Help please. I need the answer.

Mathematics

1 answer:

Deffense [45]3 years ago

3 0

Create and solve an appropriate equation: Maria's earnings = Liam's earnings

0.20x = $625+0.10x.

Find x.

0.10x = $625; thus, x = $6250. At this level of food sales, these two people earn the same amount.

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Find an equation for the plane that is tangent to the surface z equals ln (x plus y )at the point Upper P (1 comma 0 comma 0 ).

alexira [117]

Let $f(x,y,z)=z-\ln(x+y)$ . The gradient of $f$ at the point (1, 0, 0) is the normal vector to the surface, which is also orthogonal to the tangent plane at this point.

So the tangent plane has equation

$\nabla f(1,0,0)\cdot(x-1,y,z)=0$

Compute the gradient:

$\nabla f(x,y,z)=\left(\dfrac{\partial f}{\partial x},\dfrac{\partial f}{\partial y},\dfrac{\partial f}{\partial z}\right)=\left(-\dfrac1{x+y},-\dfrac1{x+y},1\right)$