Answer/Step-by-step explanation:
Part A:
![Key:\left[1 Adult = 4 Student]](https://tex.z-dn.net/?f=Key%3A%5Cleft%5B1%20Adult%20%3D%204%20Student%5D)

<u> 12 Student = 3 Adult</u>
<u>24 Student = 6 Adult</u>
<u>40 Student = 10 Adult</u>
Part B:
33 Student
Hence, divide 33 by 4 = 8 with a remainder of 1.
Therefore, 8 Adult and for the remainder 1 student either one Adult takes 5 Student or Needed 9 Adult.
The critical points of <em>h(x,y)</em> occur wherever its partial derivatives
and
vanish simultaneously. We have

Substitute <em>y</em> in the second equation and solve for <em>x</em>, then for <em>y</em> :

This is to say there are two critical points,

To classify these critical points, we carry out the second partial derivative test. <em>h(x,y)</em> has Hessian

whose determinant is
. Now,
• if the Hessian determinant is negative at a given critical point, then you have a saddle point
• if both the determinant and
are positive at the point, then it's a local minimum
• if the determinant is positive and
is negative, then it's a local maximum
• otherwise the test fails
We have

while

So, we end up with

Square root of 6 times 16 will give us 39.19
The square root of 48 times 32 [which gives us 1536] is also equal to 39.19
The square root of 1536 is equal to 39.19
Hence, x is equal to 32
Hope this helped! :D
The answer should be b=111
Since there is a common difference of one, this is an arithmetic sequence of the form a(n)=a+d(n-1) which in this case is:
a(n)=15+1(n-1)
All arithmetic sequences have a sum which is equal to the average of the first and last terms time the number of terms, mathematically:
s(n)=(2an+dn^2-dn)/2 (that is just the result of ((a+a+d(n-1))(n/2)) )
Since a=15 and d=1 this becomes:
s(n)=(30n+n^2-n)/2
s(n)=(n^2+29n)/2 so
s(10)=(100+290)/2
s(10)=195 logs