That would be 1/4 divided by 1/2 = 1/2
Benjamin's cycling rate is 1/2 lap per hour
Volume of cylinder:
Formula: pi * r^2 * h
r = 2, h = 20
pi * 2^2 * 20
pi * 4 * 20 = 20pi
Solution: A
ANSWER
The circumcenter is (2,1)
EXPLANATION
The midpoint of BC is (-3,2)
The equation of the perpendicular bisector of BC is x=2
The midpoint of AB is (-1,1)
The midpoint of AB is (-1,1)
The perpendicular bisector of AB is y=1.
These two lines intersect at (2,1).
The point of intersection of the perpendicular bisectors of a triangle is called the circumcenter of the triangle.
The standard kinematics equation is for an object projected vertically is:
H(t)=H0+v0(t)+(1/2)at^2
H0=height at time 0
v0(t)=vertical velocity at time 0
a=acceleration [equals -g for gravity]
H(t) height of projectile at time t.
We're given
H0=2.5'
v0=45 '/s
a=-32.2 '/s^2
so the kinematics equation is
H(t)=2.5+45(t)+(1/2)(-32.2)t^2= 2.5+45t-16.1t^2
Solve for H(t)=5.5 using the quadratic formula:
H(t)=5.5= 2.5+45t-16.1t^2
t=0.0683 s [ on its way up ], or
t=2.727 s [caught on its way down]
Therefore the football was in the air for 2.727 seconds.