Please Help! Riley was determined to be on the basketball team. He started practicing for 40 minutes on the first day, and then increased his practice time by 20 minutes on each subsequent day. With that pattern, how many total minutes will he have practiced in 25 days?

he would have practiced for 7000 minutes in 25 days.

Step-by-step explanation:

His practice time is increasing in arithmetic progression each day. The formula for determining the sum of n terms of an arithmetic sequence is expressed as

Sn = n/2[2a + (n - 1)d]

Where

n represents the number of terms in the arithmetic sequence.

d represents the common difference of the terms in the arithmetic sequence.

a represents the first term of the arithmetic sequence.

From the information given,

a = 40 minutes

d = 20 minutes

For minutes practiced in 25 days,

n = 25

Therefore, the sum of the first 25 terms, S205 would be

S25 = 25/2[2 × 40 + (25 - 1)20]

S25 = 12.5[80 + 480)

S25 = 12.5 × 560 = 7000

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.

5.5

step-by-step explanation: