If anything is not clear, just ask me.
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
M can be any positive real number.
Explanation:
From f(x) = √(mx) ; if x is posive m has to be positive; if x is negative m has to be negative; if x is cero m can have any value, and the range will always be 0 or positve
From g(x) = m √x; x can only be 0 or positive and the range will have the sign of m.
Given we concluded that the range of f(x) can only be 0 or positive, then me can only be 0 or positive.
Answer: (60.858, 69.142)
Step-by-step explanation:
The formula to find the confidence interval for mean :
, where 
is the sample mean , 
is the population standard deviation , n is the sample size and 
is the two-tailed test value for z.
Let x represents the time taken to mail products for all orders received at the office of this company.
As per given , we have
Confidence level : 95%
n= 62
sample mean : 
hours
Population standard deviation : 
hours
z-value for 93% confidence interval: 
[using z-value table]
Now, 93% confidence the mean time taken to mail products for all orders received at the office of this company :-
Thus , 93% confidence the mean time taken to mail products for all orders received at the office of this company : (60.858, 69.142)
Answer:
a. 15/23
b. 13/27
c. 400g
Step-by-step explanation:
a. When the denominators are the same, you can just sum the numerators.
Which becomes, 13+2=15--> 15/23
b. Same, when the denominator is the same, you can just minus the numerators. Which becomes, 25-12=13--> 13/27
c. 1kg=1000g. 1000/5=200✖️2=400
