Answer:
C
Step-by-step explanation:
3/4 of 1000 is 750 and 1/5 of 750 is 150 so your answer is C
The sum of b and f is b+f
Three times this sum is 3(b+f)
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: this is our required factor i.e.
Explanation:
Since we have given that
As we know the identity , which says that
So, we can use this here ,
Hence this is our required factor i.e.
Answer:
Increase
Step-by-step explanation:
The researcher records the following estimates: 450, 426, 310, 500, and 220.
The mean of these estimates is derived below.
Mean = (450+426+310+500+220)/5
=1906/5=381.2
If the researcher removes the estimate of 220.
The mean of the other numbers will be:
Mean =(450+426+310+500)/4
=1686/4=421.5
By comparison of the two mean, we can see that the value of the mean will increase.
