Show that the given curve c(t) is a flow line of the given velocity vector field f(x, y, z).
c(t) = (2 sin(t), 2 cos(t), 9et); f(x, y, z) = (y, −x, z)
c'(t) = ?
f(c(t)) = ?

a)

b)

Step-by-step explanation:

We are given in the question:

F(x,y,z) = (y, -x, z)  

a)

We differentiate with respect to t.

b) F(c(t))

This is a composite function.

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17