Suppose A is directly proportional to the square of B,and A=45 when B=3.
a)Find the constant of proportionality
b)Write the formula for A in terms of B
c)Use your formula to find A when B=6
Given
A=45 , B = 3
A∝B^2
That means A= k B^2
Where k is proportionality sign
a) 45 = 9 k
k = 5 ( constant of proportionality)
b) A = 5 B^2
c) when B =6 A=?
A = 36×5
A= 180
I hope it will help you.
a) The constant of proportionality can be found by solving for it in the equation A = k * B^2. Plugging in the given values, we have 45 = k * 3^2. Solving for k, we get k = 5.
b) The formula for A in terms of B is A = 5 * B^2.
c) Using the formula A = 5 * B^2, we can substitute B = 6 to find A. A = 5 * 6^2 = 5 * 36 = 180. So when B = 6, A = 180.
a) To find the constant of proportionality, we can set up the equation A = k * B^2, where k is the constant of proportionality. We know that A = 45 when B = 3. Substituting these values into the equation, we get 45 = k * 3^2. Simplifying, we have 45 = 9k. To solve for k, divide both sides of the equation by 9:
45/9 = 9k/9
5 = k
So, the constant of proportionality is k = 5.
b) The formula for A in terms of B is A = 5 * B^2. We derived this formula by substituting the constant of proportionality into the original proportionality equation.
c) To find A when B = 6, we can substitute this value into our formula:
A = 5 * 6^2
A = 5 * 36
A = 180
So, when B = 6, A is equal to 180.
To find the constant of proportionality, we can use the given information that A is directly proportional to the square of B. This can be written as:
A ∝ B^2
To find the constant of proportionality, we need to solve for it. We can start by writing the equation using the proportionality symbol (∝) as follows:
A = k * B^2
where k is the constant of proportionality.
a) To find the constant of proportionality, we can use the values A = 45 and B = 3 given in the problem:
45 = k * 3^2
Solving for k:
45 = k * 9
k = 45/9
k = 5
Therefore, the constant of proportionality is 5.
b) Now that we have the constant of proportionality (k = 5), we can write the formula for A in terms of B:
A = 5 * B^2
c) To find A when B = 6, we can substitute B = 6 into the formula we just obtained:
A = 5 * 6^2
A = 5 * 36
A = 180
Therefore, when B = 6, A equals 180.
A = k B^2
a) 45 = k * 3^2 ... k = ?
b) A = ? B^2
c) A = ? * 6^2