Angela has 15 chocolate cookies. She eats 6 of them, then goes to the store and buys 1 more. How many cookies does Angela have n
1 answer:
You might be interested in
One complete revolution of the minute hand sweeps a central angle of 360° which is equivalent to 60 minutes.
That is, the minute hand creates
(360°/(60 min) = 6 degrees/min.
From 3:35 to 3:55 is 20 minutes.
It sweeps a central angle of
(20 min)*(6 deg/min) = 120°
Because 360° = 2π radians,
120° = (120/360)*2π = (2π)/3 radians
Answer:
In decimals, this is 2.1 radians (nearest tenth)
Part 2:
Because the minute hand is 4 inches long, the length of the arc swept is
(4 in)*(2π/3 radians) = 8π/3 inches
Answer:
In decimals, this is 8.4 inches (nearest tenth).
That is, the minute hand creates
(360°/(60 min) = 6 degrees/min.
From 3:35 to 3:55 is 20 minutes.
It sweeps a central angle of
(20 min)*(6 deg/min) = 120°
Because 360° = 2π radians,
120° = (120/360)*2π = (2π)/3 radians
Answer:
In decimals, this is 2.1 radians (nearest tenth)
Part 2:
Because the minute hand is 4 inches long, the length of the arc swept is
(4 in)*(2π/3 radians) = 8π/3 inches
Answer:
In decimals, this is 8.4 inches (nearest tenth).
The distance between a point 
on the given plane and the point (0, 2, 4) is
but since
and 
share critical points, we can instead consider the problem of optimizing subject to 
.
The Lagrangian is
with partial derivatives (set equal to 0)
Solve for
:
which gives the critical point
We can confirm that this is a minimum by checking the Hessian matrix of:
is positive definite (we see its determinant and the determinants of its leading principal minors are positive), which indicates that there is a minimum at this critical point.
At this point, we get a distance from (0, 2, 4) of
but since
The Lagrangian is
with partial derivatives (set equal to 0)
Solve for
which gives the critical point
We can confirm that this is a minimum by checking the Hessian matrix of
At this point, we get a distance from (0, 2, 4) of