Answer:
3:15 pm
Step-by-step explanation:
You can imagine that they go in a circle (we can do whatever we want in theoretical math and physics). By doing so we know we can obtain a cosinusoidal wave by projecting the motion on a plane. Each one of the buses has a period (minimum time after what they're in the same point again). For the first one it's 15 minutes, for the second one it's 20 minutes. We have to take the least common multiple of the periods, that is 75 minutes. So They'll meet every 75 minutes. Add 75 minutes (1h and 15 minutes) to 2pm and there you go.
Answer:
-3m+2/3. 2/3 is a fraction
Step-by-step explanation:
Consider a circle with radius
centered at some point
on the
-axis. This circle has equation

Revolve the region bounded by this circle across the
-axis to get a torus. Using the shell method, the volume of the resulting torus is

where
.
So the volume is

Substitute

and the integral becomes

Notice that
is an odd function, so the integral over
is 0. This leaves us with

Write

so the volume is

For this case we have that the area is given by:
A = (w) * (l)
Where,
w: width
l: long
Substituting we have:
66 = (w) * (w + 5)
Rewriting
w ^ 2 + 5w - 66 = 0
(w + 11) * (w-6) = 0
Using the positive root we have:
w = 6
Answer:
the width of the frame is:
w = 6 cm