A coil has an inductance of 0.15 H and a resistance of $33 \Omega$. The coil is connected to a 6.0 V ideal battery. When the current reaches half its maximum value: (a) At what rate is magnetic energy being stored in the inductor? (b) At what rate is energy being dissipated? (c) What is the total power that the battery supplies?

State the amplitude, where appropriate, of: y = sin 4x

(a) Let $f :\mathbb{R}^3 \to \mathbb{R}, \mathbf{x}_0 \in \mathbb{R}^3$. If $\mathbf{v}$ is a unit vector in $\mathbb{R}^3$, show that the maximum value of the directional derivative of $f$ at $\mathbf{x}_0$ along $\mathbf{v}$ is $||\nabla f (\mathbf{x}_0)||$.

Zinc reacts with 100.0 mL of 6.00 M cold, aqueous sulfuric acid through single replacement. a. How many grams of zinc sulfate can be produced? b. How many liters of hydrogen gas could be released at STP?

suppose $y = f (x)$ is defined for all $x$. For each description, sketch a graph with the indicated property.

Discontinuous at $x=2$ but continuous elsewhere with $\lim _{x \rightarrow 0} f(x)=\frac{1}{2}$

Write the rule for a quadratic function with a vertex of (0,0) that passes through (-1,3).

Suggest an explanation for why aspirin has a sour taste.

A step-down transformer has a turns ratio of 1/100. An ac voltage of amplitude 170 V is applied to the primary. If the primary current amplitude is 1.0 mA, what is the secondary current amplitude?

a. For what values of a and b will

$$g(x)=\left\{\begin{array}{ll}{a x+b,} & {x \leq-1} \\ {a x^{3}+x+2 b,} & {x>-1}\end{array}\right.$$

be differentiable for all values of x? b. Discuss the geometry of the resulting graph of g.

Investigate the services and fees of two banks. Bank 1 has a branch in your neighborhood or town, and Bank 2 is an online bank. Make a multimedia presentation outlining their services and fees and present it to the class.

How did Stalin gain and maintain power in the USSR?

Evaluate the following limits or state that they do not exist.

$$\lim _ { x \rightarrow 0 } \frac { 3 \sec ^ { 5 } x } { x ^ { 2 } + 4 }$$

Sharks find their prey through a keen sense of smell and an ability to detect small electrical impulses. If f(x, y, z) indicates the electrical charge in the water at position (x, y, z) and a shark senses that $\nabla f=\langle 12,-20,5\rangle$, in which direction should the shark swim to find its prey?

William Tell is said to have shot an apple off his son 's head with an arrow. If the arrow was shot with an initial speed of $55\ \mathrm{m/ s}$ and the boy was $15\ \mathrm{m}$ away , at what launch angle did Bill aim the arrow? (Assume that the arrow and apple are initially at the same height above the ground.)