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4.  Factor the following as a difference of squares

a) x^2−25

b) x^2−169

c) 81 x^2−100

d) 64−121x^2

a) A student lands a lucrative summer job in a biophysics labstudying single cell bacteria. In order to develop an effectivebacteria containment protocol it is crucial to find k for thegrowth rate of the bacteria. For bacteria x the studentisolates asingle bacterium, places it in a 1 cm x1 cm x1 cm container, andfinds that every 10 minutes all cells in the container undergo celldivision. Find K_g

b) In addition, it is known that after 30 divisions some of thebacteria start to die with a rate constant equal to 0.065minutes^-1. Assuming that the bacteria are exactlycylindrical, have the same dimensions as E. coli, and arehexagonally close packed with cylinders lining up perfectlyend-to-end, determine if it is safe to leave them unattended for 24hours. Note that it is not safe if within 24 hours of placing thesingle bacterium in the container the bacteria spill over the edgeof the container.

Notes: i) Ignore possible solvent effects.

ii) On the square lattice, each lattice site has z=4 neighboringsites. Then the number of bond orientations for a given monomerpair of the chain, as the chain performs a random walk on thesquare lattice, to find a particular conformation, is z-1. Anestimate of the number of possible conformations, or states (sizeof the conformational space), for the N-monomer chain is(z-1)^n-1. (Note that the number of possible sequences ofH and P monomers (size of ) is 2^N. (from Lau and Diltheconformational spacethe sequence spacel, Macromolecule 22 (1989)3986-3997)

iii) A monomer at the end of the chain could potentially assumez-1 positions, depending on its contacts and whether or notneighboring lattice positions are filendled or empty. In thisproblem take any possible, different position of such monomer(s) asdefining a new conformation for the chain.

3. Factor the following trinomials (use the method of sum and product.)

a) x^2+7x+10

b) x^2+2x+1

c) x^2−3 x−18

d) x^2−4 x+3

e) x^2+5 x−14

f) x^2−13 x+36

g) x^2+6 x−27

h) x^2−10 x+25

i) −2 x^2 + 8 x+10

4.  Factor the following as a difference of squares.

a) x^2−25

b) x^2−169

c) 81 x^2−100

d) 64−121x^2

The density of a certain material is such that it weighs 4 kg for every 9 cups of volume. Express this density in ounces per gallon. Round your answer to the nearest whole number.

Note: you must use these exact conversion factors to get this question right. 

Answer: ______ ounces per gallon

Base station transmit a signal to a User. The User is 1Km away from the BS.It has a LOS connection.
If the last reflected signal travel around 1.5km to reach the User. Find the corresponding delay spread of the system. (c = 3 x ). The distortion caused by multipath transmission can be partly corrected by a tapped delay line equalizer. Show that if α « 1, the distortion in the multipath system in figure (a) can be approximately corrected if the received signal is passed through the tapped delay line equalizer shown in next figure.