Answer:
the value of x would be 13
Step-by-step explanation:
Taking

and differentiating both sides with respect to

yields
![\dfrac{\mathrm d}{\mathrm dx}\bigg[3x^2+y^2\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[7\bigg]\implies 6x+2y\dfrac{\mathrm dy}{\mathrm dx}=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B3x%5E2%2By%5E2%5Cbigg%5D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B7%5Cbigg%5D%5Cimplies%206x%2B2y%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D0)
Solving for the first derivative, we have

Differentiating again gives
![\dfrac{\mathrm d}{\mathrm dx}\bigg[6x+2y\dfrac{\mathrm dy}{\mathrm dx}\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[0\bigg]\implies 6+2\left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2+2y\dfrac{\mathrm d^2y}{\mathrm dx^2}=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B6x%2B2y%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B0%5Cbigg%5D%5Cimplies%206%2B2%5Cleft%28%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%5Cright%29%5E2%2B2y%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dx%5E2%7D%3D0)
Solving for the second derivative, we have

Now, when

and

, we have
Answer: The sphere is 0.002548 cm travel up the plane.
Step-by-step explanation:
Since we have given that
Inclination angle = 30°
Translational speed = 0.25 m/s
As we know that

and
Length of solid sphere is given by

So, it becomes,

And 
So, it becomes,

Hence, the sphere is 0.002548 cm travel up the plane.
Answer:
We can conclude that the result is significant and production differ in cost variance.
Step-by-step explanation:
Given :
n1 = 16
n2 = 16
s1² = 5.7
s2² = 2.8
α = 0.10
H0 : σ1² = σ2²
H1 : σ1² ≠ σ2²
The test statistic :
Ftest = s1² / s2² =
Ftest = 5.7 / 2.8
Ftest = 2.036
Using the Pvalue from Fratio calculator :
df numerator = 16 - 1 = 15
df denominator = 16 - 1 = 15
Pvalue(2.036, 15, 15) = 0.0898
Pvalue = 0.0898
Since the Pvalue is < α ; We can conclude that the result is significant and production differ in cost variance.