Answer: Associative property
Step-by-step explanation:
Answer:-44
Step-by-step explanation:
-16-(28)=-44
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
The common rule is (x - 1, y + 3) can be used to describe the translation.
Step-by-step explanation:
Step 1:
The point J (-3, -4) becomes 
(-4, -1).
In order to write the rule for translation from J to , we subtract the x coordinate of J from and subtract the y coordinate of J from .
The x coordinate 
The y coordinate 
Step 2:
So from the calculations, we get that the x coordinate is subtracted by 1 i.e. 
and the y coordinate is increased by 3 i.e. 
.
So the common rule is (x - 1, y + 3).
