Answer:
(A) with .
(B) with
(C) with
(D) with ,
Step-by-step explanation
(A) We can see this as separation of variables or just a linear ODE of first grade, then . With this answer we see that the set of solutions of the ODE form a vector space over, where vectors are of the form with real.
(B) Proceeding and the previous item, we obtain . Which is not a vector space with the usual operations (this is because ), in other words, if you sum two solutions you don't obtain a solution.
(C) This is a linear ODE of second grade, then if we set and we obtain the characteristic equation and then the general solution is with , and as in the first items the set of solutions form a vector space.
(D) Using C, let be we obtain that it must satisfies and then the general solution is with , and as in (B) the set of solutions does not form a vector space (same reason! as in (B)).
9514 1404 393
Answer:
3) y = √10
4) x = 5√2
Step-by-step explanation:
The side ratios of an isosceles right triangle (one of the "special" right triangles) are ...
1 : 1 : √2
So, for some multiplier k, they can be made to match the sides in your triangles.
__
3) 1·k : 1·k : k√2 = √5 : √5 : y
Clearly, k = √5, so ...
y = (√5)(√2)
y = √10
__
4) k : k : k√2 = x : x : 10
k = 10/√2 = (5√2)/2
k = x = (5√2)/2
Ok so what is 2 times 25...
50
and 50 - 9 is 41
So 41 is our answer
Answer:
The submarine will be 300 feet below sea level.
Step-by-step explanation:
If a submarine rises while underwater, then the feet below sea level will decrease.
So the submarine is at 400 feet below sea level, and if it rises 100 feat, then it will be x feet below sea level.
Lets put this into an equation: 400 - 100 = x
Now solve for the equation:
400 - 100 = x
x = 300
The submarine will be 300 feet below sea level.