Write the variation and find the quantity indicated. F varies jointly as q1 and q2 and inversely as the square of d. If F=12 when q1 =3, q2=9 and 9=3
The variation of F=
set F = k (q1 q2/d^2)
plug in the values, (I think you have a typo and you meant to say .... d = 3
12 = k(3)(9)/(9)
k = 4
so F = 4q1 q2/d^2
Ah, the variation of F, my favorite subject! In this case, F varies jointly as q1 and q2 and inversely as the square of d. So, we can say that the variation of F can be expressed as:
F = k * (q1 * q2) / d^2
Now, let's find the value of k using the given information. We have F = 12 when q1 = 3, q2 = 9, and d = 3. Plugging these values into the variation equation, we get:
12 = k * (3 * 9) / 3^2
Simplifying that, we have:
12 = k * 27 / 9
12 = k * 3
Dividing both sides by 3, we find that k = 4.
Therefore, the variation of F is given by:
F = 4 * (q1 * q2) / d^2
Enjoy the variation, my friend!
The variation of F can be expressed as:
F = k * (q1 * q2) / d^2
where k is the constant of variation.
To find the value of k, we can use the given information:
F = 12 when q1 = 3, q2 = 9, and d = 3.
Substituting these values into the equation, we have:
12 = k * (3 * 9) / (3^2)
Simplifying the expression:
12 = k * 27 / 9
12 = 3k
Dividing both sides by 3:
4 = k
Therefore, the variation of F is given by:
F = 4 * (q1 * q2) / d^2
And the quantity indicated is the value of F, which can be determined by substituting the given values of q1, q2, and d into the equation.
The given problem states that F varies jointly with q1 and q2, and inversely with the square of d. Let's break this down and determine the variation of F.
When two variables vary jointly, it means that the quantity being measured changes in direct proportion to both variables. Mathematically, this can be represented as F = k * q1 * q2, where k is a constant of proportionality.
On the other hand, when a quantity varies inversely with the square of another variable, it means that the quantity is inversely proportional to the square of that variable. In our case, this can be expressed as F = k / d^2.
Now, to find the variation of F, we can combine these two equations. Since F varies both jointly with q1 and q2, and inversely with the square of d, the equation becomes:
F = k * (q1 * q2) / d^2
Moreover, we are given that F = 12 when q1 = 3, q2 = 9, and d = 3. Substituting these values into the equation, we get:
12 = k * (3 * 9) / 3^2
Simplifying this expression:
12 = k * 27 / 9
12 = 3k
Dividing both sides by 3:
4 = k
Therefore, the variation of F is F = 4 * (q1 * q2) / d^2.