If y varies directly as the cube of x and inversely as the square root of w, fill in the missing values in the table.
I need help finding the answers
w x y
1.27 ? 3.05
? 5.66 1.93
4.66 2.75 3.87
7.07 1.56 ?
To find the missing values in the table, we need to use the given relationship between y, x, and w.
The relationship states that y varies directly as the cube of x and inversely as the square root of w. Therefore, we can write the equation as:
y = k * (x^3 / sqrt(w))
To find the constant of variation, k, we can use one of the given data points. Let's use the third row: w = 4.66, x = 2.75, and y = 3.87.
3.87 = k * (2.75^3 / sqrt(4.66))
Now, we can solve for k:
k = 3.87 * sqrt(4.66) / (2.75^3)
Using this value of k, we can find the missing values.
1. For the first row: w = 1.27 and y = 3.05, we can find x:
3.05 = k * (x^3 / sqrt(1.27))
x^3 = 3.05 * sqrt(1.27) / k
x = (3.05 * sqrt(1.27) / k)^(1/3)
2. For the second row: x = 5.66 and y = 1.93, we can find w:
1.93 = k * (5.66^3 / sqrt(w))
sqrt(w) = (5.66^3 / (k * 1.93))
w = (5.66^6 / (k * 1.93^2))
3. For the fourth row: w = 7.07 and x = 1.56, we can find y:
y = k * (1.56^3 / sqrt(7.07))
By substituting the value of k calculated earlier, we can find all the missing values.
To find the missing values in the table, we need to use the given information that y varies directly as the cube of x and inversely as the square root of w.
1. For the first row:
We are given that y is 3.05 when w is 1.27. To find the missing value for x, we can rearrange the direct variation equation equation:
y = k * x^3
Substituting the given values:
3.05 = k * (x^3)
1.27
Now we can solve for k:
k = 3.05 / (1.27^3)
Once we find the value of k, we can substitute it into the direct variation equation and solve for x.
2. For the second row:
We are given that x is 5.66 when y is 1.93. To find the missing value for w, we can rearrange the inverse variation equation:
y = k / sqrt(w)
Substituting the given values:
1.93 = k / sqrt(w)
5.66
Now we can solve for k:
k = 1.93 * sqrt(w) / 5.66
Once we find the value of k, we can substitute it into the inverse variation equation and solve for w.
3. For the third row:
We have all the values of the variables in the third row, so nothing is missing.
4. For the fourth row:
We are given that w is 7.07 when x is 1.56. To find the missing value for y, we can use the direct variation equation:
y = k * x^3
Substituting the given values:
y = k * (1.56^3)
7.07
Solving for k, we can find the value of k. Once we find the value of k, we can substitute it into the direct variation equation and solve for y.