The velocity of a bob on a simple pendulum at the lowest position is 10.56 m/s. What is the maximum vertical height it is able to rise to?

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

Certain bacteria (such as aquaspirillum magnetotacticum) tend to swim toward the earth’s geographic north pole because they contain tiny particles, called magnetosomes, that are sensitive to a magnetic field. if a transmission line carrying 100 a is laid underwater, at what range of distances would the magnetic field from this line be great enough to interfere with the migration of these bacteria? (assume that a field less than 5% of the earth’s field would have little effect on the bacteria. take the earth’s field to be 5.0 * 10-5 t, and ignore the effects of the seawater.)

To find the mass defect for uranium-238 several calculations must be made. which is the calculation that should be made first? assume atomic number for uranium-238 is 92. a. 92(1.0073) x 92(1.0087) = b. 92(1.0073) x 146(1.0087) = c. 146(1.0073) x 238(1.0087) = d. 238(1.0073) x 238(1.0087) =