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
Hi there! To round 10.95 to the nearest tenth, we find the number in the tenth place, which is 9 and look one place to the right. Round up if the number is greater than 5 or equal to 5 and round down if its less than 5.
The answer is 11.0 or just 11.
<em>Ed: Explanation below.</em>
<em />
11.00
10.99
10.98
10.97
10.96
10.95 Look at the 9. Then look to the right. Do I round up or down?
10.94
10.93
10.92
10.91
10.90
If the number is greater or equal to 5, you round up. If the number is smaller than 5, you round down. 9 is greater than 5, so we round up.
Therefore, the answer is 11.
Answer:
The distance is 
or 
.
Step-by-step explanation:
Slope of parallel: 2
Slope of perpendicular: -1/2
Pick a point for y =2x + 7. For example (0,7)
Use the perpendicular slope to get to the other line to find the other point of y=2x-3. Look at the screenshot...I got (4,5).
Distance formula 
Insert (0,7) and (4,5)
= 
Answer:
c.1,2.3.5.7.11.13.17.19.23.29.31.37.41.43.47.53.59.61.67.71.73.79.83.89.97
d.no for example 9
e.no for example 2
f. 7,1,3,9
Step-by-step explanation:
