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8 days ago

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

Mathematics

2 answers:

Leona [4.1K]8 days ago

7 0

Answer:

Step-by-step explanation:

If there’s a direct correlation between variables x and y, it can be expressed as

y = kx,

where y is the dependent variable

x is the independent variable

k signifies the constant of variation

_____________________________

For the first scenario

y = 400

x = r

using y = kx, we can derive the relation:

400 = kr

To find k here:

k = 400/r

For the second scenario

y = r

x = 4

again using y = kx, the relationship is given by:

r = 4k

Solving for k:

k = r/4

Since both conditions provide the same equation, k will have the same value in both cases.

Thus, we conclude:

400/r = r/4

=> 400*4 = r*r

=> 1600 = r^2

$\sqrt{r^{2} } = \sqrt{1600} \\r = 40$

Hence, r is calculated to be 40.

Thus, k = r/4 = 40/4 = 10.

The constant of variation is confirmed to be 10, which is the correct answer.

Verification:

k = 400/r = 400/40 = 10

zzz [4K]8 days ago

6 0

Answer:

A. 10 on Edg2020

Step-by-step explanation:

Hope this assists!!! Wishing you a wonderful day!!!: )

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