The value of c when b = 5 is approximately 202.5.
Given that A is directly proportional to b² and a is also directly proportional to √c, we can write the following equations:
A = kb²
a = mc^(1/2)
where k and m are constants of proportionality.
When b = 3, the value of c is 162. We can substitute these values into the equations to find the values of k and m:
A = kb²
A = k(3)²
A = 9k
a = mc^(1/2)
a = m(162)^(1/2)
a = 9m
Now, we can use the fact that A and a are directly proportional to find the value of c when b = 5:
A = ka²
a = mc^(1/2)
Since A and a are directly proportional, we can write:
A/a = k/m = constant
Substituting the values we found earlier, we get:
A/a = (9k)/(9m) = k/m
Therefore, we can write:
ka²/mc^(1/2) = k/m
Simplifying this equation, we get:
a²/c^(1/2) = 1
Multiplying both sides by c^(1/2), we get:
a² = c
Substituting the values we found earlier, we get:
(9m)² = c
Simplifying this equation, we get:
81m² = c
Now, we can find the value of c when b = 5:
c = 81m² = 81(a/9)² = 81(25/9) = 202.5
Therefore, the value of c when b = 5 is approximately 202.5.
Complete question:
A is directly proportional to b².
a is also directly proportional to √c.
When b = 3, the value of c is 567.
What is the value of c when b = 5?
If your answer is a decimal, then round it to 1 d.p.
Any help please??