Exam 12: Review of Basic Concepts

Solve the problem. -A formula for calculating the distance, $d$ , one can see from an airplane to the horizon on a clear day is $\mathrm { d } = 1.22 \mathrm { x } ^{1 / 2}$ , where $\mathrm { x }$ is the altitude of the plane in feet and $\mathrm { d }$ is given in miles. How far can one see in a plane flying at 18,000 feet? Round your answer to the nearest tenth mile, if necessary.

Perform the indicated operation and write your answer with positive integer exponents. - $\frac { x ^ { 2 } - 49 y ^ { - 2 } } { \left( x - 7 y ^ { - 1 } \right) \left( x + 7 y ^ { - 1 } \right) }$

Solve the problem. -A simple exercise machine can be constructed by mounting a stiff spring securely to a wall and attaching a " $T$ " handle to the free end of the spring. The arms can be exercised simply by pulling the "T" handle towards the torso. For a particular spring, the stretch distance is related to the work exerted by the equation $x = \sqrt { \frac { 2 W } { 85000 } }$ , where $W$ is the work exerted in joules and $x$ is the stretch distance in cm. How far will you stretch the spring if you exert 606 joules of work? Round your answer to three decimal places.

Find the domain of the expression. - $\frac { y } { y ^ { 2 } - 25 }$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { \sqrt { 2 } } { 2 \sqrt { 3 } - \sqrt { 2 } }$

Evaluate the expression. -11369^1/2

Evaluate the expression. - $- | 8 |$

Factor, using the given factor. Assume all variables represent positive real numbers. - $15 s ^ { 3 / 7 } - 15 s ^ { - 5 / 7 } ; \quad s ^ { - 5 / 7 }$

Insert ⊆ or ⊈ in the blank to make the statement true. -{9, 10, 11} ___ {0, 9, 10, 11, 12, 13}

Evaluate the expression for x = -2, y = 3, and a = -4. -2x2 - 9y - a

Factor the trinomial, if possible. - $( x + 5 y ) ^ { 2 } + 10 ( x + 5 y ) + 25$

Factor the trinomial, if possible. - $3 x ^ { 3 } + 3 x ^ { 2 } - 36 x$

Use these sets to find the following. Identify any disjoint sets. -Let $U = \{ 9,10,11,12,13,14,15,16,17,18,19 \} , M = \{ 9,11,13,15 \} , \mathrm { N } = \{ 10,12,14,16,18 \}$ , $Q = \{ 9,11,13,15,17,19 \}$ , and $R = \{ 9,10,11,12 \}$ . $\mathrm { Q } ^ { \prime } \cap \left( \mathrm { N } ^ { \prime } \cap \mathrm { U } \right)$

Decide whether the expression has been simplified correctly. - $x ^ { 7 } \cdot x ^ { 2 } = x ^ { 9 }$

Find the product. - $( 4 m + 7 ) ^ { 2 }$

Factor by any method. - $20 x ^ { 4 } + 27 x ^ { 2 } + 9$

Evaluate the expression. -Let $\mathrm { x } = 8 , \mathrm { y } = - 3$ . Evaluate $4 | \mathrm { x } | + 5 | \mathrm { y } |$ .

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - $\frac { x ^ { 3 } } { y } > 0$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- 4 ^ { 0 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { \frac { 9 } { x - h } + \frac { 9 } { x } } { 2 x - h }$