HELP 30 POINTS! Terrell decides to by some strawberry jam for his grandmother at the Berrien County Farmer’s Market. Terrel has enough money to buy either one large jar or three small jars of jam. A small jar has a diameter of 6 cm, a height of 7 cm, and costs $4. A large jar has a diameter of 8 cm, a height of 16 cm, and costs $12.

Would it be a better deal for Terrell to purchase three small jars or one large jar of jam for his grandmother? In a short paragraph, explain in detail how you determined which option was the better alternative. Explain which formula you used to determine the capacity (the volume) for each jar. Be sure to explain each step that requires a computation with a complete sentence.

Step-by-step explanation:

First, break down the problem, and identify what you know:

1) One small jar has a diameter of 6 cm, a height of 7 cm, and costs $4

2) A large jar has a diameter of 8 cm, a height of 16 cm, and costs $12

3) The small jar is 1/3 the price of a large jar!

Since the jars are probably cylindrical, we need to use the "volume of a cylinder" formula:

V = (pi) x (r^2) x (h)

V = total volume

r = radius of cylinder

h = height of cylinder

Let's start with the small jar! We know the height, and diameter. The diameter is twice the radius, so, simply divide the diameter in half, and plug in your values.

V = (pi) x (3^2) x (7

V = 197.9203372

Approximate Volume of the small jar: 197.92 cubic centimeters

Now, for the large jar! Simply repeat the same steps, with your other values.

V = (pi) x (4^2) x (16)

V = 804.2477193

Approximate volume of the large jar: 804.25 cubic centimeters

Now, we have our volume for BOTH jars:

Small jar: 197.92 cubic cm

Large jar: 804.25 cubic cm

Now, how do we tell which is a better deal? Since, the large jar is 3x the price of the small jar, it should be 3x the volume, OR more.

197.92 divided by 804.25 = 4.063510509

The large jar is approximately four times bigger, but only three times more expensive! So, even if you bought three small jars for the same amount, you'd be getting less!

Hope this helps! :)

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).