The sum of three consecutive integers is 31 more than the largest integer. find the integers

To solve with an equation, let's call the three consecutive integers g, g+1, and g+2.

So, (g)+(g+1)+(g+2)=(g+2)+31

3g + 3 = g + 33

2g = 30

g = 15

The integers are 15, 16, and 17.

To check:

The sum of 15, 16, and 17 is 48. 17 + 31 is also 48.

Let's express this in algebraic terms:

The expressions for the integers and respective values are expressed below:

Now, to check, we apply the original problem and the values we discovered:

We are right, so:

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

h/o/e/s mad

step-by-step explanation:

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