Answer:
i) superset (A)
ii) 0.577 (A)
Step-by-step explanation:
i) A subset is a set which has all its elements contained in another set.
For two sets A and B, if each element of set A is an element of set B, then A is a subset of B.
A superset is a set that houses another set. So if set A is a subset of set B, then B is a superset of A.
Proper subset
For a set (A) to be a proper subset of another (B) every element of A would be in B but there exists at least one element in B that is not in A.
An Empty Set (or Null Set) doesn't have aren't any elements in it. It is empty.
Since every element of the superset is in the superset. Therefore, A superset contains all the subset of superset.
ii) Square root of 1/3 = √⅓
= ± √⅓ = +√⅓ or -√⅓
+√⅓ = +(√1/√3) = +(1/√3)
+√⅓ = +(1/1.7321)
+√⅓ = +0.577
Therefore Positive square root of 1/3 is 0.577 (A)
I wasn't sure what properties the assignment was looking for... Let me know if you have any other questions!
Answer:
y=1/∛4 divides the area in half
Step-by-step explanation:
since the minimum value of x² is 0 (for x=0 ) and for y=1
1 = 25*x² → x= ±√(1/25) = ±1/5
then the total area between y=1 and y = 25*x² is bounded to x=±1/5 and y=0 . Since there is a direct relationship between x and y , we can find the value of x=a that divides the region in 2 of the same area. thus
Area below x=C = Area above x=C
Area below x=C = Total area - Area below x=C
2*Area below x=C = Total area
Area below x=C = Total area /2
∫ 25*x² dx from x=c to x=-c = 1/2 ∫ 25*x² dx from x=1/5 to x=-1/5
25*[c³/3 - (-c)³/3] = 25/2 * [(1/5)³/3 - (-1/5)³/3]
2*c³/3 = (1/5)³/3
c = 1/(5*∛2)
thus
y=25* x² = 25*[1/(5*∛2)]² = 1/∛4
thus the line y=1/∛4 divides the area in half