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'Bee flying between two trains' problem
6 votes

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 ...

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How do curves consist of points?
5 votes

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

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Can someone help me with this question of finding x as exponent?
2 votes

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 $x = 4$

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why shifting left 1 bit is the same as multiply the number by 2
2 votes

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^...

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Product of two natural numbers being greater than or equal to their sum minus one
Accepted answer
1 votes

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.

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How am I supposed to approach this probability question?
1 votes

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 = ...

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doubts in derivatives
Accepted answer
1 votes

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 ...

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If you flip a fair coin 6 times, what is the probability that you will get exactly 2 tails?
1 votes

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 ...

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What will be the remainder when $2^{31}$ is divided by $5$?
1 votes

Notice the pattern. 2 divided by 5 remainder is 2. 4 divided by 5 remainder 4. 8 divided by 5 remainder 3. 16 divided by 5 remainder 1. For 32 it is 2 again , 64 - 4, 128 - 3, 256- 1 and so on. So ...

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Finding stationary point of an implicit equation: $ xy(x+y)=2a^3 $
0 votes

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 ...

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