By Ya. S. Bugrov - S. M. Nikolski
Read or Download Matematicas Superiores - Elementos de Algebra Lineal y Geometria Analitica PDF
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Extra resources for Matematicas Superiores - Elementos de Algebra Lineal y Geometria Analitica
120 = 40 3 30 Easy Algebra Step-by-Step Step 2. The signs are opposites (one negative and one positive), so make the quotient negative. −120 = −40 3 c. 120 −3 Step 1. Divide 120 by 3. 120 = 40 3 Step 2. The signs are opposites (one positive and one negative), so make the quotient negative. 120 = −40 −3 d. −120 0 Step 1. The divisor (denominator) is 0, so the quotient is undefined. −120 = undefined 0 e. 0 30 Step 1. The dividend (numerator) is 0, so the quotient is 0. 0 =0 30 To be successful in algebra, you must memorize the rules for adding, subtracting, multiplying, and dividing signed numbers.
Add the opposite of 0. = −60 + 0 Problem Find the difference. a. −35 − 60 b. 35 − 60 c. 60 − 35 d. −35 − ( −60) e. 0 ( 60) f. −60 − 0 Remember 0 is its own opposite. ” You keep the ﬁrst number, you change minus to plus, and you change the second number to its opposite. Computation with Real Numbers 23 Solution a. −35 − 60 Step 1. Keep −35 and add the opposite of 60. −35 − 60 = −35 + −60 Step 2. The signs are the same (both negative), so use Rule 1 for addition. = −95 Step 3. Review the main results.
Find the principal fifth root of − ⎛ 32 ⎞ − ⎝ 243 ⎠ P 1/5 =5− 32 . 243 32 2 =− 243 3 When you evaluate exponential expressions that have unit fraction exponents, you should practice doing Step 1 mentally. For instance, 491 / 2 ⎛ 1⎞ ⎜⎝ 32 ⎟⎠ =7, 1/ 5 = ( )1 / 3 = −2, 1 , and so forth. 2 Rational Exponents If x is a real number and m and n are natural numbers, then (a) x m / n (x / n )m or (b) x m / n (x m ) / n, provided that in all cases even roots of negative numbers do not occur. When you evaluate the exponential expression x m / n, you can find the nth root of x first and then raise the result to the mth power, or you can raise x to the mth power first and then find the nth root of the result.