Can someone explain how to do this?
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
First, you have to remember what "vary inversely" means: cd = k
for some constant value k. Now just plug in your two numbers to find k, and use that to answer pat (b).
Vary inversely means that as one gets big, the other gets small. For example, if you have a certain amount of money, the price of burgers and the number of burgers you can buy, vary inversely. The more they cost, the fewer you can buy with the same amount of money.
To solve this problem, we need to understand what it means for two variables to vary inversely. When two variables are inversely proportional, it means that as one variable increases, the other variable decreases by the same factor, and vice versa.
a. To write an equation that models the variation, we can use the formula for inverse variation: c × d = k, where k is a constant. Since the problem mentions that d = 2 when c = 17, we can substitute these values into the equation:
17 × 2 = k
34 = k
So, the equation that models this inverse variation is c × d = 34.
b. To find d when c = 68, we can again use the equation c × d = 34 and substitute the given value:
68 × d = 34
To find the value of d, we need to isolate it, so we divide both sides of the equation by 68:
d = 34/68
d = 0.5
Therefore, when c = 68, d is equal to 0.5.