<span>y=4x-6
y=-4x+48
</span>4x-6= -4x+48
<span>0x=54
x=o</span>
Let
. Then
and
are two fundamental, linearly independent solution that satisfy
Note that
, so that
. Adding
doesn't change this, since
.
So if we suppose
then substituting
would give
To make sure everything cancels out, multiply the second degree term by
, so that
Then if
, we get
as desired. So one possible ODE would be
(See "Euler-Cauchy equation" for more info)
Let's make things easier by simplifying things.
y = 8 and x = 3 is more likely to be understood as a ratio. So for the rest of the answer, their relationship would be represented as y:x
Thus: y:x = 8:3
The problem would be finding y when x = 45
Let us proceed on using the previous equation and substitute x with 45 which would look like this:
y:45 = 8:3
Ratios can also be expressed as fractions which would make things more understandable and easy to solve. So the new form of our equation would be like this:
y/45 = 8/3
Then we proceed with a cross multiplication where the equation becomes like as what is shown below:
3y = 45 * 8
From there, you can solve it by multiplying 45 and 8 then dividing the product with 3 to get y
3y = 360
y = 120
Another way of looking at the problem, especially problems like these, is to take the whole question or statement as an equation. it would probably look like this:
y = 8 when x = 3 : y = ? when x = 45
This would make you understand what approach you can use to solve the given problem.
Answer:
A)
Step-by-step explanation:
-6x - 9/2
First convert the terms to fractional exponents
u = t^2/3 - 3t^3/2
differentiating
u' = 2/3 t^ (2/3 - 1) - 3* 3/2 t^(3/2 - 1)
= 2/3 t ^(-1/3) - 9/2 t ^(1/2)
= 2 / (3∛t) - 9 √ t / 2 in radical form
