The <em>correct answer</em> is:
maximum: 116
; range: y ≤ 116
Explanation:
This is a quadratic equation in standard form, which is y=ax²+bx+c. The maximum or minimum of a quadratic function is the vertex. To find the x-coordinate of the vertex, we find the axis of symmetry. This is given by the formula x=-b/2a:
x = -32/2(-2) = -32/-4 = 8
To find the y-coordinate, plug this into the equation:
y = -2(8²)+32(8)-12
y=-2(64) + 256 - 12 = -128+256-12 = 128-12 = 116
The coordinates of the vertex are (8, 116).
To determine if this is a maximum or minimum, look at the value of a. It is -2. Since it is negative, this means the parabola opens downward, and the vertex is a maximum.
Since this is a maximum at y=116, this means the range, our y-values, will be less than or equal to this value of 116.
Answer:
The length and width of the plot that will maximize the area of the rectangular plot are 54 ft and 27 ft respectively.
Step-by-step explanation:
Given that,
The length of fencing of the rectangular plot is = 108 ft.
Let the longer side of the rectangular plot be x which is also the side along the river side and the width of the rectangular plot be y.
Since the fence along the river does not need.
So the total perimeter of the rectangle is =2(x+y) -x
=2x+2y-y
=x+2y
So,
x+2y =108
⇒x=108 -2y
Then the area of the rectangle plot is A = xy
A=xy
⇒A= (108-2y)y
⇒ A = 108y-2y²
A = 108y-2y²
Differentiating with respect to x
A'= 108 -4y
Again differentiating with respect to x
A''= -4
For maximum or minimum, A'=0
108 -4y=0
⇒4y=108
⇒y=27.
Since at y= 27, A''<0
So, at y=27 ft , the area of the rectangular plot maximum.
Then x= (108-2.27)
=54 ft.
The length and width of the plot that will maximize the area of the rectangular plot are 54 ft and 27 ft respectively.
5 × 5 = 25
multiplication can be seen as repeated addition... if you take five 5's and add them together it is...
5+5+5+5+5= 25
Answer: 35,7
Step-by-step explanation:
151 - 100%
54 - x
151x = 5400
x = <u>5400</u>
151
x = 35,7