Explain why in a drawer containing only two different colors of socks one must draw only three socks to find a matching pair.

2 answers:

8 0

In the drawer you have a total of 4 socks: the one you already have, two of a different color and one of the same color of the first sock. If the first two socks you draw are of a different color, the third one will surely be of the color of the first sock.

lana66690 [7]4 years ago

7 0

There are two different colors of socks, so in the worst case scenario you can draw two different socks. Therefore you need to draw one more sock of any color to have a matching pair.

2+1=3 :)

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Yakvenalex [24]

Answer:

$\boxed{\dfrac{f(a+h)-f(a)}{h}=-3a^2-3ah-h^2}$

Step-by-step explanation:

$f(x)=-x^3+2\\\\\dfrac{f(a+h)-f(a)}{h}\\\\f(a+h)\to\text{substitute x = a + h}\\f(a)\to\text{substitute x = a}\\\\\dfrac{f(a+h)-f(a)}{h}=\dfrac{-(a+h)^3+2-(-a^3+2)}{h}\\\\\text{use}\ (x+y)^3=x^3+3x^2y+3xy^2+y^3\\\\=\dfrac{-(a^3+3a^2h+3ah^2+h^3)+2-(-a^3)-2}{h}\\\\=\dfrac{-a^3-3a^2h-3ah^2-h^3+2+a^3-2}{h}\\\\\text{combine like terms}$