By Josh Gregory
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9110 8. 23810 In Problems 9 to 12, convert the given binary numbers into their hexadecimal equivalents. 9. 110101112 10. 111010102 11. 100010112 12. 101001012 In Problems 13 to 16, convert the given hexadecimal numbers into their binary equivalents. 13. 3716 14. ED16 15. 9F16 16. 1 Basic operations Problem 3. Algebra is that part of mathematics in which the relations and properties of numbers are investigated by means of general symbols. For example, the area of a rectangle is found by multiplying the length by the breadth; this is expressed algebraically as A = l × b, where A represents the area, l the length and b the breadth.
Evaluate R when P = 1500, V = 5 and T = 200. 4. The velocity of a body is given by v = u + at. The initial velocity u is measured when time t is 15 seconds and found to be 12 m/s. 81 m/s2 calculate the final velocity v. 5. 7 . 6. Find the distance s, given that s = 12 gt 2 . 81 m/s2 . 7. The energy stored in a capacitor is given by E = 12 CV 2 joules. Determine the energy when capacitance C = 5 × 10−6 farads and voltage V = 240 V. 8. 7 m. 9. Resistance R2 is given by R2 = R1 (1 + αt). 6. mass .
6. p3 q 2 2 pq − p2 q 7. (a2 )1/2 (b2 )3 (c1/2 )3 8. (abc)2 (a2 b−1 c−3 )3 √ √ √ √ 3 9. ( x y3 z 2 )( x y3 z 3 ) 10. (e2 f 3 )(e−3 f −5 ), expressing the answer with positive indices only 11. (a3 b1/2 c−1/2 )(ab)1/3 √ √ ( a3 b c) Problem 26. Remove the brackets and simplify the expression (3a + b) + 2(b + c) − 4(c + d) Both b and c in the second bracket have to be multiplied by 2, and c and d in the third bracket by −4 when the brackets are removed. Thus: (3a + b) + 2(b + c) − 4(c + d) = 3a + b + 2b + 2c − 4c − 4d Collecting similar terms together gives: 3a + 3b − 2c − 4d Problem 27.