e varies inversely (y-2).if e =12 when y=4,find e when y=6 and y when e=0.5..
The given statement "e varies inversely with (y-2)" can be written as:
e = k/(y-2)
where k is the constant of variation.
To find the value of k, we can use the given information that e = 12 when y = 4. Substituting these values into the equation, we get:
12 = k/(4-2)
12 = k/2
24 = k
So the constant of variation, k, is 24.
Now we can use this value of k to find e when y = 6. Substituting these values into the equation, we get:
e = 24/(6-2)
e = 24/4
e = 6
Therefore, when y = 6, e = 6.
To find y when e = 0.5, we can rearrange the equation:
e = 24/(y-2)
0.5 = 24/(y-2)
Cross multiplying, we get:
0.5(y-2) = 24
0.5y - 1 = 24
0.5y = 25
y = 50
Therefore, when e = 0.5, y = 50.
To solve this inverse variation problem, we can use the inverse variation equation:
e = k / (y-2)
where e is the dependent variable, y is the independent variable, and k is the constant of variation.
Step 1: Find the value of k.
Given that e = 12 when y = 4, we can substitute these values into the inverse variation equation:
12 = k / (4 - 2)
12 = k / 2
To find k, we can multiply both sides of the equation by 2:
k = 12 * 2
k = 24
Step 2: Find e when y = 6.
We can now use the value of k to solve for e when y = 6:
e = 24 / (6 - 2)
e = 24 / 4
e = 6
Therefore, when y = 6, e = 6.
Step 3: Find y when e = 0.5.
To find y when e = 0.5, we can rearrange the inverse variation equation:
e = 24 / (y - 2)
0.5 = 24 / (y - 2)
Next, we can multiply both sides of the equation by (y - 2) to isolate the variable on one side:
0.5(y - 2) = 24
Distribute 0.5 to both terms in parentheses:
0.5y - 1 = 24
Next, add 1 to both sides of the equation:
0.5y = 25
Divide both sides of the equation by 0.5 to solve for y:
y = 25 / 0.5
y = 50
Therefore, when e = 0.5, y = 50.