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# math_answers-1 - of equation you may have to solve(b...

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Solutions to the Practice Problems on Required Mathematical Skills 1. Simplify each of the following expressions as much as possible: (a) - p H (b) log 10 (10 x 2 ) = log 10 10 + log 10 x 2 = 1 + 2 log 10 x (c) x (d) ( x + 1) 2 x 2 + 1 doesn’t simplify. 2. Solve the following equations for x : (a) Rewrite this equation to the form 13 x 2 +2 x - 44 = 0. This is now a quadratic equation with solutions x = - 2 ± p 2 2 - 4(13)( - 44) 2(13) = - 2 ± 2292 26 . If you run these numbers through your calculator, you get x = 1 . 7644 or x = - 1 . 9183. Note that you should try to report answers to a reasonable number of digits and that your results must be rounded correctly. Also, if you have a quadratic equation solver programmed into your calculator, you are more than welcome to use it on a test. Just tell me that you did so I know where your numbers are coming from. The same thing goes for any other type

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Unformatted text preview: of equation you may have to solve. (b) Rewrite this to the form-13 . 2 = log 10 x . Now take 10-13 . 2 = 10 log 10 x = x . Therefore x = 6 . 3096 × 10-14 . Note that the calcu-lator notation ( 6.3095E-14 ) is unacceptable . (c) Take a natural logarithm of both sides: ln 13 . 2 = ln e x 2 = x 2 . The answer falls out immediately: x = √ ln 13 . 2 = 1 . 6063. (d) Cross-multiply and rearrange: 4 . 3( x + 1) = x. ∴ 3 . 3 x =-4 . 3 . ∴ x =-1 . 3030 . 1 (e) Again, start by cross-multiplying and rearranging: a ( x + c ) = 2 x 2 + b. ∴ 2 x 2-ax + b-ac = 0 . ∴ x = a ± p a 2-4(2)( b-ac ) 2(2) = 1 4 ± a ± p a 2-8( b-ac ) ² . 2...
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math_answers-1 - of equation you may have to solve(b...

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