Suppose you need to know an equation of the tangent plane to a surface s at the point p(4, 1, 4). you don't have an equation for s but you know that the curves r1(t) = 4 + 3t, 1 − t2, 4 − 5t + t2 r2(u) = 3 + u2, 2u3 − 1, 2u + 2 both lie on s. find an equation of the tangent plane at p.

Step-by-step explanation:

We are given that

Equation of curves

Both curves lie on S.

We have to find the equation of tangent plane at P(4,1,4).

Hence, t=0 and u then it satisfied the given point.

Substitute the values in the derivatives

The equation of tangent at point P(4,1,4) is given by

answer: -2+√x,-2-√x

i hope this , i don't know if you're looking for a pair or not.

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!