Answer:
Right triangle
Step-by-step explanation:
Using pythagorean theorem,
Hence satisfied. So it is right triangle.
Which function rule best models the data in the table. X: 0,1,2,3 y: 3,4,7,12
1 answer:
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Answer:
a) , b)
, c)
,
.
Step-by-step explanation:
a) The function in terms of time and the inital angle measured from the horizontal is:
The particular expression for the cannonball is:
b) The components of the position of the cannonball before hitting the ground is:
After a quick substitution and some algebraic and trigonometric handling, the following expression is found:
The angle for a maximum horizontal distance is determined by deriving the function, equalizing the resulting formula to zero and finding the angle:
Now, it is required to demonstrate that critical point leads to a maximum. The second derivative is:
Which demonstrates the existence of the maximum associated with the critical point found before.
c) The equation for the vertical component of position is:
The maximum height can be found by deriving the previous expression, which is equalized to zero and critical values are found afterwards:
Now, the second derivative is used to check if such solution leads to a maximum:
Which demonstrates the assumption.
The maximum height reached by the cannonball is:
Vertex form of a quadratic equation is 
where (h, k) is the vertex.
Our aim is to write the expression
in the form
where (h, k) is the vertex.
Our aim is to write the expression