https://file.aiquickdraw.com/mathbot/file/17266649564443kb05ai0.jpg

It seems that the image includes a math question, specifically question 6 with different parts (a) and (b). Here's a breakdown of what I can see from the image:

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**Question 6:**

### (a)
The variables \( t \) and \( z \) in the following table are related by the formula \( z = at^n \), where \( a \) is a constant and \( n \) is a positive integer.

#### (i)
Use the data from the table to determine the values of \( a \) and \( n \).

#### (ii)
Use the values of \( a \) and \( n \) obtained in part (i) to complete the following table:

| \( t \) | \( z \)  |
|:------:|:------:|
| 0.5    | 1      |
| 1      | 2      |
| 2      | 4      |
| 3      | 13.5   |
| 4      | 5      |

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### (b)
If \( v \) varies directly as the square of \( x \) and inversely as \( \sqrt{y} \), given that \( v = 18 \) when \( x = 3 \) and \( y = 16 \), find the value of \( v \) when \( x = 5 \) and \( y = 4 \).

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Would you like me to solve part (a) or part (b) first, or both?

The variables t and z in the following table are related by the formula z = at^n, where a is a constant and n is a positive integer. Use the data from the table to determine the values of a and n. Then, complete the table using the values of a and n.
If v varies directly as the square of x and inversely as √y, given that v = 18 when x = 3 and y = 16, find the value of v when x = 5 and y = 4.

Learn how to solve problems involving direct and inverse variation with exponents and roots. This problem demonstrates how to determine constants from a table of values and apply variations to find unknowns. Suitable for Grades 10-12.

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