Answer:
The variable c represents the domain as it is the independent variable.
The domain of the function F(c) is given by c ≥ 0.
So, only positive values for the input make sense.
The upper limit of the domain is +∞ and lower limit is 0.
It is not possible for the team to earn $50.50 as it will be only multiple of 2.
Step-by-step explanation:
If F(c) represents the earning of a volleyball team from selling c cupcakes and each cupcake costs $2 each, then the equation that models the situation is
F(c) = 2c ..... (1)
The variable c represents the domain as it is the independent variable. (Answer)
The domain of the function F(c) is given by c ≥ 0. (Answer)
So, only positive values for the input make sense. (Answer)
The upper limit of the domain is +∞ and the lower limit is 0. (Answer)
It is not possible for the team to earn $50.50 as it will be only multiple of 2. (Answer)
Answer:
y2 = C1xe^(4x)
Step-by-step explanation:
Given that y1 = e^(4x) is a solution to the differential equation
y'' - 8y' + 16y = 0
We want to find the second solution y2 of the equation using the method of reduction of order.
Let
y2 = uy1
Because y2 is a solution to the differential equation, it satisfies
y2'' - 8y2' + 16y2 = 0
y2 = ue^(4x)
y2' = u'e^(4x) + 4ue^(4x)
y2'' = u''e^(4x) + 4u'e^(4x) + 4u'e^(4x) + 16ue^(4x)
= u''e^(4x) + 8u'e^(4x) + 16ue^(4x)
Using these,
y2'' - 8y2' + 16y2 =
[u''e^(4x) + 8u'e^(4x) + 16ue^(4x)] - 8[u'e^(4x) + 4ue^(4x)] + 16ue^(4x) = 0
u''e^(4x) = 0
Let w = u', then w' = u''
w'e^(4x) = 0
w' = 0
Integrating this, we have
w = C1
But w = u'
u' = C1
Integrating again, we have
u = C1x
But y2 = ue^(4x)
y2 = C1xe^(4x)
And this is the second solution
Answer:
1) 120
2) E (Z) = 12 and Variance of Z = 90
a) 5 liters
Step-by-step explanation:
1. We can find this by suing combinations.
Here n= 10 and r= 3 so n C r
= 10 C 3= 120
2. E(X) = 8 and E(Y) = 3
Z = 2X - 3Y +5
E(Z ) = 2 E (X) - 3(E)(Y) +5 ( applying property for mean)
= 2(8) - 3(3)+ 5 = 16+5-9= 21-9= 12
V(X) = 9 and V(Y) = 6.
V(Z) = E(Z )²- V(X) *V(Y) (applying property for Variance for two variables )
= 144- 54= 90
3. 55 liters contain adulterated milk in 7: 4.
So it contains 4/ 11*55= 20 liters of water
But we want to make it a ratio of 7:6
the water will be 6/13 *55= 25.38 when rounded gives 25 liters of water
So 25- 20 = 5 liters must be added to make it a ratio of 7:6
Usually there will be a line through the graph, labeling f(x) = ..... so plug in f(3) and follow the line on the x-axis to look for 3 then find y
