Answer:
attempts are required to find a matching pair if the digital fingerprint is 64 bits long.
attempts are required to find a matching pair if the digital fingerprint is 128 bits long.
Step-by-step explanation:
Each bit has two options. So
How many attempts are required to find a matching pair if the digital fingerprint is 64 bits long?
So for each of the 64 bits, we have the following number of options.
2 - 2 - 2 - 2 -... - 2
So, in all, there are

options.
So,
attempts are required to find a matching pair if the digital fingerprint is 64 bits long.
128 bits long?
Using the same logic as the first question.

So,
attempts are required to find a matching pair if the digital fingerprint is 128 bits long.
The computer salesman would have to sell 12 computers.
If

represent a family of surfaces for different values of the constant

. The gradient of the function

defined as

is a vector normal to the surface

.
Given <span>the paraboloid

.
We can rewrite it as a scalar value function f as follows:

The normal to the </span><span>paraboloid at any point is given by:

Also, the normal to the given plane

is given by:

Equating the two normal vectors, we have:
</span>

Since, -1 = 2 is not possible, therefore
there exist no such point <span>
on the paraboloid
such that the tangent plane is parallel to the plane 3x + 2y + 7z = 2</span>
.