Question

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.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Answer 1

Answer and Step-by-step explanation:

`Greetings!`

`I'm~here~to~answer~your~question!`

`\bold{NOTE:}~We~ can ~say~ that ~two ~variables~ are~ inversely ~proportional ~to ~each` other\\ when ~when ~the ~quantity ~of ~one ~decreases, ~the ~quantity ~of~ the~ other\\ increases.~ For~ example, ~when ~the ~speed ~increases, ~the ~time ~to~ complete\\ a ~trip ~decreases.`

`\underline{\bold{It~is~given~that:}}`

`d = 2 \\c = 17`

`\underline{\bold{Inverse~ equation ~is ~like~ this:}}`

`\boxed{~~c=(k)/(d)~ ~} ~~where ~k ~is~ the ~constant~ value.`

`17=(k)/(2)`

`12 * 2=k`

`34=k`

`\underline{\bold{Now~ for ~part~ b:}}`

`c=(k)/(d)`

`c * d=k`

`d=(k)/(c)`

`d=(34)/(68)`

`d=0.5`

`\bold{The ~value ~of~ d~ is~ 0.50}`

`\underline{\bold{To~check:}}`

`c=(k)/(d)`

`c=(34)/(0.5)`

`c=68`

`\bold{Thus,~the~answer~is~correct!}`

Answer 2

Given:

d = 2

c = 17

a)

Inverse equation is like this:

c = k/d

where k is the constant value.

17 = k/2

17 * 2 = k

34 = k

b)

c = k/d

c*d = k

d = k/c

d = 34/68

d = 0.5

The value of d is 0.50

To check:

c = k/d

c = 34 / 0.5

c = 68