D is partly constant and partly varies with V,where V=40,D=150,and when V=54 ,D=192 1.find the formula connecting D and V 2. Hence,find D when V=73
D = a + bV
now just plug in your values to find a and b, so you can then evaluate D(73)
a+40b = 150
a+54b = 192
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D = 30+3V
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1. Ah, the joys of variables playing with constants! Let's figure out the formula connecting D and V. We know that when V=40, D=150, and when V=54, D=192.
So, let's start by figuring out the constant part. When V=40, D=150. Simple math tells us that the constant part of D is 150.
Now, let's focus on the varying part. We can calculate the difference between D values for different V values. When V changes from 40 to 54, D changes from 150 to 192. That's an increase of 42.
To represent this variation, we can say: D = Constant + (Variation * V)
Substituting values:
D = 150 + (42 * V)
So, the formula connecting D and V is D = 150 + (42 * V).
2. Now, let's find D when V=73. Plug in the value in the formula we just found:
D = 150 + (42 * 73)
D = 150 + (3078)
D = 3228
So, when V=73, D will be 3228.
To find the formula connecting D and V, we need to determine the relationship between the two variables.
1. Finding the constant part:
When V = 40, D = 150.
When V = 54, D = 192.
To find the constant part, we observe that when V increases from 40 to 54, D increases from 150 to 192. The difference in D is 192 - 150 = 42.
2. Finding the varying part:
To find the varying part, we subtract the constant part from the total value of D.
When V = 40, D = 150.
Therefore, the varying part of D at V = 40 is 150 - (42 * 0) = 150.
So, we have determined that the constant part is 42 and the varying part is 0.
Now, let's find the formula connecting D and V using these values:
D = Constant part + (Varying part * V)
Substituting the values we found:
D = 42 + (0 * V)
D = 42
Therefore, the formula connecting D and V is D = 42.
2. To find D when V = 73, we can substitute the value of V into the formula we obtained:
D = 42
Therefore, when V = 73, D = 42.