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:for 5
Step-by-step explanation:1,5
Answer:
x=61
Step-by-step explanation:
The three angles of a triangle add to 180 degrees
37+82+x = 180
Combine like terms
119 +x = 180
Subtract 119 from each side
119-119 +x= 180-119
x = 61
Perimeter and area are two important and fundamental mathematical topics. They help you to quantify physical space and also provide a foundation for more advanced mathematics found in algebra, trigonometry, and calculus. Perimeter is a measurement of the distance around a shape and area gives us an idea of how much surface the shape covers.
Knowledge of area and perimeter is applied practically by people on a daily basis, such as architects, engineers, and graphic designers, and is math that is very much needed by people in general. Understanding how much space you have and learning how to fit shapes together exactly will help you when you paint a room, buy a home, remodel a kitchen, or build a deck.
