P(x) = 2x² - 4xq(x) = x - 3
To find the answer, we plug q(x) into p(x):
p(q(x)) = 2(x - 3)² - 4(x - 3)p(q(x)) = 2(x² - 6x + 9) - 4x + 12p(q(x)) = 2x² - 12x + 18 - 4x + 12p(q(x)) = 2x² - 16x + 30
The third option is correct.
Answer:
55.71 ft.
Step-by-step explanation:
hope this helps have a good day!
Answer:
![\sqrt[8]{197^{7} }](https://tex.z-dn.net/?f=%5Csqrt%5B8%5D%7B197%5E%7B7%7D%20%7D)
Step-by-step explanation:
The tangent to 
through (1, 1, 1) must be perpendicular to the normal vectors to the surfaces 
and 
at that point.
Let 
. Then is the level curve 
. Recall that the gradient vector is perpendicular to level curves; we have
so that the gradient of 
at (1, 1, 1) is
For the surface , we have
so that 
. We can obtain a vector normal to by taking the cross product of the partial derivatives of 
, and evaluating that product for 
:
Now take the cross product of the two normal vectors to and :
The direction of vector (24, 8, -8) is the direction of the tangent line to at (1, 1, 1). We can capture all points on the line containing this vector by scaling it by 
. Then adding (1, 1, 1) shifts this line to the point of tangency on . So the tangent line has equation
