Let x and y be the dimension of the rectangle. Suppose x is the width and y is the length. Since the perimeter is 36, we have
If we increase the length by 1, we change . Similarly, if the width is increased by 2, we change . So, the increased area is
If we substitute the value for y deduced in the first equation, we have
The solutions to this equation are
One of them is negative, so we have to choose the positive one:
Which implies
Answer:
The range is [-11, ∞).
Step-by-step explanation:
f(x)=3x^2+6x-8
This is a parabola which opens upwards.
Convert to vertex form:
= 3(x^2 + 2x) - 8
= 3 [ (x + 1)^2 - 1] - 8
= 3(x + 1)^2 - 3 - 8
= 3(x + 1)^2 - 11.
The minimum value is -11 so the range is [-11, ∞).
Step-by-step explanation:
Answer:
The roots of the equation is real and repeated
Step-by-step explanation:
Here, we want to describe the nature of the roots of the given quadratic equation
To get the nature of the roots, we find the discriminant of the equation
The discriminant is;
b^2 - 4ac
In this case, b = -28 , a = 49 and c = 4
The discriminant is thus;
-28^2 - 4(49)(4)
= 784 - 784 = 0
Since the discriminant is zero, this means that the quadratic equation has real roots which are the same
Answer:
There are an infinite number of values satisfying the requirements; every couple of numbers satisfying the following conditions are valid:
base = 60-w meters
width = w meters
0 < w <= 22
Step-by-step explanation:
Since the playground has a rectangular shape, let us us call b the base of the rectangle and w its width. In order for the rectangle to satisfy the condition of P = 120, we need for the following equation to satisfy:
2b + 2w = 120
Solving for b, we get that b = (120 - 2w)/2 = 60 - w .
Given a particular value (w) for the width, the base has to be: (60-w).
Therefore, the possible lengths of the playground are (60-w, w), where 60-w corresponds to the base of the rectangle and w to its width. And w can take any real value from 0 to 22.