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:
the slope is 1
Step-by-step explanation:
She has 648 shirts.
Work:
Lisa has 42 pineapples. 4 + 2 = 6
Johnny has 6 marbles.
42 + 4 + 2 + 6 = 54
54 + 5 + 4 = 63
63 + 6 + 3 = 72
But 72 is a multiple of 6!
Let's go further:
72 * 6 = 432
Now let's look at the word 'shirt'.
The middle letter is I.
I is the 9th letter of the alphabet.
Remember the number 72?
72*9 = 648
Answer:
<u>x = 8/23</u>
Step-by-step explanation:
<u>Adding 3.5 to each side</u>
- -3.5 + 3.5 = -4.6x - 5.1 + 3.5
- -4.6x - 1.6 = 0
<u>Adding 4.6x to each side</u>
- -4.6x - 1.6 + 4.6x = 0 + 4.6x
- 4.6x = -1.6
<u>Dividing each side by 4.6</u>
- 4.6x/4.6 = -1.6/4.6
- <u>x = 8/23</u>