For the first one it’s b and I’m sorry but I’m not sure about the second
Yo have to find the distance between point L and point M. First, you have to do the x values. 1 - -3 = 4. Then, you subtract the y values. -2 - 4 = -6. Next, you add the found numbers to the x and y of the midpoint (m). Leaving 1 +4=5 and -2 + -6 = -8.
(5,-8)
Answer: B' (5,8), C' (3,1)
Step-by-step explanation:
You can use the points A' (-1,8) and A (-2,-3) to find how many units point A was translated.
-2 + 1 = -1
-3 + 11 = 8
Then, you simply add 1 to the x-values of points B and C and 11 to the y-values of points B and C to get B' (5,8), C' (3,1).
I hope this helps!
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
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<h3>28,542-10,350-9,750=8,442</h3><h3>So the third number is 8,442</h3><h3>Hope this helps! :)</h3><h3>
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