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PolarNik [594]
3 years ago
10

PLZ HELP IM IN DESPERATE NEED OF AN ANSWER!!!

Mathematics
1 answer:
Irina18 [472]3 years ago
5 0
I believe 4(x - 3)=32 could help I haven’t done an equation from the unit in months so hopefully that looks familiar to you.
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Which of the following expressions represents "no more than 5"?
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Ox>5

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means nothing more than 5 but anything less than 5

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The price of an item yesterday was $120. Today, the price fell to $78
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Find equations of the tangent plane and the normal line to the given surface at the specified point. x + y + z = 8exyz, (0, 0, 8
Dima020 [189]

Let f(x,y,z)=x+y+z-8e^{xyz}. The tangent plane to the surface at (0, 0, 8) is

\nabla f(0,0,8)\cdot(x,y,z-8)=0

The gradient is

\nabla f(x,y,z)=\left(1-8yze^{xyz},1-8xze^{xyz},1-8xye^{xyz}\right)

so the tangent plane's equation is

(1,1,1)\cdot(x,y,z-8)=0\implies x+y+(z-8)=0\implies x+y+z=8

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 t, then ensure it passes through (0, 0, 8) by translating the line so that it does. Then the line has parametric equation

(1,1,1)t+(0,0,8)=(t,t,t+8)

or x(t)=t, y(t)=t, and z(t)=t+8.

(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)

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!!CHECK MY ANSWERS!!
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I think you're right. I'm in pre-algebra, and sucks at it. Yet, I keep a A.
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C, her results are very close to one another

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