In the area of genetics, explain what is meant by semiconservative replication.
Semiconservative replication describes the method of DNA replication. DNA replication begins with unwinding of the double helix DNA. Each strand of the DNA segment gets replicated; however, the end product consists of two daughter DNA molecules, each with one parental and one novel DNA strand, hence the name semiconservative.
Describe the differences between ionic, covalent, polar covalent, and hydrogen bonds. Describe which bonds are used by water molecules.
An ionic bond is one in which one atom gives its electrons to another, more electronegative atom, filling its valence shell. Covalent bonds involve sharing of valence electrons between two atoms, whereas a polar covalent bond involves unequal sharing of electrons so one atom is slightly more negative than the other. Such unequal charge is called a dipole moment. Hydrogen bonding differs from the previous three because it is an intermolecular force rather than an intramolecular bond. It is the attraction between a hydrogen atom from one molecule to a highly electronegative atom, such as fluorine, nitrogen, or oxygen, from another molecule. Water molecules employ polar covalent bonding between hydrogen and oxygen atoms with the electrons being slightly more concentrated near the oxygen atom. Water molecules also bind to each other through hydrogen bonding as one oxygen atom from a water molecule binds to a hydrogen atom of another water molecule.
If f(x) = sin^2(5-x), then f'(0) = ?
To find the derivative of the function, we have to use the chain rule, which formally states that d(f(g(x)) = f'(g(x))g'(x). Another way to think of the chain rule is to think of the functions as layers of a problem and the chain rule tells you to first take the derivative of the outer layer, function f, while leaving the inner layer, function g, unchanged and then differentiate the inner layer. This specific case is slightly more complicated because we have three layers, the square, the sine function, and (5-x). We first differentiate the square while leaving the sine function unchanged, obtaining 2sin(5-x)dsin(5-x). We then take the derivative of the sine function, while leaving (5-x) unchanged, which gives us 2sin(5-x)cos(5-x)d(5-x). Finally, we take the derivative of (5-x) and obtain -2sin(5-x)cos(5-x). To get the final answer, we plug in x = 0, therefore f'(0) = -2sin(5)cos(5).