How to solve...John made 70% of his baskets in basketball. He made 105 baskets. How many total baskets did he make?
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In this question (brainly.com/question/12792658) I derived the Taylor series for about
:
Then the Taylor series for
is obtained by integrating the series above:
We have , so
and so
which converges by the ratio test if the following limit is less than 1:
Like in the linked problem, the limit is 0 so the series for converges everywhere.
The path is in the shape of a parabola, the horizontal length is 24, so the middle point is at x=12, the symmetry line is x=12, the highest point (the vertex) is at (12,6)
the equation in vertex form is y=a(x-12)²+6
next, find a by using either one of the two points, the starting point (0,0) or the end point (0,24). obviously (0,0) is easier to calculate:
0=a(0-12)² +6
a=-1/24
so the quadratic equation is y=-
the equation in vertex form is y=a(x-12)²+6
next, find a by using either one of the two points, the starting point (0,0) or the end point (0,24). obviously (0,0) is easier to calculate:
0=a(0-12)² +6
a=-1/24
so the quadratic equation is y=-