The number of minutes taken for a chemical reaction if f(t,x). It depends on the temperature t degrees celcius, and the quantity, x grams, of a catalyst present. When the temperature is 30 degrees celcius and there are 5 grams of catalyst, the reaction takes 50 minutes. Increasing the temperature by 3 degrees reduces the time taken by 5 minutes. Increasing the amount of catalyst by 2 grams decreases the time taken by 3 minutes. Use this information to find the partial derivatives fx(30,5) and ft(30,5). Use the tangent plane approximation to find f(33,4). ft(30,5)

Question

contestada

Respuesta :

lcoley8 lcoley8 · Answer 1 · 2020-03-17T02:55:20+01:00

Answer:

The answer is 46.5 minutes

Explanation:

The tangent plane is a point-slope shape that is used in two dimensions.

This is written as y - y0 = m (x-x0), or its similar function notation (and moves y0 = f (x0) to the other side):

f (x) = f (x0) + fx (x0) (x-x0)

In the case where more dimensions are used, this will be equal to:

f (t, x) = f (t0, x0) + ft (t0, x0) (t-t0) + fx (t0, x0) (x-x0)

Replacing, we have:

f (t, x) = 50 + -5/3 (t-t0) + -3/2 (x-x0)

for the point t = 33, x = 4, we have:

f (33.4) ≈ 50 + -5 / 3 * (33-30) + -3/2 * (4-5) = 50-5 + 3/2 = 46.5 minutes