Answer:
k = 30, 
Step-by-step explanation:
Since
is a solution, then it must satisfy the differential equation. So, we calculate the derivatives and replace the value in the equation. We have that

Then, replacing the derivatives in the equation we have:

Since
is a positive function, we have that
.
Now, consider a general solution
, then, by calculating the derivatives and replacing them in the equation, we get

We already know that r=5 is a solution of the equation, then we can divide the polynomial by the factor (r-5) to the get the other solution. If we do so, we get that (r-6)=0. So the other solution is r=6.
Therefore, the general solution is

Answer:
The modulus of the complex number 6-2i is:

Step-by-step explanation:
Given the number

We know that
where x and y are real and 
The modulus or absolute value of z is:

Therefore, the modulus of
will be:










Therefore, the modulus of the complex number 6-2i is:

For the first one it’s 9490 & for the second it’s 860
Answer:
12.5π or ≈39.27
Step-by-step explanation:
The formula for finding the volume is V=πr^2*d (where h is the height and r is the radius).
Plug in the values: V=π(2.5)^2*2 (Diameter=2*Radius)
Solve: V=6.25π*2
V=12.5π
V≈39.27
Answer:
A. Point A is the correct answer