That would be infinite. Both the number of times it touches the trains, and which train it touches last cannot be determined. Read about Zeno's paradox, specifically the tortoise and Achilles. Here is ...

You are confusing theory with parctise. A point does not exist in the real universe. Anything you draw will have some dimensions.

Equivalent to $6*2^x - 2^x = 3^4 - 1$ solve for $2^x$, $2^x =a$ $6*a - a = 81 -1$ $5*a= 80$ $a = 16.$ $2^x = 16$, therefore $x = 4$

Take a sample binary number, 0110 , its value in decimal is (from rightmost to leftmost) 0 * 2^0 + 1 * 2^1 + 1 * 2^2 + 0 * 2^3 = 6. Now shift all digits 1 bit to the left. 1100 0 * 2^0 + 0 * 2^...

Sorry for the elementary question. Let $X = 1$, $Y = 1$. $XY = 1.$ $X+Y-1 = 1$ Now we only need to notice that $XY$ increases at a faster pace than $X+Y-1.$ So this holds for all natural numbers.

A)Probability of winning by drawing the first WIN ball = p = 1/5. Probability of not winning by drawing a LOSE ball = q = 1-p. Now, Probability of you winning, given that you draw first = ...

Acceleration is rate of change of velocity. Velocity is rate of change of displacement. Acceleration by velocity would be rate of change of velocity by rate of change of displacement. Let velocity ...

Those two outcomes can be for any coin flips in any order and not necessarily the last two, therefore 6C2, the number of combinations of two among the total six. Edit: think of it this way: The ...

Let F(x,y) = $xy(x+y) - 2a^3$ We need the gradient of F(x,y), which we can find as, Differentiating F(x,y) w.r.t to x yields $2xy+y^2$ Differentiating F(x,y) w.r.t y yields $x^2 + 2xy$ For a ...