The path of an object can be modeled by the function f(t) = 5t2 + 3 for all t > 0. Find each of the following:

The position of the object at t = 1 is
.

The position of the object at t = 3 is
.

The average speed of the object over the interval [1, 3] is
.

b

step-by-step explanation:

the distance between point a and point b is 6 units

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.

11

step-by-step explanation:

32.50-7.50=25

225/25=11