We know that
[perimeter of rectangle]=2*(<span>length+width)
</span>
Let
x-----------> length
y-----------> width
so
P=2*(x+y)-----------> 244=2*(x+y)-----> x+y=122-------> y=122-x
Area=x*y-------> x*(122-x)----> 122x-x²
find the derivative function and equals to zero
122-2x=0-----> 122=2x----------> x=61 m
y=122-x------> y=122-61---------> y=61 m
<span>the maximum area is given by a square
</span>
the answer is
is a square of side 61 m
3d + 8 = 2d - 7 equals d = -15.
First, subtract 2d from both sides. Your problem should look like: 3d + 8 - 2d = -7.
Second, simplify 3d + 8 - 2d to get d + 8. Your problem should look like: d + 8 = -7.
Third, subtract 8 from both sides. Your problem should look like: d = -7 - 8.
Fourth, simplify -7 - 8 to get -15. Your problem should look like: d = -15, which is your answer.
Hopefully this helps, I'm not exactly sure what you meant by "is equations," but this is how you solve the problem.
<h3>
Answer: 5</h3>
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Explanation:
Let's consider the expression (x-y)^2. It expands out to x^2-2xy+y^2. The terms are:
Each of those terms either has a single variable with an exponent of 2, or has the exponents add to 2. Think of 2xy as 2x^1y^1.
In short, this means that the degree of each monomial term is 2.
----------
Now consider (x-y)^3. It expands out into x^3-3x^2y+3xy^2+y^3.
We have terms that either have a single variable and the exponent is 3, or the exponents add to 3. The degree of each term is 3.
----------
This pattern continues.
In general, for (x-y)^n, where n is any positive whole number, the degree of each term in the expansion is n. If you picked any term, added the exponents, then the exponents will add to n.
<span>Since the problem specifically stated that the people
gather around the table, therefore we assume a circular table hence a circular
formation of gathering. Since the
arrangement is important therefore we use the permutation. </span>
nPr = n! / (n – r)!
<span>However before we proceed with our calculation we MUST
first affix a reference point since the formation is circle. Imagine that the
reference point is the 1st point made when you draw a circle, so it
is the both the 0 degrees and the 360 degrees.</span>
Let us say that one of the actors is the reference point.
So there are now only 8 actors which places can be interchanged. Since all
actors have to sit together, hence the arrangements are:
8P8 = 8! / (8 – 8)! = 40,320
Now since there are 13 total people, therefore the
arrangements of the other 4 people are:
4P4 = 4! / (4 – 4)! = 24
We multiply all to get the total number of arrangements:
<span>Total arrangements = 40320 * 24 * 1 (1 is the reference point)</span>
<span>Total arrangements = 967,680</span>
