Know Yourself

Repent Thesaurus: Verb :  apologize ,  be sorry, reform, regret, rue, deplore, atone ...                                           Antonyms:  defy, confront . ..  Example sentences:         ·        He sincerely repented for his actions.  ·      It's never too late to repent , so just go ahead.

Ratio and Proportion: 1. If 7a = 2b and 3b = 5c, then a:c is: Solution:             a/b = 2/7             b/c = 5/3             a = 2*5 = 10             c = 3*7 = 21             a:c is 10:21. 2. The ratio of 9 4.5 : 3 6 is Solution:                (3 2 ) 4.5 / 3 6 = 3 9 /3 6                                  = 3 3                                                  = 27               The ratio is 27:1.

Ratio and Proportion: 1. If a=2b=3c, then a:b:c is: Solution:                  Let a=2b=3c = x                 a= x, b= x/2 and c= x/3.                 a:b:c = x : x/2 : x/3                              1: 1/2: 1/3                              6:3:2. 2. If a/3 : b/5 : c/7, then a:b:c is: Solution:                 Let a/3 = b/5 = c/7 = x                 a =3x,  b = 5x and c = 7x.                 3x:5x:7x                  3:5:7.

Renown Thesaurus: Adjective :  fame ,  ce lebrity, honor, glory, kudos, luster, prestige, repute ...                                           Antonyms : unimportance                      worthlessness, triviality . ..  Example sentences:         ·        He's a cardiologist and highly renowned for that area. ·        Her good deeds won renown. 

Ratio and Proportion: 1. If x:y = 2:3, find (3x+4y) : (3x+3y). Solution:                 x/y = 2/3   [Given]                (3x+4y)/(3x+3y)                Dividing both numerator and denominator by y, we get                [3(x/y)+4 ] / [3(x/y)+3]                = [3(2/3)+4 ] / [3(2/3)+3]                = 6/5.             2. Divide 560 in the ratio 3:2. Solution:                 The sum of the ratio is 3+2 = 5.                 First part = 3*(560/5) = 3*112 = 336.                 Second part = 2*(560/5) = 2*112 = 224. 

Sneaky Thesaurus: Adjective :  dishonest ,  cowardly , deceitful, base, mean, malicious, guileful, tricky, shifty...                                            Antonyms : honest                      frank, forthright...  Example sentences:         ·        Do you still like that sneaky boy? ·        She used to do sneaky kinds of stuff .   

Problems on Ratio and Proportion: 1. If a:b = 2:3 and b:c = 7:8, find a:b:c. Solution:                 a = 2*7 = 14.                 b = 3*7 = 21                 c = 8*3 = 24.               Hence,  a:b:c is 14:21:24. 2. Find           A. The fourth proportional to 2,4 and 5;          B. The third proportional to  3 and 9:          C. the mean proportional between 9 and 64. Solution:            A. 2:4::5:d is equivalent to (4*5) = 2d                                                           20 = 2d                                                           d = 10.            B. 3:9::9:c is equivalent to (9*9) = 3c                                                          81 = 3c                                                           c = 27.           C. (9*64) 1/2  = 3*8 = 24.