Y is directly proportional to the square root of x if y = 60 when x = 36 find x when y = 80
2 answers:
Answer:
x = 64
Step-by-step explanation:
Given y is directly proportional to then the equation relating them is
y = k ← k is the constant of proportion
To find k use the condition y = 60 when x = 36, then
60 = k = 6k ( divide both sides by 6 )
10 = k
y = 10 ← equation of proportion
When y = 80 , then
80 = 10 ( divide both sides by 10 )
8 = ( square both sides )
64 = x
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Assuming the equation is:
When fractions involve numeric denominators, the fractions can be removed by multiplying (both sides) by the LCM of the denominators.
Here the denominators are 2 and 10, hence the LCM is 10.
Multiply by 10 on both sides, not forgetting to distribute when multiplying on the right side:
simplify, remember that there are always implied parentheses around numerators and denominators:
Now, distribute, i.e. remove parentheses and distribute:
5x-10x+25=30x+90-10x+140
Simplify
-5x+25=20x+230
transpose terms
25-230=20x+5x
solve
x=-205/25=-41/5
In this particular case, we can also take advantage of the term
(10x-25)/10=5(2x-5)/10=(2x-5)/2 which greatly simplifies the solution process, because the LCM will then be 2 instead of 10.
If we do that, the solution will be:
Multiply by 2 on both sides, not forgetting to distribute when multiplying on the right side:
simplify, remember that there are always implied parentheses around numerators and denominators:
Now, distribute, i.e. remove parentheses and distribute:
Simplify
-x+5=4x+46
solve
5-46=4x+x
-41=5x
x=-41/5
with the same results.