https://file.aiquickdraw.com/mathbot/file/1725529418042jsj8l5x0.jpg

The image shows a table with values for variables \( a \), \( b \), \( c \), and \( y \), along with an equation for \( k \). Here's the information extracted:

**Values:**
- \( a = 5 \)
- \( b = 0 \)
- \( c = 0 \)
- \( y = 3 \)

**Equation:**
\[
k = \left( \frac{y + c^2}{a + b} \right)^{\frac{1}{2}}
\]

Now, let's substitute the given values into the equation and simplify to find \( k \).

### Calculation:
1. Substitute \( y = 3 \), \( c = 0 \), \( a = 5 \), and \( b = 0 \) into the formula:
   \[
   k = \left( \frac{3 + 0^2}{5 + 0} \right)^{\frac{1}{2}}
   \]
2. Simplify the expression inside the fraction:
   \[
   k = \left( \frac{3}{5} \right)^{\frac{1}{2}}
   \]
3. Simplify further:
   \[
   k = \sqrt{\frac{3}{5}}
   \]
4. This can also be written as:
   \[
   k = \frac{\sqrt{3}}{\sqrt{5}}
   \]

Or approximately:

\[
k \approx \frac{1.732}{2.236} \approx 0.775
\]

### Final Answer:
\[
k = \sqrt{\frac{3}{5}} \approx 0.775
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you rationalize the denominator of \( \frac{\sqrt{3}}{\sqrt{5}} \)?
2. What happens if one of the variables \( a \), \( b \), \( c \), or \( y \) changes?
3. How would \( k \) change if \( b \) were non-zero?
4. Can you solve similar equations involving cube roots?
5. How does the exponent \( \frac{1}{2} \) affect the equation?

### Tip:
When dealing with square roots, ensure all components inside the root are simplified before taking the square root for an accurate calculation.

What is the value of k given the equation k = ((y + c^2) / (a + b))^(1/2), where a = 5, b = 0, c = 0, and y = 3?

Learn how to solve for k using the equation k = ((y + c^2) / (a + b))^(1/2) with given values a = 5, b = 0, c = 0, and y = 3. This problem focuses on substitution and the properties of square roots. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation