Question

If R = {(x , y) : x , y ∈ N , x2 + y2 = 100 } , Write R in roster form.

Also find the domain and range​

Answer 1

Answer:

{0 , 6, 8, 10}

Explanation:

x^2 + y^2 = 100

Therefore equations which satisfy the conditon are:

=> 0^2 + 10^2 = 100

or 10^2 + 0^2 = 100

=> 6^2 + 8^2 = 100

or 8^2 + 6^2 = 100

Therefore Domain (Co-factor of X) = {0, 6, 8, 10}

Range (Co-factor of Y) = {0, 6, 8, 10}

R = (6, 8) or (8, 6)

Please mark me as brainliest.

Answer 2

Answer:

R = { (10,0) , (-10,0) , (0,10), (0,-10)}

Range of R = { 10 , -10 , 0  }

Domain of R = { 0, 10 , -10 } .

Step-by-step explanation:

Given :- R = { (x,y):x, y ∈ N , x2+y2 =100 }

To find :- Write

• R in roster form ,
• and find domain and range of it .

Solution :-

Step 1) Equation is : $x^2 + y^2 = 100$ -- (1)

  can be written as , $y^2= 100-x^2 \\y = \sqrt{100-x^2 }$ --- (2)

Step 2) Put x = 0 in eqn. (2)

we get , y = +10 , -10 .

ordered pairs becomes , (0,10) ; ( 0, -10 )  .

Step 3) Put , x = 10  we get y = 0

put x = -10  , y = 0

ordered pair becomes , ( 10,0) ; (-10,0) .

Step 4) Thus , roster form of R is ,

R = { (10,0) , (-10,0) , (0,10), (0,-10)}

Step 5) Range of set :- values of x terms

             Domain of set :- values of y terms .

Hence ,

Range of R = { 10 , -10 , 0  }

Domain of R = { 0, 10 , -10 } .

#SPJ3