Answer:
11 quarters
Step-by-step explanation:
If Thomas ignores the extra 3 dimes, he can arrange his coins in groups of 3 dimes and 1 quarter, each group valued at 55¢. It takes
... 6.05/0.55 = 11
groups to bring the total value to the $6.05 remaining after ignoring the extra dimes.
Thomas has 11 quarters and 36 dimes.
<span>
The good answer is 9
(9:9=1 and 27:9=3)</span>
Divergence is easier to compute:
Curl is a bit more tedious. Denote by 
the differential operator, namely the derivative with respect to the variable 
. Then
![\mathrm{curl}\vec F=\left(D_y\left[y\tan^{-1}\dfrac xz\right]-D_z\left[e^{xy}\sin z\right]\right)\,\vec\imath-D_x\left[y\tan^{-1}\dfrac xz\right]\,\vec\jmath+D_x\left[e^{xy}\sin z}\right]\,\vec k](https://tex.z-dn.net/?f=%5Cmathrm%7Bcurl%7D%5Cvec%20F%3D%5Cleft%28D_y%5Cleft%5By%5Ctan%5E%7B-1%7D%5Cdfrac%20xz%5Cright%5D-D_z%5Cleft%5Be%5E%7Bxy%7D%5Csin%20z%5Cright%5D%5Cright%29%5C%2C%5Cvec%5Cimath-D_x%5Cleft%5By%5Ctan%5E%7B-1%7D%5Cdfrac%20xz%5Cright%5D%5C%2C%5Cvec%5Cjmath%2BD_x%5Cleft%5Be%5E%7Bxy%7D%5Csin%20z%7D%5Cright%5D%5C%2C%5Cvec%20k)
Answer:
If you've learnt sin(A+B) = sinAcosB + cosAsinB,
sin(4u)
= sin(2u+2u)
= sin(2u)cos(2u) + cos(2u)sin(2u)
= 2 sin(2u) cos(2u).
