Calculate the average rate of change of f(x) = x2 4 - 5 for 3 ≤ x ≤ 5. A) -2 B) - 4 3 C) 4 3 D) 2
1 answer:
Answer:
D)2
Step-by-step explanation:
ƒ(x) = x²/4 - 5; 3 ≤ x ≤ 5
Calculate the values of f(3) and f(5)
f(3) = 3²/4 - 5 = 9/4 - 5 = -2.75
f(5) = 5²/4 - 6 = 25/4 - 5 = 1.25
Calculate the average rate of change
Rate of change = (y₂ - y₁)/(x₂-x₁) = [1.25 -(-2.75)]/(5 - 3) = 4.00/2
= 2.00
The average rate of change is 2.00.
In the figure below, the red curve represents the function ƒ(x), while the black dashed line represents the average rate of change over the interval (3, 5).
The value of ƒ(x) increases by two units for every unit that x increases.
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The diameter of cylinder is 6 in and the height of the cylinder is 8 in.
The dimensions of the cuboid are 15 in by 9 in by 9 in.
To find:
The volume of the composite figure.
Solution:
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So, the volume of the cuboid is 1215 cubic inches.
The diameter of cylinder is 6 in. So, the radius of the cylinder is:
Volume of a cylinder is:
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Substituting , we get
The volume of the cylinder is 226.08 cubic inches.
Now, the volume of the composite figure is:
Therefore, the volume of the composite figure is 1441.08 cubic inches.