Respuesta :
Answer:
y = 86100 / w.
21 miles per gallon.
Step-by-step explanation:
If y is the consumption then:
y = k / w where k is some constant so we have:
28.7 = k / 3000
k = 3000 *28.7 = 86100
So the required equation is y = 86100 / w.
For a car weighing 4100 pounds:
y = 86100 / 4100 = 21 miles per gallon.
The required inverse relation is, yw = 86100.
The car will get 21 miles per gallon if it weighs 4,100 pounds.
What are direct and inverse relations?
A direct relation between two quantities implies that the increase in one increases the other and vice-versa.
If quantity a and b are directly related, then we write the relation as a ∝ b, which can be written as a = kb, where k is the constant of proportionality used to replace the proportionality symbol with the equal to sign.
An inverse relation between two quantities implies that the increase in one decreases the other and vice-versa.
If quantity a and b are inversely related, then we write the relation as a ∝ 1/b, which can be written as a = k/b, or, ab = k, where k is the constant of proportionality used to replace the proportionality symbol with the equal to sign.
How to solve the question?
In the question, we are given that the fuel consumption in miles per gallon (y) for a car inversely varies with its weight (w).
Thus we can write the relation like this:
y ∝ 1/w
or, y = k/w
or, yw = k.
The value of k can be determined using the given value of y = 28.7 miles per gallon and w = 3000 pounds.
Therefore, 28.7*3000 = k
or, k = 86100.
Thus, the required inverse relation is, yw = 86100.
Now, we are asked how many miles per gallon will a car get if it weighs 4100 pounds.
Therefore, w = 4100, y = ?
We know, yw = 86100.
or, y = 86100/w = 86100/4100 = 21.
Therefore, the car will get 21 miles per gallon, if it weighs 4,100 pounds.
Learn more about direct and inverse relations at
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