Answer:
i) $500 at 5% simple interest for two years. Interest = 550 - 500 = $50
ii) $500 at 3% compounded monthly for 2 years.
Interest = 530.88 - 500 = $30.88
Step-by-step explanation:
i) $500 at 5% simple interest for two years.
Initial amount, P = $ 500
Rate of interest, r = 0.05
Time in years, t = 2
Therefore Final amount A = P(1 + rt) = 500(1 + (0.05 
2) ) = $550
Therefore Interest = 550 - 500 = $50
ii) $500 at 3% compounded monthly for 2 years
Initial or Principal Amount, P = $500
Rate of interest, r =0.03
number of conversions, m = 12
Time in years, t = 3
Therefore final amount, 
= $530.88
Therefore Interest = 530.88 - 500 = $30.88
Answer:
C.
Step-by-step explanation:
10 cups divided by 4 containers = 2.5 or 5/2 cups per 1 container
Since there are 63 people divided into 3 sections, you could write 63÷3 for your division sentence.
Answer:
$107.38
Step-by-step explanation:
$91 (the price) multiplied by the percentage 18% (91 x 18 = 1630) (1638/100=16.38 [the tip})
$91 (th original price) + 15.38 (the tip) = $108.38 (final price)
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 :)
