Answer:
1120
Step-by-step explanation:
To find the possible number of steak dinners, you would multiply the number of choices for each part of the dinner. You would used combinations instead of permutations since the order of the toppings chosen or side dishes chosen do not matter. There are 5 choose 1 choices for types of steak, which is just 5. There are 8 choose 3 choices for side dishes, which is 56. There are 4 choose 3 choices for toppings, which is 4. 5*56*4 is 1120, so there are 1120 possible steak dinners.
I believe the answer is 275 miles. Hope this helps!
I hope this helps you
Area =3/4.5/12
Area =5/4.4
Area =5/16
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
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