0.3, 11/17, 1 3/5, 1.6, 19/10
Answer:
15 2/3, or 47/3
Step-by-step explanation:
I'm going to assume, correctly or not, that you actually meant f(x) = 2x^2 - (1/3)x + 5. Double check on this right now, please.
If I'm right, then evaluate f(x) at x = 0 and x = 8:
f(0) = 5
and
f(8) = 2(8)^2 - (1/3)(8) + 5 = 128 - 8/3 + 5 = 133 - (2 2/3), or: 130 1/3
Then the average rate of change of f(x) = 2x^2 - (1/3)x + 5 over the interval [0,8] is:
130 1/3 - 5 125 1/3
a. r. c. = ------------------- = ---------------- = 15 2/3, or 47/3
8 - 0 8
Answer:
Length: 10 units.
Width:6 units
Step-by-step explanation:
Part a has 1 unit =40 yards. When we have 1 unit = 20 yards, we have divided the original numbers, 40, in half, getting 20. That means that we need to double the original amount of units, like you see above.
To express the height as a function of the volume and the radius, we are going to use the volume formula for a cylinder:

where

is the volume

is the radius

is the height
We know for our problem that the cylindrical can is to contain 500cm^3 when full, so the volume of our cylinder is 500cm^3. In other words:

. We also know that the radius is r cm and height is h cm, so

and

. Lets replace the values in our formula:





Next, we are going to use the formula for the area of a cylinder:

where

is the area

is the radius

is the height
We know from our previous calculation that

, so lets replace that value in our area formula:



By the commutative property of addition, we can conclude that: