1√3
The exact value of cot(π3) cot ( π 3 ) is 1√3 .
If 2 sets are disjoint means they have not any common element.
Draw a rectangle & inscribe inside this rectangle 2 circles that do not intersect.
cercle₁ ∩ cercle₂ =Ф.
Their complement would be the part of the rectangle - the 2 circles
Just use the coefficients for each variable and put it in a matrix. Is the second question set equal to something? Because then you would put it in place as the question mark. (Did the pic come through?)
So the 3x3 matrix is made up of the coefficients and then to augment the matrix, you add another column at the end with the solutions. Good luck!
"31-inch piece of steel is cut into three pieces"
Call the pieces a,b,c
a + b + c = 31
"second piece is twice as long as the first piece"
b = 2a
"third piece is one inch more than seven times the length of the first piece"
c = 1 + 7a
Ok, we have our equations, let's substitute the second and third into the first.
a + 2a + 1 + 7a = 31
10a + 1 = 31
10a = 30
a = 30/10 = 3
b = 2a = 6
c = 1 + 7a = 22
Check: 3 + 6 + 22 = 31, good
Answer: 3 inches, 6 inches, 22 inches
17 + 23 = 40
The temperature rose 40 degrees.