Generalized De Morgan's laws for logic: $\neg (\forall xP(x))$ and $\exists x\neg P(x)$ have the same truth values. $\neg (\exists xP(x))$ and $\forall x\neg P(x)$ have the same truth values.

Calculate the electrical force that acts on one plate of a parallelplate capacitor. The potential difference between the plates is 10 volts, and the plates are squares 20 cm on a side with a separation of 3 cm. If the plates are insulated so the charge cannot change, how much external work could be done by letting the plates come together? Does this equal the energy that was initially stored in the electric field?

Use the equation 1/o + 1/i = 1/f to solve the problem. Object distance is o, image distance is i, and focal length is f. An image of a candle appears in sharp focus on a screen that is 60 cm from a lens whose focal length is 20 cm. How far is the candle from the lens?

What is the difference between a reaction intermediate and a transition state?

Which statement does NOT describe a function of ozone gas on Earth? (a) Ozone absorbs ultraviolet-B radiation from the Sun. (b) Ozone absorbs ultraviolet-C radiation from the Sun. (c) Ozone absorbs X-ray radiation from the Sun. (d) Ozone causes the upper stratosphere to become warmer than the lower stratosphere. (e) Ozone prevents DNA damage.

Design a two-sided limiting circuit using a resistor, two diodes, and two power supplies to feed a $1-\mathrm{k} \Omega$ load with nominal limiting levels of $\pm 2.2 \mathrm{V}.$ Use diodes modeled by a constant 0.7 V. In the nonlimiting region, the voltage gain should be at least 0.94 V/V.

Both matter and energy are recycled in an ecosystem.

Match the enzyme(s) with its (their) function(s). Functions may be used more than once. (1) peptidase (2) amylase (3) nuclease (4) lipase (5) pepsin (6) trypsin, chymotrypsin (7) carboxypeptidase (8) sucrase, maltase, lactase A. begins protein digestion B. breaks fats into fatty acids and glycerol C. breaks down proteins into peptides D. breaks down starch and glycogen into disaccharides E. breaks down peptides into amino acids F. breaks down nucleic acids into nucleotides G. breaks down disaccharides into monosaccharides

Use synthetic division to determine whether x - c is a factor of the given polynomial. $2 x^{6}-18 x^{4}+x^{2}-9 ; \quad x+3$

Find the equation of the line tangent to f(x) at x = 2, if $f ( x ) = \frac { x ^ { 3 } } { 2 } - \frac { 4 } { 3 x }.$

How can infectious and noninfectious diseases affect personal health?

For a normally distributed random variable x with

$$\mu = 100 \text { and } \sigma = 16,$$

find the probability. x > 100

Write the equation of the line through (2, 6) that is parallel to 3x+2y=17.

If a particle moves along the polar curve $r = \theta$ under the influence of a central force attracting it to the origin, find the magnitude of the acceleration as a function of $r$ and the speed of the particle .