Which of the following scenarios exhibits a function relation? take the first set listed to be the domain of the relation.
a. the set of tree heights and the set of trees in a forest
b. the set of car make and models and the set of people in a certain town
c. the set of birthdays and the set of students in a class
d. the set of people with social security cards and the set of social security numbers

Solution:

A relation is said to be function if for each member of domain there is unique value in range. And for no two different ranges values there should be a single domain member.

For, example , {(2,3), (4,6), (5,9),(0,7)} is a function.

But {(0,1),(0,2), (1,5),(3,6)} is not a function.

The set of first element of ordered pair is called Domain and the set of second elements of ordered pair is called range.

Option a: Take trees height found in forest as ,{1,2,3,4} and trees as, {A,B,C,D,E,F} as two trees can have same height means (1,A) and (1,E), so this can be a relation but not a function.

Option b: As, A same type and having same model car can be possessed by two different persons, so this can be relation but not a function.(C ,1),(C, 2)

Option c: As, on the same day that is single day , the birthday of two students can fall, so this can be relation but not a function.(12 January, Ran), (12 January, San)

Option d: As, different people having Social Security cards have different set of Social Security numbers. So this relation is a function.

People           Social Security numbers

A                          1

B                            2

AB                         12

C                              3

ABC                         123

True Option: d→→ the set of people with Social Security cards and the set of Social Security numbers

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet