What evolutionary advances are seen in the phyla of bilaterally symmetrical worms?

(a) Find the total energy of vibration of a string of length L, fixed at both ends, oscillating in its nth characteristic mode with an amplitude A. The tension in the string is T and its total mass is M. (b) Calculate the total energy of vibration of the same string if it is vibrating in the following superposition of normal modes: $y(x, t)=A_{1} \sin \left(\frac{\pi x}{L}\right) \cos \omega_{1} t+A_{3} \sin \left(\frac{3 \pi x}{L}\right) \cos \left(\omega_{3} t-\frac{\pi}{4}\right)$ (You should be able to verify that it is the sum of the energies of the two modes taken separately.)

When a store buys merchandise, why are individual departments not allowed to directly deal with suppliers?

Identify each of the following as a monomial, a binomial, a trinomial, or none of these.

$$7$$

Propose an evolutionary explanation for introns. Why might they have evolved?

Find the polar equation of each of the given rectangular equations.

$$x^2 + y^2=0.81$$

Find the inverse of f(x) algebraically. Hint: After swapping variables make a substitution: $u=e^y$. Solve for u then back-substitute to find y.

$$f(x)=\dfrac{e^x-e^{-x}}{2}$$

Solve the right triangle given the information in each problem.

a = 134 m, c = 182 m (angles to the nearest 0.1 deg)

Determine if these two triangles are similar. If so, state the similarity and the reason.

The mean for a particular test is 1200 and the standard deviation is 150. Find the z-value for each score:

a. 1150

b. 1430

c. 1560

d. 1090

e. 850

Each of the following objects has a radius of 0.180 m and a mass of 2.40 kg, and each rotates about an axis through its center with an angular speed of 35.0 rad/s. Find the magnitude of the angular momentum of each object a hoop.

In the following symbolized arguments, derive the line needed to obtain the conclusion (last line), and supply the justification for both lines. $1. H \supset(\sim C \vee R) \\ 2. \text{\_\_\_\_\_\_ \_\_\_\_} \\ 3. (H \cdot C) \supset R \text{\_\_\_\_\_\_}$

For each of the following lists of premises, derive the indicated conclusion and complete the justification. For double negation, avoid the occurrence of triple tildes. $1. M \vee(G \vee T) \\ 2. P \cdot(S \supset N) \\ 3. D \cdot(R \vee K) \\ 4. \text{\_\_\_\_\_\_ \_\_\_\_, Assoc}$

Explain why the reptiles are represented by more than one evolutionary lineage.