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 m =47 and R= 8/3.
*find m when *n= 47* and R = 8/3
r = k/(m+n)
so, r(m+n) is constant
so, you want m such that
8/3 (m+47) = 8(4+3)
Why did the math book go on a diet? It had too many problems to solve!
To find the value of m, we'll use the formula for inverse variation: R = k/(m + n), where k is the constant of proportionality.
We know that when m = 4 and n = 3, R = 8. So we can plug these values into the formula:
8 = k/(4 + 3)
Now we can solve for k by multiplying both sides of the equation by (4 + 3):
(4 + 3) * 8 = k
28 = k
Now that we have the value of k, we can find the value of m when R = 8/3:
8/3 = 28/(m + 3)
To solve for m, we'll cross multiply:
8(m + 3) = 3 * 28
8m + 24 = 84
Subtracting 24 from both sides:
8m = 60
Dividing both sides by 8:
m = 7.5
So when m = 47 and R = 8/3, the value of m is 7.5.
To find the value of m when m = 47 and R = 8/3, we can use the inverse proportionality relationship provided.
We are given that R is inversely proportional to the sum of m and n. This can be expressed as:
R = k/(m + n)
Where k is a constant of proportionality.
We are also given a specific condition: when m = 4 and n = 3, R = 8. We can use this information to determine the value of k.
Substituting the given values into the equation:
8 = k/(4 + 3)
8 = k/7
To find the value of k, we solve for k:
8 * 7 = k
k = 56
Now that we have the value of k, we can substitute it into the original equation and solve for m with the given values of R = 8/3:
8/3 = 56/(m + n)
Substituting m = 47 and R = 8/3:
8/3 = 56/(47 + n)
Solving for n:
8/3 * (47 + n) = 56
8 * (47 + n) = 56 * 3
376 + 8n = 168
8n = 168 - 376
8n = -208
n = -208/8
n = -26
Therefore, the value of m when m = 47 and R = 8/3 is 47.
To solve this problem, we need to establish the relationship between R, m, and n, and then use the given information to find the value of m when R is equal to 8/3.
Let's start by stating the relationship between R, m, and n. We are told that R is inversely proportional to the sum of m and n. In mathematical terms, this can be expressed as:
R ∝ 1 / (m + n)
Now let's use the given information to determine the constant of proportionality.
When m = 4 and n = 3, R = 8. Plugging these values into the equation, we have:
8 ∝ 1 / (4 + 3)
8 ∝ 1 / 7
To find the constant of proportionality, we can cross-multiply:
8 * 7 = 1
56 = 1
This indicates that the constant of proportionality is 56.
Now that we know the constant of proportionality, we can use it to find the value of m when R is equal to 8/3.
R = 8/3, which means:
8/3 = 56 / (m + n)
To solve for m, we can rearrange the equation:
(8/3) * (m + n) = 56
Multiplying both sides by 3 to eliminate the fraction:
8 * (m + n) = 56 * 3
8m + 8n = 168
Now we can substitute m = 47 into the equation and solve for n:
8(47) + 8n = 168
376 + 8n = 168
8n = 168 - 376
8n = -208
n = -208 / 8
n = -26
Therefore, when m = 47 and R = 8/3, the value of n is -26.