A taxi charges a flat rate of $3.00, plus an additional
$0.50 per mile. Carl will only take the taxi home if the
cost is under $10, otherwise he will take a bus. Carl is 15
miles from home. Explain how to write and solve an
inequality to determine if Carl will take the taxi or a bus.

See below.

Step-by-step explanation:

The cost of the taxi is the sum of two costs:

the fixed fee of $3.00 and the $0.50 per mile.

Let x = number of miles.

For x miles, the mile cost is 0.5x

The total cost is $3.00 plus 0.5x

Total cost: 0.5x + 3

We want the total cost to be under $10, so the sum of the two costs must be less than 10.

The inequality is:

0.5x + 3 < 10

Subtract 3 from both sides.

0.5x < 7

Divide both sides by 0.5

x < 14

The cost is under $10 if the distance is under 14 miles.

Since the distance here is 15 miles, the cost of the taxi is over $10, and Carl will take the bus.

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.

were is the equation