X^2 + y^2 = (3x^2 + 2y^2 - x)^2
2x + 2y f'(x) = 2(3x^2 + 2y^2 - x)(6x + 4y f'(x) - 1) = 36x^3 + 24x^2yf'(x) + 24xy^2 + 16y^3f'(x) - 4y^2 - 18x^2 - 8xyf'(x) + x
f'(x)(2y - 24x^2y - 16y^3 + 8xy) = 36x^3 + 24xy^2 - 4y^2 - 18x^2 - x
f'(x) = (36x^3 + 24xy^2 - 4y^2 - 18x^2 - x)/(2y - 24x^2y - 16y^3 + 8xy)
f'(0, 0.5) = -4(0.5)^2/(2(0.5) - 16(0.5)^3) = -1/(1 - 2) = -1/-1 = 1
Let the required equation be y = mx + c; where y = 0.5, m = 1, x = 0
0.5 = 1(0) + c = 0 + c
c = 0.5
Therefore, the tangent line at point (0, 0.5) is
y = x + 0.5
Consider the ordering
... -2 < -1
Now consider the ordering of their absolute values:
... 1 < 2
_____
Hopefully, you see that changing the sign reflects the sequence across the origin, so that the ordering is reversed when the signs are changed.
Answer:
The pattern is min-zero-max-zero-min, which is the pattern for a cosine function of the form y = acos(x) + k, but is reflected over the x-axis (so a < 0).
The amplitude is |a|, so a = –1 and |a| = 1.
The midline is exactly between the max and the min, y = (6 + 8)/2 = 7, so k = 7.
The equation is y = –cos(x) + 7.
hope it helps :)
mark brainliest!!
Step-by-step explanation:
This is a sequence of multiply by 2
3 6 12 24 48