If y varies directly as x, and y is 400 when x is r and y is r when x is 4, what is the numeric constant of variation in this relation?
10
40
100
198

10

Step-by-step explanation:

If there is a direct relation between two variables x and y then it can be represented as

y = kx ,

where y is dependent variable

x is  independent variable

k is constant of variation

_____________________________

First condition

y = 400

x = r

using y = kx then relationship will be

400 = kr

finding k here

k = 400/r

Second condition

y = r

x = 4

using y = kx then relationship will be

r = 4k

finding k

k = r/4

since  in both condition equation is same

thus, value of k will also be same

thus,

400/r = r/4

=> 400*4 = r*r

=> 1600 = r^2

Thus, 40 is the value of r

k = r/4 = 40/4 = 10

Thus, constant of variation is 10 which is correct choice.

To cross validate

k = 400/r = 400/40 = 10

A. 10   on Edg2020

Step-by-step explanation:

Hope this helps     : )

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