Answer:
Step-by-step explanation:
Given is a differential equation as
![ty' + 6y = t^2 - t + 1, y(1) = 1 6 , t > 0](https://tex.z-dn.net/?f=ty%27%20%2B%206y%20%3D%20t%5E2%20-%20t%20%2B%201%2C%20y%281%29%20%3D%201%206%20%2C%20t%20%3E%200)
Divide this by t to get in linear form
![y'+6y/t = t-1+1/t](https://tex.z-dn.net/?f=y%27%2B6y%2Ft%20%3D%20t-1%2B1%2Ft)
This is of the form
y' +p(t) y = Q(t)
where p(t) = 1/t![e^(\int 1/tdt) = t](https://tex.z-dn.net/?f=e%5E%28%5Cint%201%2Ftdt%29%20%3D%20t)
So solution would be
![yt = \int t^2-t+1 dt\\= t^3/3-t^2/2+t+C](https://tex.z-dn.net/?f=yt%20%3D%20%5Cint%20t%5E2-t%2B1%20dt%5C%5C%3D%20t%5E3%2F3-t%5E2%2F2%2Bt%2BC)
siubstitute y(1) = 16
![16 = 16^3/3-128+1+C\\C = -1206](https://tex.z-dn.net/?f=16%20%3D%2016%5E3%2F3-128%2B1%2BC%5C%5CC%20%3D%20-1206)
Answer:
2.7 hours or 2 hrs, 42 min
Step-by-step explanation:
to find the total number of sentences remaining we can multiply 130 sentences times 20 pages remaining to get
2,600 sentences
if we divide that number by 16 we'll get the number of minutes he needs to finish the novel
2600/16 = 162.5 minutes which, when divided by 60, is 2 7/10 hours
7/10 = 42/60 so it comes out to 2.7 hours or 2 hrs, 42 min
I suppose the / are absolute value lines.... so ill answer it that way, -(-2) simplifies to 2. -/-2/ simplifies to -2
Ok, ranked by axis of symmetry
basically x=something is the axis of symmetry
the way to find the axis of symmetry is to convert to vertex form and find h and that's the axis of symmetry
but there's an easier way
for f(x)=ax^2+bx+c
the axis of symmetry is x=-b/2a
nice hack my teacher taught me
so
f(x)=3x^2+0x+0
axis of symmetry is -0/(3*2), so x=0 is the axis of symmetry for f(x)
g(x)=1x^2-4x+5,
axis of symmetry is -(-4)/(2*1)=4/2=2, x=2 is axis of symmetry for g(x)
h(x)=-2x^2+4x+1
axis of symmetry is -4/(2*-2)=-4/-4=1, x=1 is the axis of symmetry for h(x)
0<1<2
axisies
f(x)<h(x)<g(x)
order based on their axises of symmetry is f(x), h(x), g(x)
Answer:
9/4<x≤4 or all real numbers
Step-by-step explanation:
I'm not sure what you are asking