Answer:
Step-by-step explanation:
a+b+c=0, a+b=-c,a+c=-b, b+c=-a
(a+b+c)^3=(a+b+c)^2*(a+b+c)=(a^2+b^2+c^2+2ab+2ac+2bc)*(a+b+c)=
a^3+ab^2+ac^2+2a^2b+2a^2c+2abc+a^2b+b^3+bc^2+2ab^2+2abc+2b^2c+a^2c+b^2c+c^3+2abc+2ac^2+2bc^2=a^3+b^3+c^3+3a^2b+3a^2c+3ac^2+3ab^2+3bc^2+3b^2c+6abc=
a^3+b^3+c^3+3a^2*(b+c)+3c^2(a+b)+3b^2(a+c)+6abc=
a^3+b^3+c^3+3a^2*(-a)+3c^2*(-c)+3b^2*(-b)+6abc=
a^3+b^3+c^3-3a^3-3c^3-3b^3+6abc=
6abc-2a^3-2b^3-2c^3=2(3abc-a^3-b^3-c^3)=
2*[3abc-(a^3+b^3+c^3)]=0
so 3abc-(a^3+b^3+c^3)=0
so a^3+b^3+c^3=3abc
Just divide 48 by 8 to give 6.
Answer:
(A) The rate of change in the price of a bushel of corn in the current year is $7.
(B) The price of a bushel of corn in the current year is $2 more than the price of a bushel of corn in the previous year.
Step-by-step explanation:
The graph for the prices of different numbers of bushels of corn at a store in the current year is shown below.
Part A:
The rate of change in the price of a bushel of corn in the current year based upon the number of bushels is known as the slope of the line.
The formula to compute the slope is:

Consider the ordered pairs: (4, 28) and (10, 70)
Compute the slope of the line as follows:


Thus, the rate of change in the price of a bushel of corn in the current year is $7.
Part B:
The data for the price of bushels in the previous year is as follows:
Number of Bushels Price
2 10
4 20
6 30
8 40
Compute the rate of change in the price of a bushel of corn in the previous year based upon the number of bushels as follows:
Consider the ordered pairs: (2, 10) and (6, 30)


The rate of change in the price of a bushel of corn in the previous year is $5.
Thus, the price of a bushel of corn in the current year is $2 more than the price of a bushel of corn in the previous year.
X = 3 y = 4
so answer is 4