Answer:
height = 7 cm
Step-by-step explanation:
The area (A) of a trapezium is calculated using the formula
A = 
h(a + b)
where h is the height and a, b the parallel bases
here a = 6, b = 12 and A = 63, hence
× h × (6 + 12) = 63
h × 18 = 63
9h = 63 ( divide both sides by 9 )
h = 7
When the penny hits the ground, h will = 0.
So: Set h(t) = 0 = -4.9t^2 + 0t + 150 m
Then 4.9t^2 = 150, and so t^2 = sqrt(150 / 4.9) = plus or minus 5.53 sec.
We can use only the positive root, as we're measuring time.
t = 5.5 sec (answer)
A parabolic function's key characteristic is either having 2 x-intercepts or 2 y-intercepts. That is the reason why the standard form of parabolic functions are:
(x-h)^2 = +/- 4a(y-k) or (y-k)^2 = +/- 4a(x-h), where
(h,k) is the coordinates of the vertex
4a is the lactus rectum
a is the distance from the focus to the vertex
This is also called vertex form because the vertex (h,k) is grouped according to their variable.
Since we don't know any of those parameters, we'll just have to graph the data points given as shown in the picture. From this data alone, we can see that the parabola has two x-intercepts, x=-4 and x=-2. Since it has 2 roots, the parabola is a quadratic equation. Its equation should be
y = (x+4)(x+2)
Expanding the right side
y = x²+4x+2x+8
y = x²+6x+8
Rearrange the equation such that all x terms are on one side of the equation
x²+6x+___=y-8+___
The blank is designated for the missing terms to complete the square. Through completing the squares method, you can express the left side of the equation into (x-h)² form. This is done by taking the middle term, dividing it by two, and squaring it. So, (6/2)²=9. Therefore, you put 9 to the 2 blanks. The equation is unchanged because you add 9 to both sides of the equation.
The final equation is
x²+6x+9=y-8+9
(x+3)²=y+1
