Answer:
The equation is,
[tex]d = \frac{3}{200} {v}^{2} [/tex]
Step-by-step explanation:
Given that d is directly proportional to the square of v. So the equation is, d ∝ v² equals to d = kv² where k is a constant. So in order to find the value of k, you have to substitue the value of d and v into the equation :
[tex]d \: ∝ \: {v}^{2} [/tex]
[tex]d = k {v}^{2} [/tex]
Let d = 6,
Let v = 20,
[tex]6 = k( {20)}^{2} [/tex]
[tex]6 = k(400)[/tex]
[tex] \frac{6}{400} = k[/tex]
[tex]k = \frac{3}{200} [/tex]
[tex]d = \frac{3}{200} {v}^{2} [/tex]
The required equation connecting d and v is d = 3/200 v².
d is directly proportional to the square of v. d = 6 when v = 20.
In mathematics it deals with numbers of operations according to the statements.
Here,
d α v²
d = kv² ----(1)
Where, k is constant
Now, d = 6 when v = 20
6 = k x 20²
6 = 400k
k = 3/200
Put this value of k in equation 1
d = 3/200 v²
Thus, the required equation connecting d and v is d = 3/200 v².
Learn more about arithmetic here:
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