answer:The formula for the curved surface area (also known as the surface area) of a sphere is given by: [ A = 4 pi r^2 ] where ( A ) is the surface area and ( r ) is the radius of the sphere. Given that the curved surface area of the sphere is ( 64 pi ) cm², we can set up the equation: [ 64 pi = 4 pi r^2 ] To find the radius ( r ), we divide both sides of the equation by ( 4 pi ): [ frac{64 pi}{4 pi} = r^2 ] [ 16 = r^2 ] Taking the square root of both sides gives us the radius: [ r = sqrt{16} ] [ r = 4 ] So, the radius of the sphere is boxed{4} cm.

answer:To implement a function that returns a generator that extracts related content from a list of dicts, let's follow these steps: 1. Validate input: Check if the input arguments are valid and raise an error if they are not. 2. Extract related content: Iterate over the list of related content IDs, retrieving the corresponding content dict from the content list. 3. Return a generator: Use `yield` to return a generator that yields tuples containing the related content ID and the corresponding content dict. 4. Handle exceptions: Handle the case where a related content ID does not exist in the content list by raising a custom exception. Here's the implementation of the `get_related_content` function: ```python def get_related_content(content, related_content_ids): if not isinstance(content, list): raise TypeError(Invalid content type. Expected a list.) if not isinstance(related_content_ids, list): raise TypeError(Invalid related content IDs type. Expected a list.) if not all(isinstance(id, int) for id in related_content_ids): raise TypeError(Invalid related content IDs type. Expected a list of integers.) for related_content_id in related_content_ids: try: related_content = next(c for c in content if c[id] == related_content_id) except StopIteration: raise Exception(fRelated content ID '{related_content_id}' does not exist.) yield (related_content_id, related_content) ```

answer:First, consider the term frac{1}{sqrt{5} + 2}. Multiply the numerator and the denominator by the conjugate of the denominator to rationalize it: frac{1}{sqrt{5} + 2} = frac{1}{sqrt{5}+2} times frac{sqrt{5}-2}{sqrt{5}-2} = frac{sqrt{5}-2}{5-4} = sqrt{5}-2. Now, substitute this back into the original expression: begin{align*} frac{1}{2 + frac{1}{sqrt{5}+2}} &= frac{1}{2 + (sqrt{5} - 2)} &= frac{1}{sqrt{5}}. end{align*} To rationalize this, multiply by sqrt{5}/sqrt{5}: begin{align*} frac{1}{sqrt{5}} times frac{sqrt{5}}{sqrt{5}} &= frac{sqrt{5}}{5}. end{align*} Thus, the simplified form with a rationalized denominator is: boxed{frac{sqrt{5}}{5}}.

answer:In AT&T syntax, the issue with your code is that the definition of the GDT appears after the `jmp gdtcode, _start` instruction. The assembler sees the `JMP` instruction and assumes that the symbol `gdtcode` is an external symbol, to be relocated by the linker, rather than a constant. This is why you're getting the error message can't handle non absolute segment in `jmp'. Additionally, you have incorrectly defined your GDT by placing `.word .- gdt` after `gdtcode:` and `gdtdata:`. These lines will emit a 16-bit word into the GDT where you don't want them. To fix these issues, you can define your GDT before the `JMP` instruction and remove the `.word .- gdt` lines. Here's an example of the corrected AT&T syntax code: ```assembly gdt: .quad 0x0000000000000000 gdtcode: .quad 0x0020980000000000 gdtdata: .quad 0x0000900000000000 gdtpointer: .word .-gdt-1 .quad gdt CODE64_SEL = gdtcode-gdt DATA64_SEL = gdtdata-gdt ``` Then, at a later point in the file, you can use a FAR `JMP` instruction like this: ```assembly jmp CODE64_SEL, _start ``` This will properly reference the GDT and resolve the error you encountered.