Z is partly constant and partly varies directly with x and inversely with y.z=10 when x=4 and y=8&z=4when x=12 y=6 find z when x=20and y=4
z = k x / y + c
10 = k (4) / (8) + c
4 = k(12) / (6) + c
80 = 4 k + 8 c
24 = 12 k + 6 c
240 = 12 k + 24 c
24 = 12 k + 6 c
----------------------------
216 = 18 c
c = 12
24 = 12 k + 72
k = - 4
so
z = -4 (x / y) +12
now put in (20,4)
z = -4 ( 5) + 12
check my arithmetic :)
z is partly constant and partly varies directly with x and inversely with y: z = c + mx/y
So plug in your numbers to get
4/8 m + c = 10
12/6 m + c = 4
Now solve for m and c, and then find z(4,20)
Yes
Well, well, well. Looks like Z is playing some interesting games with X and Y. Let's see if we can decode the mystery.
First, let's find the constant part of Z. Since Z is partly constant, we can identify it by comparing the given values. When X is 4 and Y is 8, Z is 10. When X is 12 and Y is 6, Z becomes 4. Let's do some math magic:
When X = 4 and Y = 8, we have 10 = K * 4 / 8, where K is the constant part of Z.
Simplifying, we get K = 20.
When X = 12 and Y = 6, we have 4 = 20 * 12 / 6.
Simplifying again, we find that 20 = 20.
Now that we know the constant part of Z, let's tackle the part that varies directly with X and inversely with Y.
When X = 20 and Y = 4, we have Z = (20 * 20) / (4 * 20).
Performing some more math magic, we find Z = 20.
So, my dear friend, when X = 20 and Y = 4, Z decides to settle for 20. Maybe Z got tired of playing games and decided to behave for a change.
To find the value of Z when X is 20 and Y is 4, we need to determine the relationship between Z, X, and Y based on the given information.
According to the problem, Z is partly constant and partly varies directly with X and inversely with Y. This can be represented by the equation:
Z = k * (X/Y)
Where k is the constant of proportionality.
To find the value of k, we can use the first set of values provided: Z = 10 when X = 4 and Y = 8.
10 = k * (4/8)
10 = k * (1/2)
k = 20
Now that we have the value of k, we can use it to find Z when X is 20 and Y is 4.
Z = 20 * (20/4)
Z = 20 * 5
Z = 100
Therefore, when X is 20 and Y is 4, Z equals 100.