Derive an expression for the maximum torque needed to rotate an agitator if it depends on the frequency of oscillation, the angular velocity with which the agitator rotates during an oscillation, the diameter of the agitator, the nominal height of the paddles, the length of the paddles, the number of paddles, the depth of liquid, and the liquid density.

Suppose that in the second exercise you deposit the money in a mutual fund that pays 12% annual interest.

Write a function $S$ that gives the total amount of money after $t$ years, where $t$ is a natural number.

What type of function is $S$?

What is the total amount of money after 20 years? Compare your answer with the answer you got in the previous exercise.

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y = 1 - x^2, y = 0; about the x-axis

The quantity that remains constant in a pulse-position modulator is
a. Pulse width
b. Period
c. Duty cycle
d. Space

According to monetarists, how do fluctuations in the money supply affect the economy?

Use each of the following terms in a separate sentence.

core sample

How are electrons and protons similar? How are they different?

Voting. If 220 out of 500 voters surveyed said that they would vote for the incumbent, then how many votes could the incumbent expect out of the 400,000 voters in the state?

In what ways do histone gene transcripts diff er from transcripts of other vertebrate protein-coding genes?

The flow rate of water over a weir depends on the head of water, the width of the weir, gravity, viscosity, density, and surface tension. Relate the flow rate to the other variables.

What are the two components used when figuring the time value of money?

Use the indicated letters to write the argument in symbolic form. Then use a truth table to determine whether the argument is valid or invalid. The X Games will be held in Oceanside (o) if and only if the city of Oceanside agrees to pay $200,000 in prize money (a). If If San Diego agrees to pay$300,000 in prize money (s), then the city of Oceanside will not agree to pay $200,000 in prize money. Therefore, if the X Games were held in Oceanside, then San Diego did not agree to pay$300,000 in prize money.

Use the variable x for the unknown, and write an equation representing the verbal sentence. Then solve the problem. If the product of a number and -4 is subtracted from the number, the result is 9 more than the number. Find the number.

A toroidal core has a rectangular cross section defined by the surfaces $\rho=2 \mathrm{cm}, \rho=3 \mathrm{cm}, z=4 \mathrm{cm}, \text { and } z=4.5 \mathrm{cm}.$ The core material has a relative permeability of 80. If the core is wound with a coil containing 8000 turns of wire, find its inductance.