Answer :

Final answer:

To find a possible value of c that satisfies the given conditions of cube roots, we can test different integers. The first condition states that the cube root of c is between 8 and 9. By testing different values, we find that c = 512 satisfies this condition. However, when we substitute this value into the second condition, we find that it does not satisfy the requirement. Therefore, there is no possible value of c that satisfies both conditions.


Explanation:

To solve for the possible value of c, we need to find an integer that satisfies the given conditions. Let's start by solving the first condition: the cube root of c is between 8 and 9.



To do this, we can test different integers by taking their cube root. For example, the cube root of 8 is 2, and the cube root of 9 is 2.08 (approximately). Since we want the cube root to be between 8 and 9, we can try other integers in between, such as 7. When we take the cube root of 7, we get 1.91 (approximately), which is less than 8, so 7 doesn't satisfy the condition.



Using the same approach, we can try different integers until we find one that satisfies the condition. By testing, we find that when c = 512 (which is 8 cubed), the cube root of c is 8, which is between 8 and 9.



Now, let's move on to the second condition: the cube root of 2c is between 11 and 12. We can again test different integers, but since we already have a value for c, we can substitute it into the equation and solve for c. When we substitute c = 512, we get 2(512) = 1024, and the cube root of 1024 is approximately 10.08, which is less than 11. Therefore, 512 does not satisfy this condition.



This means that there is no possible value for c that satisfies both conditions simultaneously. The given conditions are contradictory and cannot be satisfied by any integer value of c.


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