Jenny is saving for a trip to Japan. She has $2800 saved already. She takes a part-time job that pays $22 per hour. How many hours will she have to work at her part-time job to raise $5000 for her vacation?

Jenny has to work 100 hours.

Step-by-step explanation:

we are given a rate (or rather slope) of 22 per hour and the y-intercept of 2800, so we can set up an equation where h = hours worked and s = savings

we get:

s = 22h + 2800

now we can plug in 5000 for s so we can figure out how many hours she needs to work

5000 = 22h + 2800

2200 = 22h

h = 100

Jenny has to work 100 hours.

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.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.