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1.    if a watch runs 5 min fast every hour,then the angle traversed by a second hand in one min is

2.   if 2x+y=17,2z+y=15, x+y = 9, then the value of 4x +3y +z=?

3.    if [ a2+b] [m2+n2]=(am+bn) then which of the following is true

 

a.a/m=b/n                            b. a/n=b/m

 Jan 15, 2016
 #1
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1.   The second hand must traverse 5 * 360°  = 1800°  more in an hour than it should if it runs 5 minutes fast....so......in one "normal" minute....it must traverse 1/60th of this plus its normal turn  of 360°.......so.... [360 + 1800/60]°  = [ 360 + 30]°  = [ 390]°

 

2. 2x+y=17,2z+y=15, x+y = 9, then the value of 4x +3y +z=?

 

y = 9 - x      sub this into the first equation

 

2x + [9 - x]  = 17

 

x + 9  = 17     so x = 8     and y  = 9 - 8  = 1

 

And

 

2z + y = 15    ....so    2z + 1 = 15    →  2z = 14  →  z = 7

 

So   ...   4x + 3y + z  =  4(8) + 3(1) + 7  =  32 + 3 + 7  = 42

 

 

 

3.    if [ a^2+b^2 ] [m^2+n^2]=(am+bn)^2    simplify

 

[am]^2  + [an]^2 + [ bm]^2 +  + [bn]^2  = [am + bn][am + bn]

 

[am]^2  + [an]^2 + [ bm]^2 +  + [bn]^2 = [am]^2 + 2[bn][am] + [bn]^2 

 

subtract like terms from each side

 

[an]^2  + [bm]^2  = 2[bm][an]

 

[an]^2 - 2[bm][an] + [bm]^2 = 0   factor

 

[ an - bn] [am - bn]  = 0

 

[an - bm]^2  =  0        take the square root of both sides

 

[an - bm] = 0   so

 

an = bm     divide both sides by n, m

 

a/m  = b/n     and the answer is a.

 

 

cool cool cool

 Jan 15, 2016
edited by CPhill  Jan 15, 2016

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