Suppose f varies inversely with g and that f=20 when g=4. What is the value of f when g=10?
f varies inversely with g:
f = k * (1/g)
where k is some constant.
f=20 when g=4:
20 = k * (1/4)
k = 20 * 4
k = 80
f=? when g=10
f = 80 * (1/10)
f = 8
Hope this helps~ `u`
another way. You do not need to find k at all. You know that
f = k/g, so
fg = k, a constant.
That means that
20*4 = f*10
I have 18 in the denominator.
I am equivalent to 1\6.
What fraction am i? ?
1/6 = x/18
Solve for x.
Well, when f varies inversely with g, it means that as one quantity goes up, the other goes down. It's like the relationship between my clown nose and my popularity - the more I squeeze it, the less people want to be around me!
To find the value of f when g=10, we can use the inverse variation formula:
f1 x g1 = f2 x g2
In this case, f1 = 20, g1 = 4, and g2 = 10. Let's plug in the values:
20 x 4 = f2 x 10
80 = f2 x 10
To solve for f2, we need to divide both sides by 10:
80 / 10 = f2
f2 = 8
So, when g=10, f will have a value of 8. Just like when I squeeze my clown nose, my popularity decreases!
To determine the value of f when g=10, we can use the inverse variation formula. In an inverse variation, the product of the two variables remains constant.
Let's use the general equation of inverse variation: f = k/g, where k is the constant of variation.
To find the value of k, we need to use the given information: f=20 when g=4.
Plugging in these values into the equation, we have: 20 = k/4.
To solve for k, multiply both sides of the equation by 4: 20 * 4 = k.
This gives us: k = 80.
Now that we know the value of k, we can use it in our inverse variation formula to find the value of f when g=10.
f = k/g
Substitute the values of k and g into the formula: f = 80/10.
Evaluating this expression, we find that f = 8.
Therefore, when g=10, the value of f is 8.