Answer:
c 3/4
Step-by-step explanation:
the slope of the line is
m = (y2-y1)/(x2-x1)
= (-2--5)/(6-2)
= (-2+5)/(6-2)
=3/4
happy to help mark me as brainliest pls
Answer:
3
Step-by-step explanation:
It should be 3 because when you look at it divide them all and each one gives you 3. If it's not then sorry.
Let x be the number. x= 2x-17
-x=-17
x=17
If
![f(x, y, z) = c](https://tex.z-dn.net/?f=f%28x%2C%20y%2C%20z%29%20%3D%20c)
represent a family of surfaces for different values of the constant
![c](https://tex.z-dn.net/?f=c)
. The gradient of the function
![f](https://tex.z-dn.net/?f=f)
defined as
![\nabla f](https://tex.z-dn.net/?f=%5Cnabla%20f)
is a vector normal to the surface
![f(x, y, z) = c](https://tex.z-dn.net/?f=f%28x%2C%20y%2C%20z%29%20%3D%20c)
.
Given <span>the paraboloid
![y = x^2 + z^2](https://tex.z-dn.net/?f=y%20%3D%20x%5E2%20%2B%20z%5E2)
.
We can rewrite it as a scalar value function f as follows:
![f(x,y,z)=x^2-y+z^2=0](https://tex.z-dn.net/?f=f%28x%2Cy%2Cz%29%3Dx%5E2-y%2Bz%5E2%3D0)
The normal to the </span><span>paraboloid at any point is given by:
![\nabla f= i\frac{\partial}{\partial x}(x^2-y+z^2) - j\frac{\partial}{\partial y}(x^2-y+z^2) + k\frac{\partial}{\partial z}(x^2-y+z^2) \\ \\ =2xi-j+2zk](https://tex.z-dn.net/?f=%5Cnabla%20f%3D%20i%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial%20x%7D%28x%5E2-y%2Bz%5E2%29%20-%20j%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial%20y%7D%28x%5E2-y%2Bz%5E2%29%20%2B%20k%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial%20z%7D%28x%5E2-y%2Bz%5E2%29%20%5C%5C%20%20%5C%5C%20%3D2xi-j%2B2zk)
Also, the normal to the given plane
![3x + 2y + 7z = 2](https://tex.z-dn.net/?f=3x%20%2B%202y%20%2B%207z%20%3D%202)
is given by:
![3i+2j+7k](https://tex.z-dn.net/?f=3i%2B2j%2B7k)
Equating the two normal vectors, we have:
</span>
![2x=3\Rightarrow x= \frac{3}{2} \\ \\ -1=2 \\ \\ 2z=7\Rightarrow z= \frac{7}{2}](https://tex.z-dn.net/?f=2x%3D3%5CRightarrow%20x%3D%20%5Cfrac%7B3%7D%7B2%7D%20%20%5C%5C%20%20%5C%5C%20-1%3D2%20%5C%5C%20%5C%5C%202z%3D7%5CRightarrow%20z%3D%20%5Cfrac%7B7%7D%7B2%7D%20)
Since, -1 = 2 is not possible, therefore
there exist no such point <span>
on the paraboloid
such that the tangent plane is parallel to the plane 3x + 2y + 7z = 2</span>
.