Billy goes on the teacup ride at the local carnival. he is seated 16 inches from the center of his teacup, which is spinning at a rate of 4 revolutions per minute. what is billy’s angular velocity, in radians per second? round your answer to the nearest hundredth

Billy’s angular velocity, is 1508.16 radians per second

Step-by-step explanation:

We have to find angular velocity in radians per second

we have given angular velocity w = 4 revolutions per minute

we have to convert revolutions into radians and minutes into seconds.

so, we use the following conversion:

1 rev = 2* pi radians (where pi = 22/7 or 3.142)

1 min = 60 sec

putting the values in our equation : w = 4 revolutions per minute

=> w= 4 * ( 2* 3.142) *60

=> w= 1508.16 radians per second

hence Billy’s angular velocity, is 1508.16 radians per second

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).