Write the value of 4 in 305,444
2 answers:
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Answer: The function is .
Explanation:
It is given that Michael Daniels, is standing on his own 10-yard line. He throws a pass toward the opposite goal line. The football is 2 yards above the ground when the quarterback lets it go.
It follows a parabolic path. Reaching its highest point, 30 yards above the ground. It is caught 50 yards downfield at a point 2 yards above the ground.
So, the initial point is (10,2) and the other point is (60,2).
The height function of a football represents a downward parabola. The maximum point of the function is called vertex. So the vertex is (h,30).
The two point (10,2) and (60,2) have same y-coordinate, therefore the function is maximum at the midpoint of both points.
So, the function is maximum at x=35. Hence the vertex is (35,30)
The standard form of the parabola is,
Where (h,k) is vertex and a is scale factor.
Since vertex is (35,30).
The initial point is (10,2).
So the function of height is.
The graph of the function is shown below.
The volume of cone is 75.4 cubic centimeters and the volume of cylinder is 197.92 cubic centimeters. The volume of composite figure is 273.32 cubic centimeters.
Step-by-step explanation:
The given is,
Composite figure made of a cone and a cylinder.
A cone has a height of 8 centimeters and radius of 3 centimeters.
A cylinder has a height of 7 centimeters and radius of 3 centimeters.
Step:1
Volume of composite figure = Volume of Cone +
Volume of cylinder............(1)
Step:2
Formula for volume of cone,
....................(2)
Where, r - Radius of cone
h - Height of cone
From the given,
r = 3 centimeters
h = 8 centimeters
Equation (2) becomes,
= (3.14 × 9 × 2.667) (∵ = 3.1415)
= 75.4
= 75.4 cubic centimeters
Step:3
Formula for volume of cylinder,
....................(2)
Where, r - Radius of cylinder
h - Height of cylinder
From the given,
r = 3 centimeters
h = 7 centimeters
Equation (2) becomes,
= (3.14 × 9 × 7) (∵ = 3.1415)
= 197.92
= 197.92 cubic centimeters
Step:4
Equation (1) becomes,
Volume of composite figure = 75.4 + 197.92
= 273.32 cubic centimeters
Result:
The volume of cone is 75.4 cubic centimeters and the volume of cylinder is 197.92 cubic centimeters. The volume of composite figure is 273.32 cubic centimeters.