+413 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+b2 ] [m2+n2]=(am+bn)2 then which of the following is true
a.a/m=b/n b. a/n=b/m
+129852 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.
