9514 1404 393
Answer:
625 square feet
Step-by-step explanation:
The greatest area of a polygon with a given perimeter is that of a regular polygon. A regular rectangle is one that has all sides the same length -- a square. The side length of a square with 100 ft perimeter is 25 ft. The area of a square with such a side length is
A = (25 ft)² = 625 ft²
The maximum possible area is 625 ft².
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In the attached, x is the length of one side. The area versus side length is plotted. The maximum is seen to be 625 ft² for a side length of 25 ft.
Answer:
{12,2}
Step-by-step explanation:
From the given graph it is clear that the initial point of the vector is (-5,0) and the terminal point (7,2).
If initial point of a vector is and terminal point is
, then
Using this formula, we get
Using braces, we get
Therefore, the required vector is {12,2}.
Answer:
width = 10 units and length = 20 units
Step-by-step explanation:
Let the width be w
so Length will be 2w
using the rectangle formula:
Find length:
9514 1404 393
Answer:
(a) x = (3 -ln(3))/5 ≈ 0.819722457734
(b) y = 10
Step-by-step explanation:
(a) Taking the natural log of both sides, we have ...
2x +1 = ln(3) +4 -3x
5x = ln(3) +3 . . . . . . . . add 3x-1
x = (ln(3) +3)/5 ≈ 0.820
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(b) Assuming "lg" means "log", the logarithm to base 10, we have ...
log(y -6) +log(y +15) = 2
(y -6)(y +15) = 100 . . . . . . . taking antilogs
y^2 -9x -190 = 0 . . . . . . . . eliminate parentheses, subtract 100
(y -19)(y +10) = 0 . . . . . . . . factor
The values of y that make these factors zero are -19 and 10. We know from the first term that (y-6) > 0, so y > 6. That means y = -19 is an extraneous solution.
The solution is ...
y = 10
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When solving equations using a graphing calculator, it often works well to define a function f(x) such that the solution is f(x) = 0, the x-intercept(s). That form is easily obtained by subtracting the right side of the equation from both sides of the equation. In part (a) here, that is ...
f(x) = e^(2x+1) -3e^(4-3x)
