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
Answer:
5) C pink 6) A -1/2x + 1/4 7) D z ≥ 0
Step-by-step explanation:
5) White 1/6 = 4/24
Green 1/3 = 8/24
Pink 1/8 = 3/24
Yellow 3/8 = 9/24
6) 11/2x - 2(3x - 1/8) Distribute the -2
11/2x - 6x + 1/4 Combine like terms
-1/2x + 1/4
7) z ≥ 0
z is greater than or equal to 0
Answer:
The original price of the pants was $30.
Step-by-step explanation:
Let x be equal to the original price of the pants.
Because the pants are 40% off, their final price was 60% of the original price. 60% as a decimal is 0.6. Using this information, we can set up the following equation and solve:
0.6x=18
Divide both sides by 0.6
0.6x/0.6=18/0.6
x=30
I hope this helps!
12 miles/ 4mph = 3 hours
in min = 180
hope that helps
Answer:
8persons/group
Step-by-step explanation:
Give parameters:
Number fourth graders = 24
Number of groups = 3 groups
Unknown:
Number of students in each group = ?
Solution:
Solving this problem involves finding the number of persons per group.
Number of persons per group = 
Insert the parameters and solve;
Number of persons per group = 
= 8persons/group
