Answer:
The domain of the function is:
Step-by-step explanation:
Given the function
We know that the domain of a function is the set of input or argument values for which the function is real and defined.
From the function, it is clear that for the values x<-5, the function becomes undefined.
For example, for x=-6
√x+5 = √-6+5 = √-1 which is undefined
and for x=-5
√x+5 = √5+5 = √0 which is defined
Thus, the domain of the function is:
<h2>
Rewriting Words as Equations</h2>
To rewrite a word equation as a numerical equation, we can recognize certain keywords and change them into numbers or operations.
- <em>twice</em> = multiply by 2
- <em>difference</em> = subtract
- <em>'a number'</em> = let this be <em>x</em>
- <em>is</em> = equals
<h2>Solving the Question</h2>
We're given:
- Twice the difference of a number and 6 is 5
⇒ twice = (2 ×)
⇒ difference of a number and 6 = (x - 6)
⇒ is 5 = ( = 5)
To solve for <em>x</em>, isolate the variable:
2(x-6) = 5
2x-12 = 5
2x = 17
x = 
<h2>Answer</h2>
Explanation:
Differentiating the solution, we have ...
y' = c1 +8c2x^7
y'' = 56c2x^6
Putting this into the DE, we have ...
x^2y'' -8xy' +8y = 16 . . . . . . . different from your problem statement
x^2(56c2x^6) -8x(c1 +8c2x^7) +8(c1x +c2x^8 +2) = 16
56c2x^8 -8c1x -64c2x^8 +8c1x +8c2x^8 +16 = 16
x^8(56c2 -64c2 +8c2) +x(-8c1 +8c1) +16 = 16
0 +16 = 16 . . . . QED
