Math Problem Statement

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.

Solution

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:


Question 6:

(a)

The variables tt and zz in the following table are related by the formula z=atnz = at^n, where aa is a constant and nn is a positive integer.

(i)

Use the data from the table to determine the values of aa and nn.

(ii)

Use the values of aa and nn obtained in part (i) to complete the following table:

ttzz
0.51
12
24
313.5
45

(b)

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


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Math Problem Analysis

Mathematical Concepts

Direct Variation
Inverse Variation
Exponents

Formulas

z = at^n
v = k(x^2 / √y)

Theorems

Direct and Inverse Variation

Suitable Grade Level

Grades 10-12