Respuesta :
Answer:
Q = 5
Step-by-step explanation:
Given Q varies inversely with x then the equation relating them is
Q = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
To find k use the condition Q = 12 when x = 5 , thus
12 = [tex]\frac{k}{5}[/tex] ( multiply both sides by 5 )
60 = k
Q = [tex]\frac{60}{x}[/tex] ← equation of variation
When x = 12 , then
Q = [tex]\frac{60}{12}[/tex] = 5
Value of Q = 5 when x= 12.
What is inversely proportion?
" Inversely proportion is defined as when two variable 'x' and 'y' are related in such a way that value of one variable increases causes decreases in the value of other variable. It is written as x ∝ (1/y) "
Formula used
x ∝ (1/y)
⇒ x = ( k / y)
where 'k' is the constant of proportionality.
According to the question,
Given,
Q= 12
x=5
Q inversely proportional to x
Q∝ (1/x)
Using formula we get
Q = (k / x) where 'k' is the constant of proportionality.
Substitute the given value we get,
12 = k / 5
⇒ k = 12 × 5
⇒ k =60
Now x=12
k = 60
Again substitute it and get the value of Q,
Q = 60 / 12
= 5
Hence, value of Q = 5 when x= 12.
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