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Solve the 2 question part 2 find its 4 proportional

To solve the second part of question 2, which is to "Find a fourth proportional to \(4x^4, 2x^3, 18x^5\)," we use the following method:

For four numbers \(a, b, c, d\) to be in proportion, they satisfy the equation:

\[
\frac{a}{b} = \frac{c}{d}
\]

This means that the fourth proportional \(d\) is given by:

\[
d = \frac{b \cdot c}{a}
\]

Here,
- \(a = 4x^4\)
- \(b = 2x^3\)
- \(c = 18x^5\)

Now, applying the formula:

\[
d = \frac{(2x^3) \cdot (18x^5)}{4x^4}
\]

First, multiply the terms in the numerator:

\[
d = \frac{36x^8}{4x^4}
\]

Now, simplify the expression:

\[
d = 9x^4
\]

Thus, the fourth proportional is \(9x^4\).

Would you like more details on this or have any other questions?

Here are 5 related questions to expand on this topic:
1. How do we determine the third proportional in a set of proportions?
2. How would you find the fourth proportional when dealing with fractions?
3. Can you solve for a proportional where variables have different powers or are nonlinear?
4. How does the concept of proportionality apply in geometric progressions?
5. What are some real-world applications of proportions in algebra?

**Tip:** Always reduce powers of variables in proportions by carefully applying exponent rules, which help in simplifying complex expressions.

Find a fourth proportional to 4x^4, 2x^3, 18x^5.

Learn how to find the fourth proportional to 4x^4, 2x^3, and 18x^5 using algebraic principles. This problem involves the use of the proportionality formula and exponent rules. Suitable for students in Grades 9-12.

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