Answer:
2 5/12
Step-by-step explanation:
8 5/6 + 2 3/4 = 8 10/12 + 2 9/12 = 10 19/12 = 10 + 1 7/12 = 11 7/12
13 12/12 - 11 7/12 = 2 5/12
Answer:
We have to prove
sin(α+β)-sin(α-β)=2 cos α sin β
We will take the left hand side to prove it equal to right hand side
So,
=sin(α+β)-sin(α-β) Eqn 1
We will use the following identities:
sin(α+β)=sin α cos β+cos α sin β
and
sin(α-β)=sin α cos β-cos α sin β
Putting the identities in eqn 1
=sin(α+β)-sin(α-β)
=[ sin α cos β+cos α sin β ]-[sin α cos β-cos α sin β ]
=sin α cos β+cos α sin β- sinα cos β+cos α sin β
sinα cosβ will be cancelled.
=cos α sin β+ cos α sin β
=2 cos α sin β
Hence,
sin(α+β)-sin(α-β)=2 cos α sin β
Answer:
x1=-2, x2=2
Step-by-step explanation:
Answer:the price of one senior citizen's ticket is $4
the price of one student ticket is $10
Step-by-step explanation:
Let x represent the price of one senior citizen's ticket
Let y represent the price of one student ticket.
On the first day of ticket sales the school sold 6 senior citizen tickets and 10 student tickets for a total of $124. This means that
6x + 10y = 124 - - - - - - - - - - 1
The school took in 98 on the second day by selling 12 senior citizen tickets and 5 student tickets. This means that
12x + 5y = 98 - - - - - - - - - - - 2
Multiplying equation 1 by 2 and equation 2 by 1, it becomes
12x + 20y = 248
12x + 5y = 98
Subtracting, it becomes
15y = 150
y = 150/15 = 10
Substituting y = 10 into equation 1, it becomes
6x + 10 × 10= 124
6x + 100 = 124
6x = 124 - 100 = 24
x = 24/6 = 4
