National speech & debate association Interview Questions, Process, and Tips

419

(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

22.5

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NTFS — New Technology File System
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NTFS having a quota, commpress system with securites base as
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4. Annie Besant

Explanation:

The number of ways of selecting three men, two women and three children is:

= ⁴C₃ * ⁶C₂ * ⁵C₃
= (4 * 3 * 2)/(3 * 2 * 1) * (6 * 5)/(2 * 1) * (5 * 4 * 3)/(3 * 2 * 1)
= 4 * 15 * 10
= 600 ways.

Pi * radius * radius
3.14 * 5 * 5

The work done by A in 8 days is = 8/ 12 = 2/3

Means A alone completes 2/3 part of work.

Remaining work which is (1–2/3) = 1/3 is completed by B in 8–2 = 6 days

So the complete work done by B in 6/(1/3) = 18 days.

B alone can complete the work in 18 days.

9 AND 3

P+R=200
Q+R=350
+
—————-
P+Q+2R=550
P+Q+R=500
–
____________
R=50

answer :
Let the distance which I walk to the station be x km Then Time needed to reach the station at 3 km/hr = (3x​+602​) hrs and
Time needed to reach the station at 4 km/hr = (4x​+602​) hrs But 3x​+301​=4x​−301​⇒3x​−4x​=−302​=151​
⇒124x−3x​=151​⇒12x​=151​⇒x=1512​=54​ km

B. 3 : 2

Y