How many different symbols can be represented by in morse code, symbols are represented by variable-length sequences of dots and dashes. (for example, a=: -, 1 = sequences of six or fewer dots and dashes?

126 different symbols can be represented in Morse code

Step-by-step explanation:

We need to sum up the number of sequences using one single place, two places, three places, four places and so on until sequences of six places (dots and dashes).

For each case we use the fundamental counting principle.

For one single place we may have 2 possible sequences (a dash or a dot)

For two places (example: .. or ._) we may have 2*2 sequences, since each place may be filled with either dash or dot (2 possible ways) and then we multiply the ways each place can be filled, thus

Similarly, for three places we may have 2*2*2 sequences, thus

For four places we may have 2*2*2*2 sequences, thus

And so on.  

So, notice the total up to arrangements of six symbols, is:

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.