Answer:
24 premium tickets were sold.
Step-by-step explanation:
Let :
Deluxe ticket = x
Regular tickets = x + 78
Premium tickets = y
x + (x + 78) + y = 208
4x + 2(x+78) + 10y = 714
2x + y = 208 - 78
4x + 2x + 156 + 10y = 714
2x + y = 130 - - - - - (1)
6x + 10y = 558 - - - - (2)
Now we can solve the simultaneous equation using elimination method :
From (1)
y = 130 - 2x
Put y = 130 - 2x in (2)
6x + 10(130 - 2x) = 558
6x + 1300 - 20x = 558
- 14x = 558 - 1300
-14x = - 742
x = 742 / 14
x = 53
Put x = 53 in y = 130 - 2x
y = 130 - 2(53)
y = 130 - 106
y = 24
Answer:
m = - 2 is the value of m that the function y= e^mx is a solution of the differential equation, y' + 2y = 0.
Step-by-step explanation:
To determine all values of m so that the function y= e^mx is a solution of the given differential equation.
First, we will find y'.
From, y= e^mx
But, 
Hence,
∴ 
Now, we will put the values of y' and y into the given differential equation y' + 2y =0
From the question,
and
Then, 
becomes
Then, 
∴ 
Hence, m = - 2 is the value of m that the function y= e^mx is a solution of the differential equation, y' + 2y = 0.
Answer:
3/4
Step-by-step explanation:
There are 4 cards total
The card not less than 6 are 6,7,8 = 3 cards
P( not less than 6) = number of cards not less than 6 / total
= 3/4
Answer:
Step-by-step explanation:
z=xi+yj
x=-1.2=r cosθ (say)
y=-1.6=r sinθ(say)
square and add
r²cos²θ+r² sin ² θ=(-1.2)²+(-1.6)²=1.44+2.56=4
r²=4
r=2
divide
tanθ=y/x=-1.6/(-1.2)=16/12=4/3
θ=tan ^{-1}(4/3)≈53.13°
so polar coordinates are (2,53.13°)
Answer:
1.875
Step-by-step explanation:
