What is the measure of the angle formed by the minute hand and the hour hand of a clock when the clock shows 4: 00?

Step-by-step explanation:

We are asked to find the measure of the angle formed by the minute hand and the hour hand of a clock when the clock shows 4:00.

Since we know that clock is a circle made of 360 degrees.

Angle described by minute hand in one minute equals to 6 degrees (360/60). Angle described by hour hand in 1 hour equals 30 degrees (360/12).

At 4:00 minute hand will be at 12 and hour hand will be at 4. So we will multiply 4 by 30 to find the measure of angle formed when the clock shows 4:00.

Therefore, the measure of the angle formed by the minute hand and the hour hand of a clock, when the clock shows 4:00 is 120 degrees.

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.

t = 3

step-by-step explanation:

put t = 3 in this expression :

(3²-1)(3²-2)(3² - 3)(3² - 4) = 8×7×6×5 = 56×30 = 1680