? Explain


 * Since dR/dT is positive R is increasing. The answer through distributing comes out to be 3/2 ohms per second.**

13. given: s=100 s changes at 300 mph.

x^2 + y^2 = s^2 (take derivative) 2x(dx/dt) + 0 = 2s(ds/dt) x(dx/dt) = s(ds/dt) (51)^(1/2) (dx/dt) = 10(300) (dx/dt) = 424.3

Use the Pythagorean theorem to get the equation x^2 + y^2 = s^2. Then, take the derivative of the equation. Then, y^2 = 0 because the y value is a constant. Then, you plug in the values. Then, solve for (dx/dt) by walking out the equation