Exam 1: Review of Basic Concepts

Solve the problem. Round to two decimal places unless otherwise indicated. -If the average cost per unit C(x) to produce x units of plywood is given by C(x) $C ( x ) = \frac { 1200 } { x + 40 }$ , what do 400 units cost?

Factor by any method. - $9 \mathrm { k } ^ { 2 } - 64 \mathrm {~m} ^ { 2 }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $( - 2 x ) ^ { 6 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { \sqrt [ 3 ] { 270 } } { \sqrt [ 3 ] { 10 } }$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. -When determining appropriate doses of medication, it is sometimes important to estimate the body surface area (BSA) of a patient. This surface area (in $\mathrm { m } ^ { 2 }$ ) can be approximated using the Mosteller formula BSA $= \left( \frac { h \cdot w } { 3600 } \right) 1 / 2$ where $h$ is the patient's height in centimeters and $w$ is the weight in kilograms. Determine the BSA for a patient with height $172 \mathrm {~cm}$ and weight $90 \mathrm {~kg}$ . Round your answer to two decimal places.

Find the sum or difference. - $- \left( 2 x ^ { 3 } + x - 8 \right) + \left( 4 x ^ { 3 } + 2 x ^ { 2 } \right) - \left( 9 x ^ { 2 } - 3 x - 1 \right)$

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. -The NSC (Not So Consistent) Corporation has just completed its first year of business. The following chart shows its monthly profit (or loss). Month Profit (Loss) in Dollars January -14,526 February 1874 March -8977 April -14,107 May 14,073 June 14,632 July -13,834 August -13,170 September -4860 October 6630 November -3338 December -974 The profit was smallest in ? .

Factor the trinomial, if possible. - $9 z ^ { 2 } - 6 z - 8$

Write in radical form. Assume all variables represent positive real numbers. - $( 3 m + n ) ^ { 3 / 4 }$

Find the domain of the expression. - $\frac { 4 } { m - 8 }$

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 6,7,8,9,10,11 \} , \mathrm { B } = \{ 8,10,12 \} , \mathrm { C } = \{ 6,7,9,11 \} , \mathrm { D } = \{ 6,11 \}$ , and $\mathrm { U } = \{ 6,7,8,9,10,11,12 \}$ $C \subset \varnothing$

Simplify the expression. Assume all variables represent positive real numbers. - $- \sqrt [ 3 ] { \frac { 5 x } { y } }$

Insert $\in \mathbf { O r } \notin$ in the blank to make the statement is true. -

Factor the trinomial, if possible. - $4 x ^ { 3 } + 8 x ^ { 2 } - 60 x$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 7 } { 8 } } - \sqrt { \frac { 63 } { 72 } }$

Determine the degree of the polynomial. - $- a + 7 a ^ { 3 } - 6 a ^ { 7 } + 4 a ^ { 2 }$

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. -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 x is the altitude of the plane in feet and d is given in miles. How far can one see in a plane flying at 20,000 feet? Round your answer to the nearest tenth mile, if necessary.

Factor out the greatest common factor. Simplify the factors, if possible. - $15 x ^ { 6 } + 6 x ^ { 3 } - 20 x ^ { 3 } - 8$

Factor, using the given factor. Assume all variables represent positive real numbers. - $4 ( 2 x - 1 ) ^ { - 3 / 4 } + 8 ( 2 x - 1 ) ^ { 1 / 4 } + 16 ( 2 x - 1 ) ^ { 5 / 4 } ; \quad 4 ( 2 x - 1 ) ^ { - 3 / 4 }$

Evaluate the expression. - $( - 2 ) ^ { 3 } - ( - 2 ) ^ { 2 }$