If you divide any natural number n by 4, you get a remainder r. Find r if n=13; 34; 43; 100. What is the domain of the
function? What is the range?

Given:

If you divide any natural number n by 4, you get a remainder r.

To find:

The values of r if . Also find the domain and range.

Solution:

It is given that any natural number n by 4, you get a remainder r.

Where, n is a natural number, q is quotient, r is the remainder.

For ,

So, .

For ,

So, .

For ,

So, .

For ,

So, .

Therefore, the required value are if respectively.

The domain of the function is and the range of the function is .

15 batches are the most you can make

step-by-step explanation:

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15