@scrabbler i tried it by using apollonius thereom ..i cnt get were i went wrong
@iLoveTorres said:meine calculate nahi kiya tha.. it was jus an approximation.. i kno the difficult part would be done by some1 else in this case it was you
@mohitjain said:@scrabbler i tried it by using apollonius thereom ..i cnt get were i went wrong
if you apply appolinius you wil get ED as 4 and from the given info it is clear CF =1/5 BC. but BC=AD=8 so CF=1.6 now you can treat area(CDEF)= area of parellogram + area of triangle. think lil you wil get the approach
@scrabbler said:Well....BE is a median (apply Appollonius)So ED = 1/2 long side AD, FC = 1/5 AD so in the trapezium DEFC, 1/2(ED + FC) = 7/20 of AD. Height same. So ratio of areas = 7:20 if I have done this right. Figure bahut ganda sa draw kiya OA? regardsscrabbler
Is BE a median, very obvious? I had to apply cosine formula to see that. 
@karl said:Is BE a median, very obvious? I had to apply cosine formula to see that.
Not obvious....but I started off with the assumption that there must be some easy way to solve....and the number looked interesting, 2rt6, and after drawing the figure it made sense to check before trying a complicated approach. So I tried and found that 4^2 + 8^2 = 2[4^2 +(2rt6)^2] so it must be a median!
regards
scrabbler
regards
scrabbler
@karl said:Is BE a median, very obvious? I had to apply cosine formula to see that.
i actually applied appolinius theorem and got AE=ED so i guess BE should be the median.
@mohitjain said:If f(x) = 2x2 + (ab^2 + ac^2 – 2abc)x + abc and the minimum value of f(x) is at x = –54, then what is the minimum value of (a + 2b – 2c)? (Given that a > b > c)
bhai yeh kaise solve kiya..? thoda explain kar do
@iLoveTorres
see its given dat minimum of f(x) is x=-54 ..minmum we get as -b/2a(aftr differentiating) so we equate -b/2a=-54 where b is (ab^2 + ac^2 창€“ 2abc) and a is 2 so we get d equation as a(b-c)^2=216..den i applied a.m>=g.m as we need 2 find a+2(b-c)..hope u get it!!!
see its given dat minimum of f(x) is x=-54 ..minmum we get as -b/2a(aftr differentiating) so we equate -b/2a=-54 where b is (ab^2 + ac^2 창€“ 2abc) and a is 2 so we get d equation as a(b-c)^2=216..den i applied a.m>=g.m as we need 2 find a+2(b-c)..hope u get it!!!
a+(b-c)+(b-c)/3>=(a.(b-c)^2)^1/3..so a+2(b-c)=18
@mohitjain said:ABCD is a parallelogram. A point E is selected on AD such that BE = 2 ˆš6 units. Also 2AE = 2AB = BD = 8 units and 5CF = BC where F is a point on BC. Find the ratio of the area of quadrilateral DEFC to the area of parallelogram ABCD.
angle A = angle C
=> cos A = cos C
=> [ AB^2 + AE^2 - (2 ˆš6)^2 ] / [ 2 AB. AE] = [ BC^2 + CD^2 - (8)^2 ] / [ 2 BC.CD ]
=> (4^2 + 4^2-24) / (2.4.4) = ( 4^2+25(x^2)-64 ) / (2.4.5x)
where CF=x
=> x=8/5
Now BC = 5x and BC=AD
=> BC = AD = 5(8/5) = 8
=> ED = 4
Now question is ( Ar. quad DEFC ) / ( Ar. parrel. ABCD )
= [ (1/2) . (x+ED) . h ] / [5x . h]
= 7/20
2 boys + 6 girls + 1 faculty member.
total no f sitting arrangements when Faculty member shud be in middle & 2 boys shud not sit together?
@The_Loser said:2 boys + 6 girls + 1 faculty member. total no f sitting arrangements when Faculty member shud be in middle & 2 boys shud not sit together?
432 cases when the boys are on opposite sides from the faculty member and 96 when they are on the same side...
Edited - solved for 4 girls, I just realised :(
Umm....31680?
regards
scrabbler
@The_Loser said:2 boys + 6 girls + 1 faculty member. total no f sitting arrangements when Faculty member shud be in middle & 2 boys shud not sit together?
8!-2*7!=6*7!
@The_Loser 2 boys + 6 girls + 1 faculty member.
total no f sitting arrangements when Faculty member shud be in middle & 2 boys shud not sit together?
7!*6 ..???
@mohitjain said:ABCD is a parallelogram. A pointEis selected on AD such that BE = 2 ˆš6 units.
Also 2AE = 2AB = BD = 8 units and 5CF = BC where F is a point on BC. Find the ratio of the area of quadrilateral DEFC to the area of parallelogram ABCD.
let ad be y
y^2+16-64/2*y*4=4^2+4^2-(2root6)^2/2*4*4
y comes out as 8
so ed=4
now cf=8/5
ratio of areas of defc and abcd = (4+(8/5))/(8+8)
28/80=7/20
@The_Loser said:2 boys + 6 girls + 1 faculty member.total no f sitting arrangements when Faculty member shud be in middle & 2 boys shud not sit together?
let faculty be in middle
_ _ _ _ f _ _ _ _
now in 8 blanks we arrange them as 8!
now let the 2 boys b together
all can be arranged in 2*7!
so 8!-2*7!
now do the question for this
3 boys + 5 girls + 1 faculty member
total no f sitting arrangements when Faculty member shud be in middle & 2 boys shud not sit together?
How many ordered pairs of integers (a,b) are there such that 1/a+1/b=1/200 ?