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.