I couldn't solve the following questions? Please help.?

Question

1. Students of a class are made to stand in rows. If 4 students are extra in a row, there would be two rows less. If 4 students are less in a row, there would be 4 more rows. find the number of students in the class.
2. The interior angles of a polygon are in arithmetic progression. The smallest ange is 52 and the common difference is 8. Find the number of sides of teh polygon.
3. If x/a cos + y/b sin = 1 and x/a sin -y/b cos = 1, prove that x2/a2 + y2/a2 = 2. (x square divided by a square)

Answer 1

1. Let s - number of students in a row originally, r - number of rows
then sr is the total no. of students
If s + 4 per row, then r - 2 rows and (s + 4)(r - 2) = sr
If s - 4 per row, then r + 4 rows and (s - 4)(r + 4) = sr
Simplify:
(s + 4)(r - 2) = sr .......... sr - 2s + 4r - 8 = sr .......... -2s + 4r - 8 = 0
(s - 4)(r + 4) = sr .......... sr + 4s - 4r - 16 = sr ......... 4s - 4r -16 = 0
................................................................................... 2s - 24 = 0
s = 12 and r = 8 and sr = 96 (total no. of students)

2. Let n = number of terms/sides/angles
a1 = 52, d = 8
Sum of an arithmetic progression
Sn = n [ 2a1 + d(n - 1)] / 2
The sum of the angles is
Sn = n [ 104 + 8(n - 1)] / 2 = 52n + 4n^2 - 4n = 4n^2 + 48n
The sum of angles with n sides is defined as
Sn = 180(n-2) = 180n - 360
Equating the two:
4n^2 + 48n = 180n -360
Simplify and solve:
4n^2 - 132n + 360 = 0
n^2 - 33n + 90 = 0
(n - 3)(n - 30) = 0
n = 3 sides or 30 sides

3. [ x/a cos + y/b sin = 1 ] ^ 2
....[ x/a cos - y/b sin = 1 ] ^ 2

x^2 / a^2 cos^2 + y^2 / b^2 sin^2 + 2xy/ab sin cos = 1
x^2 / a^2 sin^2 + y^2 / b^2 cos^2 - 2xy/ab sin cos = 1

Adding the two equations:
x^2 / a^2 cos^2 + x^2 / a^2 sin^2 + y^2 / b^2 sin^2 + y^2 / b^2 cos^2 = 2
x^2 / a^2 (cos^2 + sin^2) + y^2 / b^2 (cos^2 + sin^2) = 2
x^2 / a^2 + y^2 / b^2 = 2

It's good that I finished first!!!

Answer 2

Only answering the first, partially: I am not here to do your home work.
The problem with these problems is usually to put the text into equations:
1st sentence: students in rows make a class:
Xstudendperrow * Yrows = Nstudents
-> x * y = N
2nd sentence: 4 more students, two rows less:
(Xstudentsperrow + 4) * (Yrows - 2) = Nstudents
-> (x + 4) * (y - 2) = N
3rd sentence: 4 less students, 4 more rows.
(Xstudentsperrow - 4) * (Yrows + 4) = Nstudents
-> (x - 4) * (y + 4) = N
You now have a system of three equations. Easy to solve.

Second question:
Start with the exterior angles of the polygon! Their sum is always 360 degrees. So the first external angle is 180 - 52 = 128.
Repeat Subtracting 8 degrees from 128 until the sum of the external angles reaches 360: you have the number of sides.
(BTW it is a triangle 128 + 120 + 118 = 360).

Third question:
x / a sin... what? sin(x), sin (a)?

Answer 3

answers
1)) Let's call n number of raws and p number of persons in a raw
the total in the class is T = np
Also we have
T= (n-2) (p+4)
T = (n+4) (p-4)
So :
np +4n-2p -8 = np
np = np -4n+4p-16
4n-2p = 8
2n-p = 4
p-n = 4
so in adding the 2 equations :
n= 8 number of raws
p = 12 number of children by raw
so the total is 96

2)) the sum of interior angles of a polygon is :
(n-2) 180
And the sum of angles is :
= 52 *n +8 n (n-1)/2
so n²-33n +90 = 0
(n-3) (n-30) = 0
so a polygone with 3 (troaangle) or 30 sides

3)) elevate on square the 2 equations then add them :
x²/a² cos²+y²/b² sin² + 2 x/a y/b cossin = 1
x²/a² sin²+y²/b² cos² - 2 x/a y/b cossin = 1
as cos²+sin² = 1
x²/a²+y²/b² = 2

Answer 4

i think of you're asserting its a real angled triangle. you need to first attempt to entice out the triangle with a real attitude(the hint) then label the splendid label (A, B and C). In those type of question, utilising SIN rule is incredibly effective, the place: SinA/a = SinB/b For the 1st question i did for you, and that i'm getting C= 24º42' b= 80 5.23 a= ninety 3.80 one attempt with different question if my solutions are superb. I do only, ought to have some calculation concern. yet following my approach would be clever for distinctive those question. good success peeps

Answer 5

96 total number of student
12 students in each row
8 number of rows


q2 hite sinx2 +cosx2 =1