Answer:
The graph of the rectangle missing in the question is shown in the figure attached.
Coordinates of the points are:
A(1,8)
B(4,5)
C(14,21)
D(17,18)
The area of the rectangle is AB*BD.
The length of a segment given two points (x1, y1) and (x2, y2) is computed as follows:
√[(y2 - y1)^2 + (x2 - x1)^2]
For segment AB:
√[(5 - 8)^2 + (4 - 1)^2] = √18
For segment BD:
√[(18 - 5)^2 + (17- 4)^2] = √338
Then, the area is:
AB*BD = (√18)*(√338) = √(18*338) = √6084 = 78
The formula for the volume of a cone is (1/3)*pi)*r^3*h. Here, r = 2 units.
Thus, the volume of this particular cone is:
V = (1/3)(3.14)((2 units)^2*(9 units). Please do the math, and then round off your answer to 2 decimal places.
The standard form of a quadratic equation is: ax^2 + bx + c = 0
a = 1 ; b = -2 ; c = -8
To find the zeros, you put in x=0 which gives (0,-8) and use the quadratic formula to find the other zeros; f(x) = 0
Quadratic formula:
x = (-b+/-√(b^2-4ac))/2a
The x-value for the vertex is -b/2a
x = 1
put this in for x and solve for the f(x)
1 - 2 - 8 = -9
vertex: (1, -9)
The vertex form of a quadratic equation: f(x) = a(x-h)^2 + k
where (h, k) is the vertex.
If you don't know the vertex, you would need to factor it into this form. Look at the center term bx, what you could be added to the equation to make a perfect square.
f(x) = (x^2 - 2x + 1) - 9
By splitting the -8 into 1 - 9 we've created a perfect square (x-1)^2
f(x) = (x-1)^2 - 9
