9+10=?
9 = 3x3
10= 5x2
3 (from 3x3) x 5 (from 5x2) = 15
3 (from 3x3) x 2 (from 5x2) = 6
15+6=21
Therefore 9+10=21
Answer:
4.243
step by step explanation:
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:
Step-by-step explanation:
x = 2 is the equation of a vertical line passing through x = 2. This is shown in the lower left graph: a solid vertical line 2 units to the right of the y-axis.
Answer:
2x - 3y
Step-by-step explanation:
Distribute -1/4 to all the terms in the brackets.
-1/4(-8x) -1/4(12y)
2x - 3y
