Explain the reason why celebrity sources sometimes is effective. What are the risks affiliated with using a celebrity source?

Water flows out of a tap at the bottom of a cylindrical tank of height 4 m and radius 2 m. The tank is initially full and the water escapes at a rate proportional to the square root of the depth of the water remaining. After 2 hours the depth of water is 1 m. How long will it take for the tank to empty?

Use the formula for the arc length of a curve in parametric form to derive the formula for the arc length of a polar curve.

Two capacitors give an equivalent capacitance of 9.00 pF when connected in parallel and an equivalent capacitance of 2.00 pF when connected in series. What is the capacitance of each capacitor?

A program to simulate a leaky bucket.

A $2.50-\mu \mathrm{F}$ capacitor is charged to 857 V and a $6.80-\mu \mathrm{F}$ capacitor is charged to 652 V. These capacitors are then disconnected from their batteries. Next the positive plates are connected to each other and the negative plates are connected to each other. What will be the potential difference across each and the charge on each? [Hint: charge is conserved.]

In the following problem, identify the domain of the given function.

f(x) = $2^x$

Define the spontaneous recovery and explain how it is affected by successive sessions of extinction.

Suppose you had to measure the rate at which zinc is used up in the reaction above. Which of these units would be suitable? Explain your choice.

a. litres per minute

b. grams per minute

c. centimetres per minute

Solve the following problem for x.

(x+3) $\div$ (x - 5) = 0

Using the graph of $f(x)=\frac{1}{x}$ as a guide, describe the transformation and graph the function.

$$g(x)=\frac{2}{x+4}$$

Find the matrix A of the quadratic form associated with the equation. Then find the eigenvalues of A and an orthogonal matrix P such that $P^TAP$ is diagonal. $3 x^{2}-2 \sqrt{3} x y+y^{2}+2 x+2 \sqrt{3} y=0.$

How much work is required, using an ideal Carnot refrigerator, to change 0.500 kg of tap water at 10.0$^ { \circ } \mathrm { C }$ into ice at −20.0$^ { \circ } \mathrm { C }$? Assume that the freezer compartment is held at −20.0$^ { \circ } \mathrm { C }$ and that the refrigerator exhausts energy into a room at 20.0$^ { \circ } \mathrm { C }$.

Three capacitors are in series: $C_1=45 \mu \mathrm{F}, C_2=65 \mu \mathrm{F}$, and $C_3=80 \mu \mathrm{F}$. (c) Compute the energy stored in each capacitor.