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

Three singers are chosen at random from a group of 5 Chinese, 4 Indians and 2 British singers.

slega [8]

<h2>Answer:</h2><h3>14 ways.</h3>

Please see the attached picture for full solution..

Hope it helps...

Good luck on your assignment...

6 0

3 years ago

Write in simplest form 12:3

prisoha [69]

To put this into simplest form, you can see what common factors they have. 3 can go into 12, so we can divide 12 by 3.
12÷3= 4
3÷3=1
So 4:1 is the simplest form of 12:3.
Tell me if this helps!!

3 0

3 years ago

Read 2 more answers

4.1 Number Talk: Division

Gnesinka [82]

Answer:

645/100 = 129/20 or 6.45

645/50 = 129/10 or 12.9

48.6/30 = 1.62

48 divided by x = 48.6/x

Step-by-step explanation:

645/100

Factor the number:

= 5*129/100

Factor the number:

= 5*129/5*20

Cancel the common factor:

= 129/20

645/50

Factor the number:

5*129/50

Factor the number:

5*129 / 5*10

Cancel the common factor:

= 129/10

48.6/30

Write the problem in long division format

Multiply the quotient digit (1) by the divisor (30)

Subtract 30 from 48

Add a decimal and bring down the next number

Divide 186 by 30 to get 6

Continue...A few steps later...

Subtract 60 from 60

Solution is 1.62

48.6/x

Re-write division as a fraction:

48.6/x

6 0

3 years ago