The sum of the first n positive integers can be found using the formula n(n+1)/2. how many integers must be added to get 253 as the sum.

22

Step-by-step explanation:

Using the given expression and the sum, we can set up an equation and solve for the value of 'n':

Multiply both sides by '2':  

n(n+1) = 506

Distribute: n² + n - 506 = 0

Factor:  (n + 23) (n - 22) = 0

Set each equation equal to '0' and solve:

n + 23 = 0    n - 22 = 0

n = -23   or n = 22

Since the problem says the integers are positive, then n = 22.

9.55 degrees.

step-by-step explanation:

the given angle is

1 cycle is equal to 2π radians. so 4π will be equal to two cycles.

5.166667π-4π = 1.166667π

hence, this angle goes a little more than negative x axis.

1.166667π-π= 0.166667π

hence, the reference angle is 0.166667π radians.

1 radian = 57.2958 degrees

now, in degrees, this should be equals to 9.55 degrees.

step-by-step explanation:

try remembering the steps