0,8x= y
y – 0,7y = 270
y= 270 / 0,3
y=900
0,8x=900
x=1125
(x**2 – 6* x + 5) = (x-1)*(x-5)
(x**2 + 2 * x + 1) = (x + 1) * (x+1) = (x+1)**2
For what x is (x-1)*(x-5)/( (x+1)**2) a minimum?
One way to answer this question is by using calculus.
Take the derivative, and set to zero.
Since this is a fraction of polynomials, and a fraction is
zero only if it’s numerator is zero, we need calculate only
the numerator of the derivative and set it to zero.
The numerator of the
Derivative of (x-1)*(x-5)/( (x+1)**2) is
( (x-1) + (x-5) ) ( x+1)**2 – (x-1)(x-5)( 2 (x+1) )
= (2 x – 6) (x+1)**2 – (2) (x-1)(x-5) (x+1)
= 0
Divide through by 2 (x+1)
(x-3)(x+1) – (x-1)(x-5) = 0
(x**2 – 2 x – 3 ) – (x**2 – 6 x + 5) = 0
x**2 – x**2 – 2 x + 6 x – 3 – 5 = 0
4 x – 8 = 0
x = 2
Plugging in x = 2 into the original
(x**2-6*x+5)/(x**2+2*x+1)
gives us (2**2 – 6 * 2 + 5)/(2**2 + 2*2 + 1)
= (4 – 12 + 5) / (4 + 4 + 1) = -3/9 = -1/3
Least value is -1/3
b
Three man’s on day work = 1/6+1/7+1/8=73/168
three man’s can complete the work in 1/73/168 days
= 168/73 days
Now if they works together fro the alternet days they will
complete the worksin 2*168/73 days
(If three mans working for the alternate days then work
completion time will be doubbled)
previous ans wrong again..!!!!
first find x its 2 hours
total journey 6 hrs 3km up and also down
jill takes one hr to come down and jack takes 3 hrs so x
is 2 hours….
And while going up jack goes at 1.5km/hr and jill goes at
0.75 km hr so to travel 3 km they take 2 hrs and 4 hrs
respectively…!!! x again is 2 hrs…
so jack totally takes 5 hrs to travel 6 km
therfore speed is 6/5 km per hour
thats is 1.2 km per hour is the correct answer
5 litre jug contains 4 litres of salt water solution
with 15% of salt, that means it has 4000*.15 = 600 ml salt
in it.
If 1.5 litres solution is spills out, remaining solution
is 2.5 litres, then the salf content is 2500*.15 = 375ml.
Now, the jug is filled to full capacity with water i.e.,
now the jug has 5 litre solution in it.
Now, the salt content is 375/5000 = 7.5%
4/9
x and y can be equal to 1..
If so,then he gets 1/1 of Rs.10 which is equal to 10 and
again 1/1 of Rs.10=Rs.10..so,he gets total of 20..and
returns 20..so,no gain and no loss..
If x=1,y=2,he gets, 5+20=25..and returns 20..so he may not
lose..
So,whatever be the values of x and y,only these two answers
are possible..
so its a)He never loses..
Barber
Green bricks
If n = no. of revolutions for back wheel
9n = 7n + 10*7
n=315
10%=394;50%=1970;250%=9850;30%=1182;
250%+30%=9850+1182=11032