Given the parabola whose equation is , find the focus and determine if the parabola opens up or down.

Part of the total score for each program is the sum of five program component scores. on the free program, the sum of these five program component scores is multiplied by a factor of 2.0. yuzuru hanyu, of japan, earned scores of 9.07, 8.96, 8.89, 9.21, and 9.36 for the program components portion of his free program. how many total points did he receive for this portion?

Enter the number of complex zeros for the polynomial function in the box. f(x) = x+ + 5x² +6

Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =