PLEEASEEE HELP ME NOONE WILL HELP ME PLEASE HELP ME
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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 :)
Answer: a) 15 b)
Step-by-step explanation:
Let X be the number of days:
a)
For LESSONS:
Jordan does 10 / day ( 10*X)
Marco 5 / day ( 5*X)
Junyi 5 / day ( 5*X)
For TESTS:
Jordan does 5 / day ( 5*X)
Marco 10 / day ( 10*X)
Junyi 8 / day ( 8*X)
for each they need a total of 300
a) days for the lessons
b) days for the tests
so they need 15 days to finish both tasks
now if Junyi gets sick we just eliminate his contribution
a) days for the lessons
b) days for the tests
so in 20 days they will finish without him
If jordan works 10 hours a day, we just replace him with 10/24
a) days for the lessons
b) days for the tests
so at the end to complete both tasks they need 29.58 days