Answer:
(d) The functions are not inverses because for each ordered pair (x, y) for one function, there is no corresponding ordered pair (y, x) for the other function.
Step-by-step explanation:
If functions are represented by a table of ordered pairs, their inverse function is the set of ordered pairs with the x- and y-values swapped.
Here, for (x, y) = (0.75, 1038.18), the pair from the other table that begins to correspond is (y, x) = (0.75, 1057.81). These reversed pairs are not the same, so the functions are not inverses of each other.
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<em>Comment on the tables</em>
Table A is for a 5-year investment; table B is for a 7.5 year investment. They cannot be inverses of each other.
Answer:
(5h-4t)(5h+4t)
Step-by-step explanation:
25h² - 16t²
adding and subtracting 20ht from it (√25 and √16 = 5x4 = 20):
25h² + 20ht - 20ht -16t²
factor:
(5h-4t)(5h+4t)
Answer:
y=-2/5x-3
Step-by-step explanation:
the slope is m and the y intercept is b
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)).
