if n varies inversely as kv/k+v and it is equal to 16. When k=4 v=8 find the relationship between k v and n
Is the question actually (note punctuation and parentheses) the following?
if n varies inversely as kv/(k+v), and n is equal to 16 when k=4 v=8, find the relationship between k v and n.
To find the relationship between k, v, and n, we'll start by writing the inverse variation equation given:
n = k * v / (k + v)
Given information:
n = 16, k = 4, v = 8
Substituting these values into the equation, we have:
16 = 4 * 8 / (4 + 8)
Simplifying further:
16 = 32 / 12
To solve for n, we need to cross-multiply:
16 * 12 = 32
192 = 32
This is not true, so the given information does not satisfy the equation. Please check the values provided for k and v again.
To find the relationship between k, v, and n, we first need to understand what it means for n to vary inversely with the expression kv/k+v.
In inverse variation, as one variable increases, the other variable decreases, and vice versa. Mathematically, inverse variation can be represented by the equation:
n = k * (a / b)
where n is the dependent variable, k is a constant of variation, and a and b are the independent variables.
Given that n varies inversely with kv/k+v and n is equal to 16, we can rewrite the equation as:
16 = k * (kv / (k+v))
Now, we are asked to find the relationship between k, v, and n when k = 4 and v = 8. Let's substitute these values into the equation:
16 = 4 * (4 * 8 / (4 + 8))
Simplifying further:
16 = 4 * (32 / 12)
16 = 4 * (8/3)
16 = 32/3
To find the relationship between k, v, and n, we need to isolate n and express it in terms of k and v. Multiplying both sides of the equation by 3 gives:
3 * 16 = 32
48 = 32
The equation is not true, which means there is no relationship between k, v, and n that satisfies the given conditions.
Therefore, in this particular scenario where k = 4 and v = 8, there is no valid relationship between k, v, and n that corresponds to the given inverse variation equation.