Answer:
y = 3sin2t/2 - 3cos2t/4t + C/t
Step-by-step explanation:
The differential equation y' + 1/t y = 3 cos(2t) is a first order differential equation in the form y'+p(t)y = q(t) with integrating factor I = e^∫p(t)dt
Comparing the standard form with the given differential equation.
p(t) = 1/t and q(t) = 3cos(2t)
I = e^∫1/tdt
I = e^ln(t)
I = t
The general solution for first a first order DE is expressed as;
y×I = ∫q(t)Idt + C where I is the integrating factor and C is the constant of integration.
yt = ∫t(3cos2t)dt
yt = 3∫t(cos2t)dt ...... 1
Integrating ∫t(cos2t)dt using integration by part.
Let u = t, dv = cos2tdt
du/dt = 1; du = dt
v = ∫(cos2t)dt
v = sin2t/2
∫t(cos2t)dt = t(sin2t/2) + ∫(sin2t)/2dt
= tsin2t/2 - cos2t/4 ..... 2
Substituting equation 2 into 1
yt = 3(tsin2t/2 - cos2t/4) + C
Divide through by t
y = 3sin2t/2 - 3cos2t/4t + C/t
Hence the general solution to the ODE is y = 3sin2t/2 - 3cos2t/4t + C/t
Distance = speed x time
time = distance/speed
= 340/85
= 4h
The first one, the six is in the one's place. the second on the six is in the tenths place.
Answer:
$41.25
Step-by-step explanation:
We can use this formula to solve this problem:
s
=
p
−
(
d
×
p
)
Where:
s
is the sales price: what we are solving for in this problem.
p
is the original price: $55 for this problem.
d
is the discount rate: 25% for this problem. "Percent" or "%" means "out of 100" or "per 100", Therefore 25% can be written as
25
100
.
Substituting and calculating
s
gives:
s
=
$
55
−
(
25
100
×
$
55
)
s
=
$
55
−
$
1375
100
s
=
$
55
−
$
13.75
s
=
$
41.25
