Find an equation of variation in which y varies jointly as x and z, and y=4 when x=4 and z=1. Simplify
y = kxz
4 = k*4*1
k = 1
y = xz
Well, let's start by writing the equation of variation in its general form:
y = kxz
Now, we can use the given values of y, x, and z to solve for the constant of variation, k. Plug in y = 4, x = 4, and z = 1:
4 = k(4)(1)
4 = 4k
Divide both sides by 4:
1 = k
So, the equation of variation can be simplified to:
y = xz
Therefore, y varies jointly as x and z, and the equation of variation is y = xz.
To find an equation of variation where y varies jointly as x and z, we can use the formula:
y = k * x * z
where k is the constant of variation.
Given that y = 4 when x = 4 and z = 1, we can substitute these values into the equation:
4 = k * 4 * 1
Simplifying this equation gives us:
4 = 4k
Dividing both sides of the equation by 4, we find:
k = 1
Now that we know the value of k, we can substitute it back into the equation:
y = 1 * x * z
Simplifying further, we get:
y = xz
Therefore, the equation of variation in which y varies jointly as x and z, simplified, is y = xz.
To find an equation of variation in which y varies jointly as x and z, we can use the equation:
y = k * x * z,
where k is the constant of variation.
To find the value of k, we can substitute the given values of y, x, and z:
4 = k * 4 * 1.
Simplifying this equation, we have:
4 = 4k.
Dividing both sides of the equation by 4, we get:
k = 1.
Now that we know the value of k is 1, we can substitute it back into the original equation:
y = 1 * x * z.
Simplifying further, we have:
y = xz.
Thus, the equation of variation in which y varies jointly as x and z is y = xz.