A detailed conceptual representation related to direct variation and mathematical calculations. There should be an abstract variable 'y' that varies directly with the square root of another abstract variable 'x'. Depict a scenario where x is demonstrated in the squares and roots format. The value of 'y' should be determined when x is at distinct points, primarily at 4 and 25. Please ensure the image does not contain any text.

a variable y varies directly as the square root of a varies x,and equals 6 when x=4 find y when x=25

y = k sqrt x

6 = k (2)
k = 3

y = 3 sqt x
y = 3 (5)

y = 15

Well, since y varies directly as the square root of x, we can use a proportion to solve this.

We have y ∝ √x.

Let's set up the proportion:

y/√x = k, where k is the constant of variation.

Now, we can solve for k by plugging in the given values when x = 4 and y = 6:

6/√4 = k.

Simplifying, we get:

6/2 = k.

So, k = 3.

Now that we have found k, we can use it to find y when x = 25:

y/√25 = 3.

Simplifying, we get:

y/5 = 3.

Cross-multiplying, we get:

y = 15.

Therefore, when x = 25, y = 15.

To find the value of y when x = 25, we can use the concept of direct variation and the given information.

Step 1: Set up the direct variation equation using the information provided:
y = k * sqrt(x), where k is the constant of variation.

Step 2: Use the given data to find the value of constant k.
When x = 4, y = 6.

Plugging in these values into the equation:
6 = k * sqrt(4)
6 = k * 2
k = 6 / 2
k = 3

Step 3: Substitute the value of k in the direct variation equation:
y = 3 * sqrt(x)

Step 4: Substitute x = 25 to find the value of y:
y = 3 * sqrt(25)
y = 3 * 5
y = 15

Therefore, when x = 25, y = 15.

To find the value of y when x = 25, we need to use the information given that y varies directly with the square root of x.

Let's break down the given information:

Variable y varies directly with the square root of x.
This means that we can represent this relationship using the equation:

y = k * √x

where k is the constant of variation.

We are also given that when x = 4, y equals 6.

Substituting these values into the equation, we have:

6 = k * √4

Simplifying:

6 = k * 2

Dividing both sides by 2:

k = 3

Now that we have the value of k, we can find the value of y when x = 25.

Plugging in the values into the equation:

y = 3 * √25

Simplifying:

y = 3 * 5

y = 15

Therefore, when x = 25, y = 15.