D is partly constant and partly varies with v ,when v=40, D=150 and when v=54 D=73
a)find the formula connecting D and v
b)hence find D when v=73
D = a + kv
now plug in your two points to find a and k.
To find the formula connecting D and v, we can start by observing that D is partly constant and partly varies with v. This means that there is a constant term that does not change with v and a variable term that changes based on v.
Let's denote the constant term as C and the variable term as k. Therefore, the formula connecting D and v can be written as:
D = C + kv
To find the values of C and k, we can use the information provided:
When v = 40, D = 150:
Substituting these values into the formula:
150 = C + 40k
When v = 54, D = 73:
Substituting these values into the formula:
73 = C + 54k
Now, we have a system of two equations with two unknowns. We can solve this system to find the values of C and k.
First, subtracting the second equation from the first equation to eliminate C:
(150 - 73) = (C + 40k) - (C + 54k)
77 = -14k
Dividing both sides by -14:
k = -5.5
Now, substitute the value of k back into one of the original equations to solve for C:
150 = C + 40(-5.5)
150 = C - 220
C = 370
Therefore, the formula connecting D and v is:
D = 370 - 5.5v
To find D when v = 73, substitute v = 73 into the formula:
D = 370 - 5.5(73)
D = 370 - 401.5
D ≈ -31.5
Therefore, when v = 73, D ≈ -31.5.