In the following table of inverse variations, what are the values of A, B and C respectively? M 15 -6 2 C N -4 A B 60
10, -30, -1
Understanding Inverse Variation in the Given Table
This question requires us to determine the missing values (A, B, and C) in a table that demonstrates an inverse variation. An inverse variation occurs when the product of two quantities remains constant. If we denote the two quantities as M and N, their relationship can be written as:
\( M \times N = k \)
Here, k represents the constant of variation.
Analyzing the Data Table for Inverse Variation
The problem presents the following data, which we can format to better understand the relationships:
| M | 15 | -6 | 2 | C |
| N | -4 | A | B | 60 |
We need to find the values of A, B, and C using the principle of inverse variation.
Step 1: Calculate the Constant of Variation (k)
To find the constant of variation, k, we use a pair of values where both M and N are provided. From the first column of the table, we have M = 15 and N = -4.
Using the formula for inverse variation:
\( k = M \times N \)
Substitute the known values:
\( k = 15 \times (-4) \)
\( k = -60 \)
Thus, the constant of variation for this table is -60.
Step 2: Determine the Value of A
We use the constant k = -60 to find A. According to the table, when M = -6, N = A.
Applying the inverse variation formula:
\( M \times N = k \)
\( (-6) \times A = -60 \)
To solve for A, we divide both sides by -6:
\( A = \frac{-60}{-6} \)
\( A = 10 \)
Step 3: Determine the Value of B
Similarly, we use k = -60 to find B. The table shows that when M = 2, N = B.
Using the formula:
\( M \times N = k \)
\( 2 \times B = -60 \)
To solve for B, we divide both sides by 2:
\( B = \frac{-60}{2} \)
\( B = -30 \)
Step 4: Determine the Value of C
Finally, we use k = -60 to find C. The table indicates that when M = C, N = 60.
Using the formula:
\( M \times N = k \)
\( C \times 60 = -60 \)
To solve for C, we divide both sides by 60:
\( C = \frac{-60}{60} \)
\( C = -1 \)
Summary of Calculated Values
We have found the following values for A, B, and C:
- A = 10
- B = -30
- C = -1
Therefore, the values of A, B, and C respectively are 10, -30, and -1.
Matching with Provided Options
Let's compare our results with the given options:
- Option 1: 10, -30, -1
- Option 2: 10, -1, 30
- Option 3: -30, 10, -1
- Option 4: -1, -30, 10
Our calculated values (A=10, B=-30, C=-1) match Option 1.
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