i kinda need help with these 2 please:
assume (y) varies direcly as (x)
if (x)=32 when (y)=6, what is the value of k?
and
(y) varies directly as (x)
find the constant when (x)=0.5, and
(y)=0.3
and can someone also explain what they mean by find the constant and how 2 do it in the 2nd one please? thank u
y=kx
6=k*32 or
k=6/32 or 3/16 on the first.
One the second, y=kx, again, solve for the constant k.
Sure! I can help you with both of these problems.
In the first problem, where (y) varies directly as (x), we are given that (x) equals 32 when (y) equals 6. To find the constant of variation, denoted as (k), we can use the formula for direct variation:
(y) = (k)(x)
We substitute the given values into the equation:
6 = (k)(32)
To solve for (k), we need to isolate it. We can do this by dividing both sides of the equation by 32:
k = 6/32
Simplifying the right side, we get:
k = 3/16
So when (x) varies directly as (y), the constant of variation is k = 3/16.
In the second problem, we are given that (y) varies directly as (x) and we need to find the constant of variation when (x) equals 0.5 and (y) equals 0.3.
Using the same formula as before:
(y) = (k)(x)
We substitute the given values into the equation:
0.3 = (k)(0.5)
To solve for (k), we divide both sides of the equation by 0.5:
k = 0.3/0.5
Simplifying the right side, we get:
k = 3/5
So in this case, the constant of variation is k = 3/5.
To "find the constant" in these problems means to determine the value of the constant of variation (k) in the equation that relates the variables (x) and (y). The constant is a unique value that represents the rate at which (y) changes with respect to (x) in a direct variation relationship. To find the constant, you use the given values of (x) and (y) and solve for (k) using the formula for direct variation.