Evaluate the derivative of the following functions. $f(w)=w^{2}-\tan ^{-1} w^{2}$

Calculate the maximum wavelength of light capable of removing an electron for a hydrogen atom from the energy state characterized by n = 1, by n = 2.

Solve the given differential equation by separation of variables. $d y-(y-1)^{2} d x=0$

Proceed as in Example 5 and find an explicit solution of the given initial-value problem. $\frac{d y}{d x}=y e^{-x^{2}}, \quad y(4)=1$

You work 40 hours per week at a candy store and earn $7.50 per hour. You also earn$7.00 per hour babysitting and can work as many hours as you want. You want to earn $370 a week. How many hours must you babysit?

Use computer software to obtain a direction field for the given differential equation. By hand, sketch an approximate solution curve passing through each of the given points. $\frac{d y}{d x}=\frac{1}{y}$ (a) y(0) = 1 (b) y( - 2) = -l

What observation about molecules compels us to consider the hybridization of atomic orbitals?

You are shopping for DVDs. You want to buy 7 DVDs for $19.99 each. Show how you can use the Distributive Property to find the total cost of the DVDs mentally.

Solve for x $(0 \leq x<2 \pi)$. $\tan (4 x)+\frac{\sqrt{3}}{3}=0$

Write five indirect commands telling various family members what to do next weekend.

Using data from the text, determine the following values (justify your answer):

Listed below are some of the things and people you find at a birthday party. Rewrite using the diminutive form. sillas ______

Use the four-step plan to solve each problem. For today's lunch, the school cafeteria is offering make your own pizzas with the options shown at the right. How many different pizzas can be ordered with one cheese and one topping?

$$\begin{matrix} \text{Pizza Options}\\ \text{Crust} & \text{Cheese} & \text{Toppings}\\ \text{thin} & \text{mozzarella} & \text{pepperoni}\\ \text{deep dish} & \text{Cheddar} & \text{sausage}\\ \quad & \quad & \text{onions}\\ \quad & \quad & \text{mushrooms}\\ \end{matrix}$$

Solve the equation and check your solution. 4 - (z + 6) = 8