(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
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It is due to the counter clockwise motion of the motor. The motor rotates in the counter clockwise direction the blades of the fan are attached to the motor hence the blades rotates in the anti clockwise direction. So it is due to the motor rotation the fan rotates in counter clockwise direction.
at least 2, at most 4….
2 if you get lucky the first 2 times you draw a jelly bean, 4 would be if in the first 3 tries you get one of each color and the next draw will get you 2 of the same color
2, 6, 12, 72, 824
2
6*2=12
12*6=72
72*12=864
6+3.50= 2.50
A
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no combinations is there because a number divisible by 36
also divisible by its divisors anu.sum of 4 digits=20,whis
is not multiple of 3.so it is cannot divisible by 3
26