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:

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

Evaluate the gradient at the given point:

$\nabla f(1,0,0)=(-1,-1,1)$

Then the equation of the tangent plane is

$(-1,-1,1)\cdot(x-1,y,z)=0\implies-(x-1)-y+z=0\implies\boxed{z=x+y-1}$

7 0

3 years ago

Ph testing strips are selling for $2.25 per packet of 80 strips. How many while packets can you buy for $18?

Natali [406]

8 packets of Ph testing strips

6 0

3 years ago

The dot plot shows the number of flowers each science student was able to identify. A dot plot whose number line is labeled Numb

irina [24]

Answer:

The dot plot shows the number of flowers each science student was able to identify.

A dot plot whose number line is labeled Number of flowers identified. There are 2 dots above 0, 4 dots above 1, 5 dots above 2, 7 dots above 3, 4 dots above 4, 3 dots above 5, 2 dots above 6, 1 dot above 7, 2 dots above 8, 1 dot above 9, 1 dot above 10, and 1 dot above 12.

Select from the drop-down menus to correctly complete the statement.

The distribution of data is 1 "skewed right", with a mode of 2 "3", and a range of 3 "12".

Step-by-step explanation:

I took the test!

3 0

3 years ago