The equation would be x+5*-2=6.
The result of that equation would be x=16
I'm going to assume you meant to write fractions (because if
are all non-negative integers, the series would clearly diverge), so that



and so on.
a. If the pattern continues as above, we would have the general term

b. Note that we can write
as

The series diverges by comparison to the divergent series

Answer:
The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches
Step-by-step explanation:
We have that:

Let the dimension of the paper be x and y;
Such that:


So:

Substitute 128 for Area

Make x the subject

When 1 inch margin is at top and bottom
The length becomes:


When 2 inch margin is at both sides
The width becomes:


The New Area (A) is then calculated as:

Substitute
for x

Open Brackets

Collect Like Terms



To calculate the smallest possible value of y, we have to apply calculus.
Different A with respect to y

Set

This gives:

Collect Like Terms

Multiply through by 


Divide through by 2

Take square roots of both sides



Recall that:



Recall that the new dimensions are:


So:




To double-check;
Differentiate A'




The above value is:

This means that the calculated values are at minimum.
<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>
Attached
Step-by-step explanation:
From the question x is the number of stools and y is the number of recliners
Given that the coffee shop can hold no more than 50, then the inequality for number of seats will be;
x+y≤ 50
Also, the owner wants at least 20 of the seats to be stools, this can be written as;
x≥20
Using a graph tool to visualize the inequalities, you get the attached graph;
Learn More
Inequalities graph : brainly.com/question/11234618
Keyword : graph, inequalities
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