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
Hopes this if it doesn’t I any so sorry if I got it wrong:
Answer: 6561
Answer:
50% pen first box and 62.5% crayon from second box
Step-by-step explanation:
The first box contains 4 items, 2 of each. This means there are 
pens. This gives you a chance of picking out a pen. This can be written as 50%.
The second box contains 8 items, 3 color pencils and 5 crayons. This means 
of the contents are crayons, meaning you have a or 62.5% chance of picking a crayon.
*For working out the percentages, you should convert the fraction to a decimal and then multiply that by 100.
**This content involves fractions, decimals and percentages, as well as basic probability, which you may want to revise. I'm always happy to help!
It will be six laps because 8 times three equal 24 and 2 laps in 8 minutes each 8 min will be two so 2 times three equal six
Step-by-step explanation:
2 days= 24 hours in 1 day, so multiply that by 2 to get 48 hours total.
Now find the amount of time the wild fire doubles by dividing 48 total hours by 6. So it will double 8 times
The size was 1 acre. Let's multiply by 2, 8 times
1
2
4
8
16
32
64
128
The fire will cover 128 acres in two days.
