y varies jointly as x and z, and y=98/3 when x=2 ans z=7. Find y when x=7 and z=3.
Options:
A: y=7/3xz; 49
B: y=6/7xz; 18
C: y=14/3xz; 98
D: y=3/7xz; 9
Let
y=kxz
98/3=k(2*7)
k=98/3/14=7/3
Therefore y=(7/3)xz
when x=7, z=3
then y=(7/3)*7*3=49
To find the value of y when x=7 and z=3, we can apply the concept of joint variation. Joint variation is a mathematical relationship where a variable varies directly with two or more other variables, and the variation can be expressed using a constant of variation.
In this case, we are given that y varies jointly as x and z. Mathematically, this can be written as:
y = kxz
where k is the constant of variation.
To find the value of k, we can use the given information that y=98/3 when x=2 and z=7:
98/3 = k * 2 * 7
To solve for k, we can first simplify the equation:
k * 2 * 7 = 98/3
14k = 98/3
Now, divide both sides of the equation by 14 to isolate k:
k = (98/3) / 14 = 7/3
Now that we have found the value of k, we can substitute it back into the original equation to find the value of y when x=7 and z=3:
y = (7/3) * 7 * 3
y = 49/3
Therefore, the correct answer is option A: y = 7/3xz; y = 49/3.