Respuesta :
Answer:
p = 304
Step-by-step explanation:
Given p is inversely proportional to q² then the equation relating them is
p = [tex]\frac{k}{q^2}[/tex] ← k is the constant of proportion
To find k use the condition p = 19 when q is 8, then
19 = [tex]\frac{k}{8^2}[/tex] = [tex]\frac{k}{64}[/tex] ( multiply both sides by 64 )
k = 1216
p = [tex]\frac{1216}{q^2}[/tex] ← equation of proportion
When q = 2, then
p = [tex]\frac{1216}{2^2}[/tex] = [tex]\frac{1216}{4}[/tex] = 304
The value of p is equal to 304 when q is equal to 2
Given :
If p is inversely proportional to the square of q
when y is inversely proportional to x then [tex]y=\frac{k}{x}[/tex]
given that p is inversely proportional to the square of q. the equation becomes
[tex]p=\frac{k}{q^2}[/tex]
when p is 19 the value of q is 8
Replace the values and find out k
[tex]p=\frac{k}{q^2}\\19=\frac{k}{8^2}\\19=\frac{k}{64}\\[/tex]
Multiply both sides by 64
k=1216
Now we find out p when q is 2
Replace k value and q value to find out p
[tex]p=\frac{k}{q^2} \\\\p=\frac{1216}{2^2} \\p=304[/tex]
The value of p is equal to 304 when q is equal to 2
Learn more : brainly.com/question/16069814
