Answer:
2.75 seconds and 133 feet
Step-by-step explanation:
We require to find the coordinates of the vertex of the parabola
the t coordinate ( time ) for a quadratic in standard form is
= -
with a = - 16 and b = 88
t = - = 2.75 seconds ← time taken to reach max
to find the max height evaluate f(2.75 )
f(2.75 ) = - 16( 2.75)² + 88(2.75) + 12 = - 121 + 242 + 12 = 133 feet
Answer:
693 sq. m.
Step-by-step explanation:
The figure consists of a triangular prism (Bottom Part) and a Triangular Pyramid (Top Part). We will find the volume of each and add it up to get volume of total figure.
1. Volume of Triangular Prism = Area of Triangular Base * Height
Area of Triangular Base = (1/2)*base*height
Given that the triangle is a right triangle, we find the unknown side by using Pythagorean Theorem, which tells us:
Leg^2 + Another Leg^2 = Hypotenuse^2
8.8^2 + Another Leg^2 = 13.7^2
77.44+ Another Leg^2 = 187.69
Another Leg (unknown side, or the base of the triangle) = Sqrt(187.69-77.44) = 10.5 (this is base of triangle)
So, we have:
Area of Triangular Base =
Thus,
Volume of Triangular Prism = 46.2 * 10(given) = 462 sq.m.
2. Volume of Triangular Pyramid = (1/3) * area of triangular base * height
Here, area of triangular pyramid is 46.2 (already found)
the height of the pyramid is 25 - 10 = 15
SO, we have:
Volume of Triangular Pyramid = sq. m.
Now we sum them up and get total volume of the figure:
Total Volume of Figure = 462+ 231 = 693 sq. m.
