Find the constant of proportionality for the following situation: "y is jointly proportional to x and z and inversely proportional to w."
w=2, x=5, y=4, and z=9
So i think the equation is y=xz/w
But what is the constant of proportionalit supposed to mean?
You're almost right.
y = kxz/w, where k is the constant of proportionality.
Plugging in your values,
4 = k*5*9/2
8 = 45k
k = 8/45
Well, the constant of proportionality is like the secret recipe that determines how all the variables are connected. In this case, it represents the fixed relationship between y, x, z, and w.
But before I give you the answer, I must confess that I have a terrible sense of math humor. So brace yourself! Ready?
The constant of proportionality is like the glue that holds this mathematical relationship together. It's what keeps everything in perfect balance, preventing any variable from going rogue and causing chaos in the equation!
Now, to find it, let's plug in the values you provided into the equation: y = xz/w
y = 4, x = 5, z = 9, and w = 2.
Substituting the values, we get:
4 = (5 * 9) / 2
Now, let's do some calculations:
4 = 45 / 2
Finally, simplifying it further:
4 = 22.5 (approximately)
So, the constant of proportionality for this situation would be approximately 22.5. Just remember, it's the magical number that keeps this mathematical relationship in check, like a wizard with a wand, casting proportional spells!
The constant of proportionality, often represented by the letter k, is a value that expresses the relationship between the variables in a proportional relationship. In this case, when two variables (y and xz) are directly proportional and one variable (w) is inversely proportional to y, the relationship can be written as y = k * xz / w.
To find the constant of proportionality, we can use the given values (w=2, x=5, y=4, and z=9) and solve for k using the equation:
4 = k * (5 * 9) / 2
First, multiply 5 and 9:
4 = k * 45 / 2
Next, divide 45 by 2:
4 = k * 22.5
Lastly, divide both sides by 22.5 to solve for k:
k = 4 / 22.5 = 0.1778 (rounded to four decimal places)
Therefore, the constant of proportionality in this situation is approximately 0.1778.
The constant of proportionality, often denoted by the letter k, represents the relationship between the variables in a proportional equation. It quantifies how the dependent variable (y) changes in proportion to the independent variables (x, z, and w) in the equation.
In this particular situation, where y is jointly proportional to x and z and inversely proportional to w, we can write the equation as follows:
y = k * (x * z) / w
To find the constant of proportionality (k), we need to rearrange the equation and substitute the given values of x, z, y, and w:
4 = k * (5 * 9) / 2
Simplifying the equation:
4 = 45k / 2
Multiply both sides by 2:
8 = 45k
Now, divide both sides by 45 to isolate k:
k = 8 / 45
Hence, the constant of proportionality for this situation is k = 8/45.