If z = f(x, y), where f is differentiable, and x = g(t) y = h(t) g(9) = 6 h(9) = 4 g' (9) = −6 h' (9) = 4 fx(6, 4) = 9 fy(6, 4) = 1 find dz/dt when t = 9.

dz / dt = -50

Step-by-step explanation:

To solve the chain rule must apply, we have all the necessary values to make the calculation, as follows:

using the chain rule, we find:

dz / dt = (∂z / ∂x) * (∂x / ∂t) + (∂z / ∂y) * (∂y / ∂t)

Evaluating when t = 9, we have to:

fx (6, 4) * g '(9) + fy (6, 4) * h '(9)

We know that g '(9) = −6; h '(9) = 4; fx (6, 4) = 9; fy (6, 4) = 1

Replacing:

(9 * -6) + (1 * 4) = -50

Por lo tanto dz / dt = -50

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

the 3rd option is right

step-by-step explanation: