If Siny = x Sin (a+y). Prove that
dy/dx=[Sin²(a+y)]/Sina​

Use Trigonometric formulae to simplify expressions

Step-by-step explanation:

Re-order to group the x and y,

Sin(y) / Sin(a+y) = x

to differentiate apply d/dx to both sides

Sin(y) / Sin(a+y) = x

use division rule on left side which will give

Cos(y)Sin(a+y) - Cos(a+y)Sin(y) / Sin²(a+y) = 1

Group them so dy/dx is on the left hand side:

= Sin²(a+y) / Cos(y)Sin(a+y) - Cos(a+y)Sin(y)

Apply trigonometric sum formula to expand Sin(a+y) and Cos(a+y),

=  Sin²(a+y) / Cos(y)[Sin(a)Cos(y) + Cos(a)Sin(y)] - Sin(y)[Cos(a)Cos(y) - Sin(a)Sin(y)]

Simplify it

= Sin²(a+y) / (Cos²(y) + Sin²(y))(Sin(a))

= Sin²(a+y) / (1)(Sin(a))

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

$2416.6

step-by-step explanation:

per hour = $ 25

total work time = 35

commission = 15%

total she has to make = $ 4,500

let she sold x dollar products

so her commission will be 15 % of x

now

total = weekly basic pay + commission

4500= (25*35) + 15 % of x

4500=875 + * x

4500-875 =   * x

3625= * x

multiplying wwith 100 on both sides gives

36250 = 15 x

now

x =  

x= $2416.6