Question 4: 20 pts The sum of the digits of a two-digit number is 11. When the digits are reversed the new number is
27 more than the original number. Find the original number. Check your answer.

The numbers are 74 and 47

Step-by-step explanation: X and Y represent the digits. A digit in the Tens place has 10 times its base value. So we can set up equations to model the information given:

10x+y = 10y + x +27

X + Y = 11

y =11-x Rewritten to substitute for y in the first equation.

10x + 11-x = 10(11-x)+x +27 Distribute and then combine like terms.

10x -x +11 = 110 -10x +x

9x + 11 = 110 +27 - 9x Add 9x to both sides and subtract 11 from both sides.

9x +9x = 110 + 27 - 11 Combine like terms:

18x = 126 Divide both sides by 18

x = 7

7 +y= 11 Substitute 7 for x to solve for y.

y= 4

Substitute the values of x and Y into the original equation.

70 +4 = 40 +7 + 27 Combine

The numbers look like 74 and 47.

Check:

74 = 47 + 27 Add 47+27

74 = 74

True!

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.

37

step-by-step explanation: