Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x2 + y2 and the ellipsoid 4x2 + 3y2 + 7z2 = 35 at the point (−1, 1, 2). (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)

Step-by-step explanation:

A tangent vector to the curve of intersection is given by N1 × N2

Where N1 is normal to the graph of

G(x, y, z) = z= x² + y² at the point P(-1,1,2) and

N2 is normal to the level surface

F(x, y, z)=4x² + 3y²+ 7z²= 35 at the point P(-1,1,2).

Now,

G(x, y, z)=x²+y²-z

Then, taking the grad of G will give a vector perpendicular to the paraboloid

∇G = ∂G/∂x •i + ∂G/∂y •j + ∂G/∂z •k

∇G= 2x•i +2y•j -k

At the point (-1,1,2)

N1=(-2,2,2)

Also to get N2

F(x, y, z)=4x² + 3y²+ 7z² - 35

∇F = ∂F/∂x •i + ∂F/∂y •j + ∂F/∂z •k

∇F = 8x•i + 6y•j + 14z•k

At point (-1,1,2)

N2=(-8,6,28)

Computing N1×N2

Note

i×i=j×j=k×k=0

i×j=k, j×i=-k

j×k=i, k×j=-i

k×i=j, i×k=-j

Then,

a×b= (a•i + b•j + c•k) × (x•i + y•j + z•k)

a×b = a•i×(x•i + y•j + z•k) + b•j×(x•i + y•j + z•k) + c•k×(x•i + y•j + z•k)

a×b= (a•i × x•i)+ (a•i × y•j) + (a•i × z•k) + (b•j × x•i) + (b•j × y•j) + (b•j × z•k) + (c•k × x•i) + (c•k × y•j) + (c•k × z•k)

a×b= 0 + ay•k - az•j - bx•k + 0 + bz•i + cx•j - cy•i + 0

a×b= ay•k - az•j - bx•k + bz•i + cx•j -cy•i

Then, rearranging

a×b= (bz - cy)•i+ (cx - az)•j + (ay-bx)•k

Now let assume that

N1=(-2,2,2) a=-2, b=2 and c=2

N2=(-8,6,28) x=-8, y=6 and z=28

N1×N2=(56-12)•i+(-16+56)•j+(-12+16)•k

N1×N2=44i + 40j + 4k

We compute N1 × N2 = (44,40,4) which is tangent to the curve of intersection at the point P.

The equation of the line is given as

x=r + λt

Where r is the point (-1,1,2)

And λ is the direction (44,40,4)

Hence the tangent line is given by

x = 1 + 44t, y = −1 + 40t, z = 2 + 4t.

part a

in a city ice cream is mostly only bought when the temperature is very high as ice cream cools down our

so we can derive the conclusion that as the temperature increases the number of ice creams sold also increases

part b

y intercept is 5

slope is 2

happy to

pls mark as brainliest

the answer is 31.27mph