1. Mark each of the following graphs as (a) a function, but not one-to-one, (b) one-to-one function, or (c) not a function. In e
ach case, explain how you know. (1 point each)
1 answer:
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Answer: Team one = 1/5
Team 2 = 4/21
Team A is the fastest
Step-by-step explanation: Answer: Team one = 1/5
Team 2 = 4/21
Team A is the fastest
Step-by-step explanation: TEAM A
Tammy working alone in 1hr can clean 1/2
Melissa working alone in 1 hr can clean 1/3
working together in 1hr ,let x represent the area they will clean we have
+
= 1/x
⇒ 3 + 2 = 1/x
5 = 1/x
x = 1/5
TEAM B
Santay working alone can clean 1/4
Leticia working alone in 1 hr can clean 4/5
working together in 1 hr ,let y represent the amount they clean, we have
+
= 1/y
4 + 5/4 = 1/y
21/4 = 1/y
y = 4 /21
comparing x and y , 1/5 is greater than 4/21 , therefore Team A is faster
Answer: Yes, the given set of vectors is a basis of R³.
Step-by-step explanation: We are given to determine whether the following set of three vectors in R³ is a basis of R³ or not :
B = {(-1, 1,-1), (1, 0, 2), (1, 1, 0)} .
For a set to be a basis of R³, the following two conditions must be fulfilled :
(i) The set should contain three vectors, equal to the dimension of R³
and
(ii) the three vectors must be linearly independent.
The first condition is already fulfilled since we have three vectors in set B.
Now, to check the independence, we will find the determinant formed by theses three vectors as rows.
If the value of the determinant is non zero, then the vectors are linearly independent.
The value of the determinant can be found as follows :
Therefore, the determinant is not equal to 0 and so the given set of vectors is linearly independent.
Thus, the given set is a basis of R³.