Question

f is inversely proportional to g. g is directly proportional to h². When f = 24, the value of g is 3. When f = 20, the value of h is 6. e this information to work out the value of h when g = 28. If your answer is a decimal, round it to 1 d.p. ​

Answer 1

To find the value of h when g = 28, we need to use the given information about the relationships between f, g, and h. By utilizing the given values of f and g and the equations f = k/g and g = k/h², we can solve for h and find that h ≈ 1.6.

Step-by-step explanation:

To find the value of h when g = 28, we need to use the given information about the relationships between f, g, and h. We are told that f is inversely proportional to g, which means that as f increases, g decreases and vice versa. We are also told that g is directly proportional to h², which means that as g increases, h also increases.

First, we can use the given values of f and g to find the constant of proportionality k in the equation f = k/g. When f = 24 and g = 3, we can substitute these values into the equation to solve for k: 24 = k/3. Cross multiplying gives us k = 72.

Next, we can use the equation g = k/h² and the given value of g = 28 to solve for h: 28 = 72/h². Rearranging the equation to isolate h² gives us h² = 72/28. Simplifying this expression gives us h² = 2.57. Taking the square root of both sides, we find that h ≈ 1.6 (rounded to 1 decimal place).