z is partly constant and partly varies as D when d=1,z=11and when d=2,z=5 find Z when d=4
z = a + bd
Now plug in your numbers
a + 1b = 11
a + 2b = 5
Note that adding b lowered z by 6
You don't even need to know a and b, since when d=4, z(4) will be z(2) - 12.
To find z when d=4, we can use the information given about z partly being constant and partly varying as D.
When d=1, z=11.
When d=2, z=5.
From the given information, we can see that as d increases from 1 to 2, z decreases from 11 to 5.
To find the relationship between z and D, we need to find the change in z for each unit change in d.
The change in z for each unit change in d is calculated by subtracting the initial value of z from the final value of z and dividing it by the change in d.
Change in z = (Final z value - Initial z value) / (Final d value - Initial d value)
Change in z = (5 - 11) / (2 - 1)
Change in z = -6
So, for each unit change in d, z decreases by 6.
To find z when d=4, we need to find the change in z from d=1 to d=4.
Change in z = Change in d * Change in z
Change in z = (4 - 1) * -6
Change in z = -3 * -6
Change in z = 18
Now, let's calculate z when d=4 by adding the change in z to the initial z value at d=1:
z = Initial z value + Change in z
z = 11 + 18
z = 29
Therefore, when d=4, z=29.
To solve this problem, we need to find the relationship between z and D when d=1 and d=2. Then, we can use this relationship to find z when d=4.
Let's first consider when d=1, and z=11. This means that when d=1, z=11.
Next, let's consider when d=2, and z=5. This means that when d=2, z=5.
We are given that z is partly constant and partly varies as D. Therefore, we can express z as the sum of a constant term, k, and a term that depends on D.
So, z = k + D.
From the given information, we know that when d=1, z=11. Plugging in these values, we get:
11 = k + D (equation 1)
Similarly, when d=2, z=5. Using the equation we derived earlier, we can write:
5 = k + 2 (equation 2)
Now, we have a system of two equations with two variables (k and D). We can solve this system to find the values of k and D.
Subtracting equation 2 from equation 1, we get:
6 = D - 1
Simplifying, we find that D = 7.
Substituting this value of D back into equation 1, we can solve for k:
11 = k + 7
k = 4.
Now, we have found the values of k and D. We can use the expression for z to find z when d=4.
z = k + D
z = 4 + 4
z = 8.
Therefore, when d=4, z=8.
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