If D varies jointly as the square of E and F, and D = 210 , when E = 32 and F = 70
D = k(EF)^2
when D = 210, E = 32 , and F = 70
210 = k(32*70)^2
210 = k(5017600)
k = 3/71680
D = (3/71680)(EF)^2
so , now what?
To determine the relationship between D, E, and F, we need to understand how "vary jointly" and "varies square" work in this context.
When a quantity varies jointly, it means that it is directly proportional to the product of two or more variables. Mathematically, this can be expressed as D = k * E * F, where k is a constant.
When a quantity varies square, it means that it is directly proportional to the square of a variable. Mathematically, this can be expressed as D = k * (E^2) * (F^2), where k is a constant.
In this case, we are told that D varies jointly as the square of E and F. So we can write the equation as:
D = k * (E^2) * F
To find the value of k, we can use the given data point where D = 210, E = 32, and F = 70:
210 = k * (32^2) * 70
To solve for k, divide both sides of the equation by (32^2) * 70:
k = 210 / (32^2 * 70)
Now we can substitute the value of k back into the equation to find the relationship between D, E, and F:
D = (210 / (32^2 * 70)) * (E^2) * F
Therefore, the relationship between D, E, and F is determined by the equation above.