Given that p=(2q^2-5)^2. when q=3, it is increased by 0.7%. find the appropriate percentage in p.
solution
dp = 2(2q^2-5) (2dq)
dp = (4x(18-5)(0.7%)
dp = 4(13)(0.7%)
am lost from here
is dp=52x0.7/100= 0.364%
Responses
Differential Calculus - bobpursley, Friday, August 14, 2009 at 1:52pm
p=(2q^2-5)^2
dp=2(2q^2-5)(4q)dq
ok from here
dp= -8
you have the expression for dp.
q=3, dq=.007*3
Now solve for dp and solve for P at q=3
percentage change in p then is dp/p divided by 100.
y^4=c(x^2+4y^2)
To find the appropriate percentage in p, you need to calculate dp as given by the equation dp = 2(2q^2-5)(4q)dq.
Now, let's substitute the value of q when it is increased by 0.7%. Since the original value of q is 3, we need to calculate dp when q = 3 + 0.7% of 3.
To find 0.7% of 3, we can multiply 3 by 0.7% or 0.007.
0.7% of 3 = 3 * 0.007 = 0.021
Therefore, q becomes 3.021 when increased by 0.7%.
Now, let's substitute the updated q value into the equation dp = 2(2q^2-5)(4q)dq.
dp = 2(2(3.021)^2-5)(4(3.021))(0.021)
Simplifying this equation further, we get:
dp = 2(2(9.126241)-5)(4(3.021))(0.021)
Next, let's calculate the value inside the parentheses:
dp = 2(18.252482-5)(4(3.021))(0.021)
Further simplifying:
dp = 2(13.252482)(4(3.021))(0.021)
Now, multiply the values inside parentheses:
dp = 2(13.252482)(12.084)(0.021)
Finally, multiply all the values together to get the final result:
dp ≈ 6.3846
So, the appropriate percentage in p is approximately 6.3846%.