Answer:
the maximum area is 256 in^2
Step-by-step explanation:
It is well-known that the rectangle of given perimeter with maximum area is a square. A square with a perimeter of 64 inches has a side length of 64/4 = 16 inches. The area of that square is the square of the side length, ...
(16 in)^2 = 256 in^2
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<em>Derivation of the well-known fact</em>
Let P represent the perimeter of a rectangle with side lengths x and (P/2 -x). The area is the product of these dimensions:
A = x(P/2 -x)
This is the equation of a downward-opening parabola with zeros at x=0 and at x=P/2. The vertex (maximum) is halfway between these zeros, at x=P/4. Hence, the dimensions of the rectangle are ...
x = P/4 . . . . . . . . . . . length
(P/2 -P/4) = P/4 . . . . width
The length and width are the same, and both are 1/4 of the perimeter, so the rectangle is a square. Its area in terms of perimeter is ...
A = (P/4)^2 = P^2/16
Answer:
342.
Step-by-step explanation:
Let x represent the number of adults and y represent the number of senior citizens.
We have been given that on a recent weekend evening 514 people paid for the admission. We can represent this information in an equation as:
We have been given that the Family Fine Arts Center charges $20 per adult and $13 per senior citizen for its performances.
The cost of x adult tickets would be 
and cost of y senior citizen tickets would be 
.
We are also told that total receipts were $7886 on a recent weekend evening. We can represent this information in an equation as:
From equation (1), we will get:
We can represent this information in an equation as:
Substitute this value in equation (2) as:
Therefore, 342 senior citizens paid for the art center.
As we can find that
-8² is -8 x -8 and -7² is -7 x -7
It has the same meaning with rules of positive and negative numbers operation in math :
- If a negative value timed/divided by a negative value, the result is a positive value.
- if a positive value timed/divided by a negative value or vice versa, the result is a negative value.
Answer:
The answer for the first one is 1/2.
The answer for the second one is -1/1
Step-by-step explanation:
Hope that helps you :)
Write as a function equation: where f(x) is the same as "y"
f(x) = 5 + 1x ------ y = 1x + 5
Use: y = mx + b (Where m = slope and b is y intercept)
Slope is 1 and y intercept is +5
Remember slope is rise over run so 1 can be written as 1 / 1 and interpreted as rise 1 and run 1 both in the positive direction.
