Evaluate 6z + 4x for x = 3 and z = 2*
1 answer:
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Let . The tangent plane to the surface at (0, 0, 8) is
The gradient is
so the tangent plane's equation is
The normal vector to the plane at (0, 0, 8) is the same as the gradient of the surface at this point, (1, 1, 1). We can get all points along the line containing this vector by scaling the vector by , then ensure it passes through (0, 0, 8) by translating the line so that it does. Then the line has parametric equation
or ,
, and
.
(See the attached plot; the given surface is orange, (0, 0, 8) is the black point, the tangent plane is blue, and the red line is the normal at this point)
Answer:
Option B and D are correct.
Step-by-step explanation:
Given: A line passes through the points (2,4) and (5,6).
* Case 1:
If a line passes through the points (2, 4) and (5, 6)
Point slope intercept form:
for any two points and
then the general form for linear equations where m is the slope given by:
First calculate slope for the points (2, 4) and (5, 6);
then, by point slope intercept form;
* Case 2:
If a line passes through the points (5, 6) and (2, 4)
First calculate slope for the points (5, 6) and (2, 4);
then, by point slope intercept form;
Yes, the only equation of line from the given options which describes the given line are;
and
First term: 3
Exiplicit formula:
or 3x5^n-1
Hope this helps!