Question
Mon April 21, 2014 By: Beauchelle Lobo

Please help to solve the sums

 

1. If x/x^1.5 = 8x^(-1)  and x>0 then x = ?

 

2. if g=t^(2/3) + 4t^(-1/2) what is the value of g when t=64

Expert Reply
Mon April 21, 2014
a)
 
x over x to the power of 1.5 end exponent equals 8 x to the power of minus 1 end exponent  rightwards double arrow x over x to the power of 1.5 end exponent equals 8 over x  rightwards double arrow x to the power of bevelled 1 half end exponent equals 8  rightwards double arrow x equals 8 squared equals 64
 
 
 
b)g equals t to the power of bevelled 2 over 3 end exponent plus 4 t to the power of minus bevelled 1 half end exponent  equals t to the power of bevelled 2 over 3 end exponent plus 4 over t to the power of begin display style bevelled 1 half end style end exponent n o w space s u b s t i t u t i n g space t equals 64  rightwards double arrow g equals open parentheses 64 close parentheses to the power of bevelled 2 over 3 end exponent plus 4 over open parentheses 64 close parentheses to the power of begin display style bevelled 1 half end style end exponent equals open parentheses 4 cubed close parentheses to the power of bevelled 2 over 3 end exponent plus 4 over open parentheses 8 squared close parentheses to the power of begin display style bevelled 1 half end style end exponent equals 4 squared plus 4 over 8 equals 16 plus 1 half equals 33 over 2
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