Answer: Identify which of the following functions are eigenfunctions of the operator d/dx: (a) eikx, (b) cos kx, (c) k, (d) kx, (e) e−ax2
Step-by-step explanation: First, we going to apply the operator derivate to each item. Remember that a function f is an eigenfunction of D if it satisfies the equation
Df=λf, where λ is a scalar.
a) D(eikx)/dx= ik*eikx, then the function is a eigenfunction and the eingenvalue is ik.
b) D(cos kx)/dx= -ksen kx, then the funcion is not a eigenfunction.
c) D(k)/dx=0, then the funcion is not a eigenfunction.
d) D(kx)/dx=k, then the funcion is not a eigenfunction.
e) D(e-ax2)/dx= -2ax*e-ax2, then the function is a eigenfunction and the eingenvalue is -2ax
The answers are B) and E)
The volume of the cylinder is the amount of fruit juice it can contain.
The relationship between the volume and the surface area is:
![\mathbf{A = \pi (\sqrt[3]{\frac{V}{2\pi}})^2 + \frac{0.946}{(\sqrt[3]{\frac{V}{2\pi}})}}](https://tex.z-dn.net/?f=%5Cmathbf%7BA%20%3D%20%5Cpi%20%28%5Csqrt%5B3%5D%7B%5Cfrac%7BV%7D%7B2%5Cpi%7D%7D%29%5E2%20%2B%20%5Cfrac%7B0.946%7D%7B%28%5Csqrt%5B3%5D%7B%5Cfrac%7BV%7D%7B2%5Cpi%7D%7D%29%7D%7D)
The given parameter is:
The volume of a cylinder is calculated as:
Make h the subject
The surface area (A) of a cylinder is:
Substitute
Differentiate
Set to 0
Rewrite as:
Multiply through by r^2
Solve for r
![\mathbf{r = \sqrt[3]{\frac{V}{2\pi}}}](https://tex.z-dn.net/?f=%5Cmathbf%7Br%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7BV%7D%7B2%5Cpi%7D%7D%7D)
So, we have:
Hence, the relationship between the volume and the surface area is:
Read more about surface areas and volumes at:
brainly.com/question/3628550
Answer:
combine 4m -8m to get -4m
Answer:
6,000
Step-by-step explanation:
500x12
