The second partial derivatives of 
exist everywhere in its domain. By Schwarz's theorem, the mixed second-order partials derivatives are equal:
Then
We don't actually need to compute 
and 
to know that they are both free of 
. So when we differentiate for a second time with respect to , the whole thing cancels out.
the volume of the ball is 523.3. since the formula for the volume is 4/3*pi*r^3, the radius of ball is 5 in. Therefore, the diameter of the ball and the height of the box is 10.
A. Since the area of a triangle is equal to A = 0.5bh, we just plug in numbers given to us:
So, that's your answer.
B. The answer is a
2nd-degree trinomial because it has three terms and it's highest exponent is 2.
C. Polynomials are closed under multiplication because if you multiply two polynomials, you get another polynomial (except if you multiply by the inverse which is excluded anyways).
N=1→f(n)=f(1)=-5.25 (First term)
f(n)=f(n-1)+1.75, for n=2, 3, 4, ...
Second term:
n=2→f(2)=f(2-1)+1.75=f(1)+1.75=-5.25+1.75→f(2)=-3.5
Third term:
n=3→f(3)=f(3-1)+1.75=f(2)+1.75=-3.5+1.75→f(3)=-1.75
Fourth term:
n=4→f(4)=f(4-1)+1.75=f(3)+1.75=-1.75+1.75→f(4)=0
Fifth term:
n=5→f(5)=f(5-1)+1.75=f(4)+1.75=0+1.75→f(5)=1.75
Answer:
Sequence of the terms:
First, second, third, fourth, fifth:
-5.25, -3.5, -1.75, 0, 1.75
