Assume that all the given functions have continuous second-order partial derivatives. if z = f(x, y), where x = 9r cos(θ) and y = 9r sin(θ), find the following: a) ∂z / ∂r b) ∂z / ∂θ c) ∂^2z / ∂r ∂θ

Answer with Step-by-step explanation:

We are given that all the given functions have continuous second-order partial derivatives.

Where

We have to find

A.

We know that

Using this formula

B.

C.

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc