Two small metal spheres A and B have different electric potentials (A has a higher potential). Describe in words and mathematically what happens if you connect them with a wire. What assumptions did you make?

Prove that the sum of the squares of the lengths of the three medians of any triangle is equal to three-fourths the sum of the squares of the lengths of the three sides.

For a circuit with three capacitors in series, the equivalent capacitance must always be a) equal to the largest of the three individual capacitances. b) equal to the smallest of the three individual capacitances. c) larger than the largest of the three individual capacitances. d) smaller than the smallest of the three individual capacitances.

The mean time between collisions in iron is $4.2 \times 10^{-15} s$. What electron cur rent is d riven through a 1.8-mm-diameter iron wire by a 0.065 V/m electric field?

Area A wire 24 inches long is to be cut into four pieces to form a rectangle whose shortest side has a length of $x$.

Determine the domain of the function and use a graphing utility to graph the function over that domain.

A long thin wire, hundreds of meters long, carries a uniformly distributed charge of $-7.2 \mu \mathrm{C}$ per meter of length. Estimate the magnitude and direction of the electric field at points (a) $5.0 \mathrm{~m}$.

Identify three water-soluble and three fat-soluble vitamins.

A $22 \Omega$ wire-wound resistor is rated at $+200$ PPM for a temperature range of $-10^{\circ} \mathrm{C}$ to $+75^{\circ} \mathrm{C}$. Determine its resistance at $65^{\circ} \mathrm{C}$.

A wire of resistance 5.0 $\Omega$ is connected to a battery whose emf $\xi$ is 2.0 V and whose internal resistance is 1.0 $\Omega$. In 2.0 min, how much energy is transferred from chemical form in the battery?

Prove the the sum of any three consecutive integers is divisible by three.

Solve the given problems.

The displacement $d$ (in mm) of a piano wire as a function of the time $t$ (in s) is $d=3.0\sin 188t\cos118t$. How fast is the displacement changing when $t=2.0$ ms?

Under a tension F, it takes 2.00 s for a pulse to travel the length of a taut wire. What tension is required (in terms of F) for the pulse to take 6.00 s instead? Explain how you arrive at your answer.

The average of three numbers is 20. What is the sum of the three numbers?

The sum of three consecutive integers is 264. What are the three integers?