What is the pattern? 1,1 / 2,3 / 3,6 / 4,10 / 5,15. (x,y). Whoever answers gets brainliest!
1 answer:
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<h3>Answer:</h3>
(x, y) ≈ (1.49021612010, 1.22074408461)
<h3>Explanation:</h3>This is best solved graphically or by some other machine method. The approximate solution (x=1.49, y=1.221) can be iterated by any of several approaches to refine the values to the ones given above. The values above were obtained using Newton's method iteration.
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Setting the y-values equal and squaring both sides of the equation gives ...
... √x = x² -1
... x = (x² -1)² = x⁴ -2x² +1 . . . . . square both sides
... x⁴ -2x² -x +1 = 0 . . . . . polynomial equation in standard form.
By Descarte's rule of signs, we know there are two positive real roots to this equation. From the graph, we know the other two roots are complex. The second positive real root is extraneous, corresponding to the negative branch of the square root function.
The sum of the inner angles of any triangle is always 180°, i.e. you have
In the particular case of an equilater triangle, all three angles are the same, so
and the expression becomes
which implies
So, if you rotate the triangle with respect to its center by 60 degrees, the triangle will map into itself. In particular, if you want point A to be mapped into point B, you have to perform a counter clockwise rotation of 60 degrees with respect to the center of the triangle.
Of course, this is equivalent to a clockwise rotation of 120 degrees.
Finally, both solutions admit periodicity: a rotation of 60+k360 degrees has the same effect of a rotation of 60 degrees, and the same goes for the 120 one (actually, this is obvisly true for any rotation!)