Yz = 7ln(x + z), (0, 0, 1) (a) the tangent plane correct: your answer is correct. (b) parametric equations of the normal line to the given surface at the specified point. (enter your answer as a comma-separated list of equations. let x, y, and z be in terms of t.)

The equation of tangent plane is    7x - y + 7z - 7 = 0

Parametric equation of normal line

x = 7 t         , y=-t                 , z=1+7 t

Step-by-step explanation:

Equation of tangent

fₓ (x₀ , y₀ , z₀) (x-x₀) + fy (x₀ , y₀ , z₀) (y-y₀) +fz(x₀ , y₀ , z₀)(z-z₀)=0                (1)

From taking derivation we get

fₓ (x₀ , y₀ , z₀) = 7

fy (x₀ , y₀ , z₀)= -1

fz(x₀ , y₀ , z₀) = 7

putting these value in equation 1

 (7) (x-0) + (-1)(y-0) + 7(z-1)=0

  7x - y + 7z - 7 = 0

The equation of tangent plane is    7x - y + 7z - 7 = 0

b) Parametric equation

x=x +f ₓ (P)t , y = y₀ +f y (P) t , z=z₀ +f z (P) t

x=0 +7 t      , y =0+(-1) t        , z=1+7 t

x=7 t            ,y=-t                  , z= 1+7 t

Parametric equation of normal line

x = 7 t         , y=-t                 , z=1+7 t

i would need to see the dot plot : )

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have