What is the volume of the cone with diameter 4 ft and height 4 ft? Round to the nearest cubic foot.
2 answers:
Answer:
Step-by-step explanation:
The volume of a cone can be calculated with the following formula:
Where "r" is the radius and "h" is the height.
The radius is half the diameter, then "r" is:
Since we know that radius and the height, we can substitute them into the formula.
The volume of the cone to the nearest cubic foot is:
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<h3>Answer: -7 < x < 17</h3>
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Explanation:
Plug in the lower bound of the domain, which is x = -3
f(x) = 3x+2
f(-3) = 3(-3)+2
f(-3) = -9+2
f(-3) = -7
If x = -3, then the output is y = -7. Since f(x) is an increasing function (due to the positive slope), we know that y = -7 is the lower bound of the range.
If you plugged in x = 5, you should find that f(5) = 17 making this the upper bound of the range.
The range of f(x) is -7 < y < 17
Recall that the domain and range swap places when going from the original function f(x) to the inverse
This swap happens because how x and y change places when determining the inverse itself. In other words, you go from y = 3x+2 to x = 3y+2. Solving for y gets us y = (x-2)/3 which is the inverse.
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In short, we found the range of f(x) is -7 < y < 17.
That means the domain of the inverse is -7 < x < 17 since the domain and range swap roles when going from original to inverse.