Answer:
Answer for the question :
Consider the optimization problem where A m × n , m ≥ n , and b m .
a. Show that the objective function for this problem is a quadratic function, and write down the gradient and Hessian of this quadratic.
b. Write down the fixed-step-size gradient algorithm for solving this optimization problem.
c. Suppose that Find the largest range of values for α such that the algorithm in part b converges to the solution of the problem.
is explained din the attachment.
Step-by-step explanation:
Let's begin ! ^_^
You have got informations in your problem that you just have to translate in a "mathematic language".
Company A :
"$40 membership fee and $2 per video stream."
Thanks to that, you can guess :
c = 40 + 2s
Now let's do the same thing to the company B.
Company B :
"charges a one-time $20 membership fee and $4 per video stream."
Therefore, c = 20 + 4s.
I think you have guessed !! =D And yes the system of equation that you have to solve and you're looking for is :
{c=40+2s ( Option B)
c=20+4s.
Second step : For how many video streams will the cost be the same for both companies?
We just have to solve the system :) And there is only one variable, the letter "s".
We know that we have to find equal costs as it is said in the question " the cost be the same for both companies", so :
=> 40 + 2s = 20 +4s
=> 4s - 2s = 40 - 20
=> 2s = 20
=> s = 20/2
=> s = 10
Verification :
Company A :
=> 40 + 2s = 40 + 2*10 = 40 + 20 =60.
Company B :
=> 20 + 4s = 20 + 4*10 = 20 + 40 = 60
As you have seen, the costs are the same for both companies.
We can say that as a conclusion for 10 video streams, the cost will be the same for both companies.
In short, the answer would be : 10.
Let me give you an advice : Usually the word "per" means a multiplication is the mathematic language.
Hope this helps !
Photon
For every 2 you pay your dad pays 3
52.20 / 2 = 26.1
26.1 * 3 = 78.30 ( amount dad pays)
total = 78.30 + 52.20 = 130.50
