Step-by-step explanation:
If a cannonball is shot directly upward with a velocity of 160 ft per second. Its height as a function of time is given by :
.......(1)
t is in seconds
(a) Velocity is given by :
Acceleration is given by :
(b) For maximum height put
i.e.
Put t = 5 s in equation (1). So,
(c) When the ball reaches ground, its height is equal to 0. So,
h(t) = 0
Hence, this is the required solution.
has no antiderivative in terms of elementary functions (polynomials, exponentials, logarithms, trigonometric functions, etc), but there is a special function defined to fit that role called the error function,
, where
By the fundamental theorem of calculus, we can see that
which means we have
The distance between the points C(-3,1) and D(5,6) is 10.3 units.
<u>Step-by-step explanation:</u>
Let us consider CD is a line segment.
The point C is (-3,1) and D is (5,6).
The Cartesian formula for line is used to find the length between the CD.
Distance between two points = .
The points are (-3,1) and (5,6).
=.
=
=.
=.
=.
=10.295 ≈ 10.3.
Distance between two points 10.3 units.