Suppose c and d vary inversely, and d = 2 when c = 17.
a. write an equation that models the variation?
b. find d when c = 68
cd = k
now you can find k, and then the new d
a. To write an equation that models the variation, we need to express the relationship between c and d using the concept of inverse variation. Inverse variation is usually represented by the equation y = k/x, where k is the constant of variation.
In this case, we are given that c and d vary inversely, so we can write the equation as:
d = k/c
Now, to find the value of k, we can use the given information. It is specified that when c = 17, d = 2. Substitute these values into the equation to solve for k:
2 = k/17
To solve for k, multiply both sides of the equation by 17:
k = 2 * 17
k = 34
Therefore, the equation that models the variation is:
d = 34/c
b. Now that we have the equation d = 34/c, we can find the value of d when c = 68. Substitute this value into the equation:
d = 34/68
Simplify the expression by dividing both the numerator and denominator by the greatest common divisor (GCD):
d = 1/2
Therefore, when c = 68, d is equal to 1/2.
To solve this problem, we can use the formula for inverse variation, which states that two variables, c and d, vary inversely if their product remains constant.
a. The equation that models the inverse variation can be written as:
c * d = k
where k is the constant of variation. We can find the value of k using the given information that d = 2 when c = 17. Plugging in these values, we have:
17 * 2 = k
34 = k
So, the equation that models the inverse variation is:
c * d = 34
b. To find the value of d when c = 68, we can plug in the values into the equation we just found:
68 * d = 34
To solve for d, divide both sides of the equation by 68:
d = 34 / 68
d = 0.5
Therefore, when c = 68, d is equal to 0.5.