Answer:
Standard deviation of the length of granola bars produced at Bernie's Bars is 0.50
Step-by-step explanation:
We are given the following information in the question:
Formula:
where,
μ is the mean and σ is the standard deviation.
Putting the values we get:
Solving the two obtained equations:
Subtracting the two obtained equation, we have:
Hence, standard deviation of the length of granola bars produced at Bernie's Bars is 0.50
The perimeter of a rectangle is (2 lengths) plus (2 widths).
If one side is missing, then it sounds like you still have enough information
to know what the length and the width are. Just take each number and use
the first line up there /\ to calculate the perimeter with them.
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: please see the attachments for the solution.
Step-by-step explanation:
