Find the transfer function of a second-order bandpass filter for which the center frequency $f_{0}=10 \mathrm{kHz},$ the 3-dB bandwidth is 500 Hz, and the center-frequency gain is 10. Also, give the locations of the poles and zeros.

Verify that

$$\frac{\partial^3 f}{\partial x\partial y\partial z}=\frac{\partial^3 f}{\partial z\partial y\partial x}$$

for $f (x, y, z) = ze^{xy} + yz^3x^2$.

A direct-coupled amplifier has a dc gain of 1000 V/V and an upper 3-dB frequency of 100 kHz. Find the transfer function and the gain–bandwidth product in hertz.

Solve. 4y + 20 = 2(3y + 5)

Solve the equation for the given domain.

$$\sin ^ { 2 } \theta + 2 \sin \theta - 2 = 0 \text { for } 0 ^ { \circ } \leq \theta < 360 ^ { \circ }$$

Many (but not all) calculators experience an overflow error when computing $_{365} P_{n}$ for $n>39$ and when computing $365^{n}$. Explain how you would evaluate P(E) for any $n>39$ on such a calculator.

In many cases, a guess for the form of a particular solution may seem logical but turn out to be a bad guess. Identify the criterion for whether a guess is ultimately good or bad.

Determine the inverse Laplace transform $f(t)$ of the function $F(s)=\frac{s+1}{s^{2}+2 s+10}$.

A room is 10 feet by 12 feet. If the scale of the blueprints to the room is 1 inch to 2 feet, fmd the dimensions of the room on the blueprints.

Over a time interval of 2.16 years, the velocity of a planet orbiting a distant star reverses direction, changing from +20.9 km/s to - 18.5 km/s. Find

the total change in the planet's velocity (in m/s)

Write the exponential equation as a logarithmic equation.

$$12 ^ { - 2.6 } = N + 1$$

Measurements made on the internally compensated amplifiers listed below provide the dc gain and the frequency at which the gain has dropped by 20 dB. For each, what are the 3 dB and unity-gain frequencies? $(a)\ 2 \times 10^{5} \mathrm{V} / \mathrm{V}$ and $5 \times 10^{2} \mathrm{Hz}$ $(b)\ 20 \times 10^{5} \mathrm{V} / \mathrm{V}$ and 10 Hz (c) 1800 V/V and 0.1 MHz (d) 100 V/V and 0.1 GHz (e) 25 V/mV and 250 kHz

Show that the square of a noncentral T random variable is a noncentral F random variable.

In your own words, phrase each of Newton's three laws of motion as a statement about momentum.