Answer: Hello mate!
Clairaut’s Theorem says that if you have a function f(x,y) that have defined and continuous second partial derivates in (ai, bj) ∈ A
for all the elements in A, the, for all the elements on A you get:
This says that is the same taking first a partial derivate with respect to x and then a partial derivate with respect to y, that taking first the partial derivate with respect to y and after that the one with respect to x.
Now our function is u(x,y) = tan (2x + 3y), and want to verify the theorem for this, so lets see the partial derivates of u. For the derivates you could use tables, for example, using that:
and now lets derivate this with respect to y.
using that
Now if we first derivate by y, we get:
and now we derivate by x:
the mixed partial derivates are equal :)
Answer:
980.18 cm^3
Step-by-step explanation:
Volume of cylinder w/out spheres = pi r^2 h
= pi 8^2 *6
now subtract the volume of the TWO spheres
2 * 4/3 pi * 3^3
for result = 980.18 cm^3
Answer:
Step-by-step explanation:
Set this up as a proportion
20/8 = 15/vx Cross multiply
20*vx = 8 * 15
20 * vx = 120 Divide by 20
vx = 6
Answer:
Vertex is (2,1) according to your information. In general, V(h,k). Equation must be y - k =a(x-h)2 for any quadratic function (parabola). Furthermore, you know that (0,5) is a point on the curve, so substitute for h, k, x and y to determine what coefficient "a" has to be.
Answer:
Step-by-step explanation:
x=115/11