Step-by-step explanation:
440÷100×12
52.8
440-52.8
387.2
MARK ME BRAINLIEST PLSSSSSS
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:
Number of trucks = 24
Number of SUVs = 24
Step-by-step explanation:
A)
The ratio of cars to trucks is 9:4
The total ratio of cars to trucks is
9+4 = 13
Let x = sum of cars and trucks.
There are 54 cars. Therefore,
x = 54 + t trucks
Number of cars = ratio of cars/ total ratio × sum of cars and trucks. This means,
54 = 9/13 × x
9x / 13 = 54
9x = 13 × 54
9x = 702
x = 702 / 9 = 78
x = 54 + t trucks = number of trucks = 78 = 54 + t trucks
t trucks = 78 - 54 = 24
Number of trucks = 24
B)
The ratio of trucks to SUVs is 12:21
The total ratio of cars to trucks is
12 + 21 = 33
Let y = sum of trucks and SUVs
There are 24 trucks. Therefore,
x = 24 + s SUVs
Number of trucks = ratio of trucks / total ratio × sum of trucks and SUVs. This means,
24 = 12 / 33 × y
12y / 33 = 24
12y = 24 × 33
12y = 792
y = 792 / 12 = 66
y = 24 + s SUVs
66 = 24 + s SUVs
s SUVs = 66 - 24 = 42
Number of SUVs = 24
Answer:
12,195.122
Step-by-step explanation:
there are 5 million people
there are also 410 square miles
the solution for this is 5,000,000÷ 410 which is 12,195.122 people p/sqrm
