b. Carlos monthly office supply budget is $250. He needs to buy ink cartridges which cost $40 a piece. He will need to save at l
1 answer:
ANSWER
Find out the what is the range of ink cartridges he can buy and still have enough money left over for the reams of paper.
To proof
let us assume that the number of the ink cartridges buy be x.
As given
Carlos monthly office supply budget is $250.
He needs to buy ink cartridges which cost $40 a piece.
He will need to save at least $50 of his budget for reams of paper.
than the inequality is written in the form
x ≤ 5
the range of the ink cartridges he can buy be 0 ≤ x ≤ 5 when he saves
at least $50 of his budget for reams of paper.
Hence proved
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Answer: Hello mate!
Clairaut’s Theorem says that if you have a function f(x,y) that have defined and continuous second partial derivates in (ai, bj) ∈ A
for all the elements in A, the, for all the elements on A you get:
This says that is the same taking first a partial derivate with respect to x and then a partial derivate with respect to y, that taking first the partial derivate with respect to y and after that the one with respect to x.
Now our function is u(x,y) = tan (2x + 3y), and want to verify the theorem for this, so lets see the partial derivates of u. For the derivates you could use tables, for example, using that:
and now lets derivate this with respect to y.
using that
Now if we first derivate by y, we get:
and now we derivate by x:
the mixed partial derivates are equal :)