Suppose the oscillatory motion of an object can be modeled using the equation s(t) = 3.6sin(3.5t) where time is measured in seconds and distance is measured in inches.  Find the number of cycles (oscillations) the object makes per second.  (Provide 4 decimal places.) Answer:

Suppose the oscillatory motion of an object can be modeled using the equation s(t) = 3.3sin(0.11t) where time is measured in seconds and distance is measured in inches. Find the time (in seconds) required for the object to complete one oscillation. (Provide 4 decimal places.) Answer:

The voltage, V (in volts), across a circuit is given by Ohm's law: V = IR, where I is the current (in amps) flowing through the circuit and R is the resistance (in ohms). If we place two circuits, with resistance R₁ and R₂, in parallel, then their combined resistance, R, is given by 1 1 + R R₁ volts/sec = 1 R₂ Suppose the current is 5 amps and increasing at 0.02 amps/sec and R₁ is 3 ohms and increasing at 0.4 ohms/sec, while R₂ is 4 ohms and decreasing at 0.3 ohms/sec. Calculate the rate at which the voltage is changing. HINT. Using the Chain Rule, you have to find the partial derivatives of R with respect to R₁ and R₂, and before that you have to express R in terms of R₁ and R₂ using the given relation between them. Alternatively, you can use this trick, which introduces new, auxiliary variables and, therefore, makes the dependence tree bigger, but, on the other hand, makes the calculations very simple. Namely, introduce the conductivities C = 1/R, C₁ = 1/R₁ and C₂ = 1/R₂. Then the…