Answer:
1/3
Step-by-step explanation:
The average rate of change of a function f(x) on an interval [a, b] is given by the formula ...
rate of change = (f(b) -f(a))/(b -a)
__
For the given function and interval, this is ...
(log₂(4·8) -log₂(4·2))/(8 -2) = (5 -3)/(6) = 1/3
The average rate of change is 1/3.
_____
In the attached graph, the line between the points at the ends of the interval can be seen to have a rise of 1 for a run of 3. Its slope is 1/3.
Answer:
The number of hours Jackie worked = 80hours
Step-by-step explanation:
Last summer:
Jackie made $960
Rachel made $960
let number of hours Jackie worked = x
Rachel worked 16 hours more than Jackie:
Number of hours Rachel worked = x + 16
if Jackie earned $y per hour
Rachel earned $2 less per hour = y-2
Jackie: 960 = x × y = xy
Rachel: 960 = (x+16)(y-2)
960 = xy -2x +16y -32
recall xy = 960, insert the value for xy
960 = 960 - 2x +16y -32
- 2x +16y -32 = 0
2x -16y = -32
x-8y = -16
x = 8y-16
recall xy = 960, insert the expression for x
(8y-16)y = 960
8y² -16y = 960
y² -2y - 120 = 0
y²+10y-12y -120 = 0
y(y+10) -12(y+10) = 0
(y-12) = 0 or (y+10) = 0
y = 12 or -10
since y can't be negative, y = 12
x = 8y-16
x = 8(12) -16 = 80
The number of hours Jackie worked = x = 80 hours
1 cup is equal to 8 oz, so
3 cups x 8 = 24 oz.
you'll do the same for the two cups
2 x 8 = 16 oz
so adding them all together will be
24 + 6 + 16 + 9 = 55 total oz.
You can solve this problem through factoring.
First, you have the equation,
Then, you can factor the numerator.
You can cancel out the x-6 in both the numerator and the denominator because they would equal to just 1.
You are left with 
The function is removable noncontinuous at x=6 because if you plug in 6 in x-6, your denominator would be undefined.
I think you meant "y = 4 arccot (x)."
This is equivalent to:
y
---- = arccot x
4
and so cot (y/4) = x
