Philip S

The isotope Hg-197 is used in kidney scans. It has a half-life of 64.128 h. After that time, half the isotope will have decayed. Write the exponential decay function for a 12-mg sample. Find the amount remaining after 72 h.

41. The work done in joules (J) by a gas expanding from volume V1 to volume V2 is modeled by the equation W = nRT ln V2 - nRT ln V1, where n is the quantity of gas in moles (mol), T is the temperature in kelvin (K), and R = 8.314

.

a. Write the equation in terms of the ratio of the two volumes.

b. Find the work done by 1 mol of gas at 300 K as it doubles its volume.

By measuring the amount of carbon-14 in an object, a paleontologist can determine its approximate age. The amount of carbon-14 in an object is given by y = ae-0.00012t, where a is the amount of carbon-14 originally in the object, and t is the age of the object in years.

35. A fossil of a bone contains 32% of its original carbon-14. What is the approximate age of the bone?

Also, give an example of one that is not

1) ∫C (z-zo)^n dz = 0, n any integer ≠ 1.

2) ∫C (1/(z-zo)) dz = 2Πi

where C is the closed contour consisting

of the line segment from 0 to 1, followed by the line segment from 1

to 1 + i, followed by the line segment from 1 + i to 0

1) Show that ᴴ≡ is an equivalence relation on G

2) Show that the equivalence classes under ᴴ≡ are the left cosets of H in G

3) Show that for a,b within G, aH = bH iff (a^-1)b is within H

Let X = {1,2,3,4,5} and let Y = {1,2,3}. Let G = (P(X), Δ). H = (P(Y), Δ). Find [G:H]

Let G be a group and for a,b within G let aRb mean that ab=ba. Must R be an equivalence relation on G? If so, prove it; if not, indicate for which groups R is an equivalence relation

Suppose G is a group and define a relation R on G x G by:

(a,b) R (c,d) iff ad = cb

Supose H and K are subgroups of a group G and x,y are within G