Area of the rectangle is given as = 16 square inches
We know
Length * width = Area
Then
Width = Area/Length
Now
Perimeter = 2 (Length + Width)
Perimeter = 2[ {Length + (Area/Length)}]
Perimeter = 2[Length + (16/Length)]
When d(Perimeter)/d(length) = 0,
Then
2[Length + (16/Length)] = 0
Length + (16/Length) = 0
Length^2 + 16 = 0
(Length)^2 = -(4)^2
Then
Length = 4 inches
Now
Width = Area/Length
= 16/4
= 4 inches.
Distance is dependent and Time is independent
This is how I think of it. The distance she goes DEPENDS on the time she spent running
Answer:
1). Increases
2). Slope = 4
3). Slope = -1
4). y = 4 when x = 5
Step-by-step explanation:
1). Initially, as x increases, y also increases. (Linear growth has been shown in the graph initially).
2). Afterward, the slope of the graph of the function is equal to 4 for all x between x = 3 and x = 5.
[Slope of the line passing through two points (3, 0) and (5, 4)
m = \frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}
(x
2
−x
1
)
(y
2
−y
1
)
= \frac{4-0}{5-3}
5−3
4−0
= \frac{4}{1}
1
4
= 4 ]
3). The slope of the graph is equal to -1 for x between x = 5 and x = 9.
[Slope of the line passing through two points (5, 4) and (9, 0),
Slope = \frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}
(x
2
−x
1
)
(y
2
−y
1
)
= \frac{4-0}{5-9}
5−9
4−0
= -\frac{4}{4}
4
4
= -1 ]
4). The greatest value of y is y = 4, and it occurs when x = 5. (From the given graph)
