Have a great day as well! sending good vibes your way <3
Answer:
y=t−1+ce
−t
where t=tanx.
Given, cos
2
x
dx
dy
+y=tanx
⇒
dx
dy
+ysec
2
x=tanxsec
2
x ....(1)
Here P=sec
2
x⇒∫PdP=∫sec
2
xdx=tanx
∴I.F.=e
tanx
Multiplying (1) by I.F. we get
e
tanx
dx
dy
+e
tanx
ysec
2
x=e
tanx
tanxsec
2
x
Integrating both sides, we get
ye
tanx
=∫e
tanx
.tanxsec
2
xdx
Put tanx=t⇒sec
2
xdx=dt
∴ye
t
=∫te
t
dt=e
t
(t−1)+c
⇒y=t−1+ce
−t
where t=tanx
Right now it is noon..... you are traveling 75 miles per hour meaning you'll move 75 miles... every hour. so you're 120 miles away so now we need to figure out the time.... to do this we already know 1 hour is 75 miles so now you can subtract one hour 120-75= 45 so 75 per hour, what would 45 be?..... so we can set up a fraction to figure out how long it takes to travel one minute.... so 60/75(the 60 is for minutes in an hour). which is .8 of a second to travel one mile so.... now you can multiply to check your work. .8*75=60 mins.... so now multiply.8*45(miles left)=36 so you'd get there at 1:36 it would take an hour and 36 mins to get to your destination going 75mph
If 1 inch = 2.5 yards then
x inch = 80 yards
cross multiplying we have:
80 × 1 = x × 2.5
x = 80÷ 2.5 = 32 inches
therefore the picnic area is 32 inches in the drawing.
