Math Problem Statement
If a is inversely proportional to 1/b and bis inversely proportional to c square then find the value of 9a + 5c, when b = 27. Given that when b = 3 then a = 4 and c = 6.
Solution
We are given two inverse proportionalities:
-
is inversely proportional to , meaning , which implies . So, we can express this as: where is a constant.
-
is inversely proportional to , meaning . So, we can express this as: where is another constant.
Step 1: Find the values of and
We are given the following conditions:
- When , and .
From :
Using and : Thus, .
From :
Using and : Thus, .
Step 2: Find the value of and when
Using the equation , substitute :
Now, use the equation and substitute :
Step 3: Find the value of
Now that we have and , calculate :
Thus, the value of is .
Would you like more details on any of these steps, or do you have further questions?
Here are 5 related questions:
- How do we derive the relationship for inverse proportionality?
- What happens if both quantities are inversely proportional to each other?
- How would the solution change if was proportional to ?
- Can we have multiple constants of proportionality in a single problem?
- How does inverse proportionality differ from direct proportionality?
Tip: In inverse proportionality, as one quantity increases, the other decreases at a rate dictated by the constant of proportionality.
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Math Problem Analysis
Mathematical Concepts
Inverse Proportionality
Algebra
Formulas
a = k1 * b
b = k2 / c^2
9a + 5c
Theorems
Inverse Proportionality Theorem
Suitable Grade Level
Grades 9-12