From the choice in parentheses, underline the correct word or words for the following sentence. Notice that the sentence contains two sets of words in parentheses. Example 1. My watch has stopped; (its, $\underline{\text{it’s}}$) ($\underline{\text{later}}$, latter) than we think.

Having no (lead, led) for my mechanical pencil is a (miner, minor) annoyance.

Perform the operations and simplify the result when possible.

$$2 x + 3 + \frac { 1 } { x + 1 }$$

Classify the expression, name the operation or operations, and identify any variables. $9 \div 2$

In a shuttle craft of mass $m = 3000\text{~ kg}$, Captain Janeway orbits a planet of mass $M = 9.50\times 10^{25}\text{~ kg}$, in a circular orbit of radius $r = 4.20 \times 10^7 \text{m}$. Janeway briefly fires a forward-pointing thruster, reducing her speed by $2.00\%$. Just then, what is the mechanical potential energy of the shuttle craft?

Perform the operations and simplify.

$$\frac { x ^ { 3 } + 1 } { 4 } \div \frac { x + 1 } { 2 }$$

Perform the indicated operations and simplify.

$$\sqrt{12 x^3 y} \cdot \sqrt{3 x^2 y}$$

(a) What is the mechanical advantage of a wheelbarrow if the center of gravity of the wheelbarrow and its load has a perpendicular lever arm of 5.50 cm, while the hands have a perpendicular lever arm of 1.02 m? (b) What upward force should you exert to support the wheelbarrow and its load if their combined mass is 55.0 kg? (c) What force does the wheel exert on the ground?

Simplify each expression. Use the order of operations. $-8(\sqrt{64})-(-3)(-7)$

Simplify the expression using the order of operations. $4 \times ( 9 \div 3 ) ^ { 2 }$

Perform the operations. Write the answer in the form a + bi.

$$\frac { 2 + i } { 3 - i }$$

Perform the indicated operations. Simplify when possible.

$$\dfrac{5 a b}{a^2-b^2}-\dfrac{a-b}{a+b}$$

During a cold day, you can warm your hands by rubbing them together. Assume the coefficient of kinetic friction between your hands is $0.500$, the normal force between your hands is $35.0 \text{~N}$, and that you rub them together at an average relative speed of $35.0 \text{~cm/s}$. $(a)$ What is the rate at which mechanical energy is dissipated?

Explain why grinding operations may be necessary for components that have previously been machined.

Perform the indicated operations and simplify. $\frac { 1 } { x - 1 } - \frac { 1 } { x ^ { 2 } - 1 }$