if Y varies jointly as X and the square of Z, and if Y=24 when X=2 and Z=6, find Y when X=10 and Z=9
y = kxz^2 , where k is a constan
given: y = 24, x=2, z=6
24 = k(2)(36)
k = 24/72 = 1/3
y = (1/3)xz^2
when x=10,z=9
y = (1/3)(10)(81) = 10/243
y varies jointly with z and the square of x. y=16 when z =2 and x=3, find y when z=3 and x=4
Well, let's throw a joke into the mix first:
Why don't scientists trust atoms?
Because they make up everything!
Now, let's solve the problem at hand.
If Y varies jointly as X and the square of Z, we can write the equation as:
Y = k * X * Z^2
where k is the constant of variation.
To find the value of k, we can substitute the given values of Y, X, and Z:
24 = k * 2 * 6^2
Simplifying:
24 = k * 2 * 36
24 = k * 72
Dividing both sides by 72:
k = 24 / 72
k = 1/3
Now that we know k, we can substitute the new values of X and Z to find Y:
Y = (1/3) * 10 * 9^2
Y = (1/3) * 10 * 81
Y = 270
So when X = 10 and Z = 9, Y would be equal to 270.
Hope that helps! If you have any more questions, feel free to ask.
To find the value of Y when X=10 and Z=9, we can use the joint variation formula.
The joint variation formula states that Y varies directly with X and the square of Z. Mathematically, it can be expressed as:
Y = kXZ^2
where k is the constant of variation.
To find the value of k, we can substitute the given values of Y, X, and Z into the equation:
24 = k(2)(6^2)
24 = k(2)(36)
24 = 72k
Divide both sides of the equation by 72 to solve for k:
k = 24/72
k = 1/3
Now that we have the value of k, we can substitute the new values of X and Z into the equation to find Y:
Y = (1/3)(10)(9^2)
Y = (1/3)(10)(81)
Y = (1/3)(810)
Y = 270
Therefore, when X=10 and Z=9, Y equals 270.
To find the value of Y when X = 10 and Z = 9, we can use the principle of joint variation.
The relationship "Y varies jointly as X and the square of Z" can be written as:
Y = k * X * Z^2
where k is a constant of proportionality.
To find the constant of proportionality (k), we can use the given information that "Y = 24 when X = 2 and Z = 6". Plugging these values into the equation, we get:
24 = k * 2 * 6^2
24 = k * 2 * 36
24 = 72k
To solve for k, divide both sides of the equation by 72:
k = 24 / 72
Simplifying further:
k = 1 / 3
Now we have the value of k, we can substitute it back into the equation:
Y = (1/3) * X * Z^2
To find Y when X = 10 and Z = 9, plug in these values into the equation:
Y = (1/3) * 10 * 9^2
Y = (1/3) * 10 * 81
Y = (1/3) * 810
Y = 270
Therefore, when X = 10 and Z = 9, Y equals 270.