A triangular pyramid is cut by a plane. In which case is the cross section a quadrilateral?
1 answer:
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Problem 2
Part (a)
The 3D shape formed when rotating around the y axis forms a pencil tip
The shape formed when rotating around the x axis is a truncated cone turned on its side.
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Part (b)
Check out the two diagrams below.
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Problem 3
Answer: Choice A and Choice C
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Explanation:
Think of stacks of coins. Let's say we had 2 stacks of 10 quarters each. The quarters are identical, so they must produce identical volumes. Those sub-volumes then add up to the same volume for each stack. Now imagine one stack is perfectly aligned and the other stack is a bit crooked. Has the volume changed for the crooked stack? No, it hasn't. We're still dealing with the same amount of coins and they yield the same volume.
For more information, check out Cavalieri's Principle.
With all that in mind, this leads us to choice C. If the bases are the same, and so are the heights, then we must be dealing with the same volumes.
On the other hand, if one base is wider (while the heights are still equal) then the wider based block is going to have more volume. This leads us to choice A.
The function is a cube root function and the function end behavior is:
→
∞,
→
∞, and as
→ - ∞,
→
∞
- The end behavior of a function f defines the behavior of the function's graph at the "ends" of the x-axis.
- In other words, the end behavior of a function explains the graph's trend when we look at the right end of the x-axis (as x approaches +) and the left end of the x-axis (as x approaches ).
To determine the end behavior:
- The equation of the function is given as:
- To determine the end behavior, we plot the graph of the function f(x).
- We can see from the accompanying graph of the function:
- As x approaches infinity, so does the function f(x), and vice versa.
- As a result, the function end behavior is:
→
∞,
→
∞, and as
→ - ∞,
→
∞
Therefore, the function is a cube root function and the function end behavior is:
→
∞,
→
∞, and as
→ - ∞,
→
∞
Know more about functions' end behavior here:
#SPJ4
The complete question is given below:
What is the end behavior of the function f of x equals negative 4 times the cube root of x?
As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.
As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞.
As x → –∞, f(x) → 0, and as x → ∞, f(x) → 0.
As x → 0, f(x) → –∞, and as x → ∞, f(x) → 0.
