R is inversely proportional to the sum of m and n when m=4 and n=3 r=8, find the value of m when n=47 and r=8/3
r = k/(m+n)
so, you want m such that
8(4+3) = 8/3 (m+47)
To find the value of m when n=47 and r=8/3, we can use the concept of inverse proportionality.
First, let's write the inverse variation equation with the initial values:
R = k / (m + n)
Where k is the constant of variation.
Using the given values m=4, n=3, and r=8, we can substitute them into the equation to solve for k:
8 = k / (4+3)
8 = k / 7
To find the value of k, we multiply both sides of the equation by 7:
56 = k
Now that we have the value of k, we can use it to find the value of m when n=47 and r=8/3:
8/3 = 56 / (m + 47)
To solve for m, we cross-multiply:
(8/3)*(m + 47) = 56
Divide both sides by 8/3:
m + 47 = (56*3)/8
m + 47 = 21
Subtract 47 from both sides of the equation:
m = 21 - 47
m = -26
Therefore, when n=47 and r=8/3, the value of m is -26.
To solve this problem, we need to use the concept of inverse proportionality and set up a proportion equation.
According to the given information, we know that R is inversely proportional to the sum of m and n. Mathematically, we can express this relationship as:
R ∝ 1 / (m + n)
or
R = k / (m + n)
Where R represents the value we are trying to find, m and n are the variables, and k is a constant of proportionality.
Let's use the values provided to solve for the constant k:
When m = 4, n = 3, and r = 8, we can substitute these values into the equation above:
8 = k / (4 + 3)
8 = k / 7
To find the value of k, we can multiply both sides of the equation by 7:
8 * 7 = k
k = 56
Now, we have the value of k. We can use it to find the value of m when n = 47 and r = 8/3.
Substituting these values into the equation:
8/3 = 56 / (m + 47)
To solve for m, we need to isolate it on one side of the equation. Multiply both sides by (m + 47):
(8/3) * (m + 47) = 56
Next, we can simplify the equation:
8(m + 47) = 168
8m + 376 = 168
8m = 168 - 376
8m = -208
Divide both sides by 8 to solve for m:
m = -208 / 8
m = -26
Therefore, when n = 47 and r = 8/3, the value of m is -26.