Write the electron configuration for S.
To write the electron configuration, we look at the different electron shells and subshells. There 4 main shells we use: s, p, d, f. There are 2 electrons allowed per subshell. The s shell has one subshell, the p has 3 subshells, d has 5 subshells, and f has 7 subshells. Then, we combine the subshells with the appropriate period number (1, 2, 3, 4). The period numbers go down the periodic table, with 1 as the first row and 7 as the last row. Using this information we can describe any atom. The ordering of electron configuration depends on the energy of the shells. S shells have the least energy and f has the highest energy. (Energy: s < p < d < f) We also need to look at how many electrons there are in each atom. Remember, if the atom does not have a charge, the number of electrons is equal to the atomic number. For S, the atomic number is 16, so there are 16 electrons. Now we fill the shells: S: $$(1s^2 2s^2 2p^6 3s^2 3p^4 $$
What is the derivative of $$ y = cos(x^2) $$?
To find the derivative we must remember that the derivative of $$ cos(x) = -sin(x) $$. We must also remember chain rule, since there is a function ($$ x^2$$) inside another function ($$sin(x)$$). For chain rule, we remember that $$ f'(y(x)) = y'(x)*x' $$. The derivative of $$ x^n = n*x^(n-1) $$. So $$ y' = -sin(x^2) * 2*x $$
If there is a right triangle with one side length 4 and the angle directly opposite from it is 30 degrees, what is the length of the hypotenuse?
Here we will use trigonometry. If we remember SOH-CAH-TOA (sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent) we know we can use the sine function to figure out the length of the hypotenuse. $$ sin(30) = 4/x $$. if we rearrange the function, $$ x = 4/sin(30) $$. For the ACT you will usually not have to simplify further than this.