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Answer:
The height of the pole is 105ft,
Step-by-step explanation:
Let us call the height of the pole, then we know that the distance from the bottom of the pole to the anchor point is 49, or it is
.
The wire length is 14 ft longer than height
, hence
.
Thus we get a right triangle with hypotenuse , perpendicular
, and base
; therefore, the Pythagorean theorem gives
which upon expanding we get:
further simplification gives
,
which is a quadratic equation with solutions
Since the first solution will give the triangle base length of
which is negative; therefore, we disregard it and pick the solution
.
Hence, the height of the pole is 105ft.
If X and Y are Boolean variables, then X + Y represents disjunction (OR) and XY represents conjunction (AND), and X' denotes the negation (NOT). So X + Y = 1 if either X = 1 or Y = 1, and XY = 1 only if both X = 1 or Y = 1.
Now,
(X + Y) (X + Y') = XX + YX + XY' + YY'
… = X + X (Y + Y') + 0
… = X + X
… = X
or in table form,