Which equation shows the relationship between the numbers of parent and daughter nuclei after one half-life of a radioactive isotope has passed?
A. Parent nuclei = 2 x daughter nuclei
B. Parent nuclei = daughter nuclei
C. Parent nuclei = 0
D. Daughter nuclei = 2 x parent nuclei

(2) (a) you have a simple circuit that consists of only a battery (δvbat=1.5v) and two resistors with resistance r1=10ω and r2=5ω, connected in series with each other. what is the current running through the battery? (b) you re-arrange your circuit so now r2 is attached in parallel to r1 rather than in series. what is the current running through the battery? (c) you add an additional resistor r3=7ω on the same branch as r2. what is the current running through the battery? (d) what is the power dissipated in r3?

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k

Hydroelectricity provides about 7 percent of the electricity generated in the united states. (a) explain how a hydroelectric power plant converts energy stored in water into electricity. (b) identify two factors that determine the amount of electricity that can be generated by an individual hydroelectricity power plant. (c) describe the two main types of land-based hydroelectric power plants. (d) describe two economic advantages and two environmental disadvantages of hydroelectricity.