Using the formula where a0 is the initial value and an is the 'nth' term, while 'd' is the common difference:
a7 = a0 + (n-1) x d = 6 + (7-1) * x 6 = 6 + 36 = 42
Using implicit differentiation:
x^-2 + y^-2 = cos(3x) - sin(3x)
-2x^-3 (dx/dx) + -2y^-3 (dy/dx) = -3sin(3x)(dx/dx) - 3cos(3x)(dx/dx)
crossing out dx/dx (which simplifies to 1) and isolating the dy/dx term:
-2y^-3 (dy/dx) = -3sin3x - 3cos3x + 2x^-3
finally we solve for dy/dx...
The quadratic formula assumes you have a quadratic equation equal to zero. In general: ax^2 + bx + c = 0.
In this case, 7x^2 + 123x - 4 = 0, so a = 7, b = 123, and c = -4 (c is negative because the standard form
assumes a, b, and c are positive).
Now, we can use the quadratic...