Answer:
The constraints are
and 
Step-by-step explanation:
Let
x ----> represent the number of male birds
y ----> represent the number of female birds
we know that
The flock needs to have exactly three times more females than males to thrive
so
----> equation A
The zoo only has room for a maximum of 20 male birds
so
----> inequality B
we know that
The maximum number of male birds is 20
For x=20
substitute in the equation A

so
The maximum number of female birds is 60
so
----> inequality C
therefore
The constraints are
and 
Answer: This is what Khan Academy said the answer was
Answer: 109.5 km/ hr
Step-by-step explanation:
Distance = 73 km
Time = 40 minutes = 40/60 = 2/3 hours
Speed = Distance / time
= 73 / 2/3
= 73 x 3/2 = 219 / 2 = 109.5 km/hr
Answer:
4y is your answer........
Answer:
765 J
Step-by-step explanation:
We are given;
Mass of bucket = 30 kg
Mass of rope = 0.3 kg/m
height of building= 30 meter
Now,
work done lifting the bucket (sand and rope) to the building = work done in lifting the rope + work done in lifting the sand
Or W = W1 + W2
Work done in lifting the rope is given as,
W1 = Force x displacement
W1 = (30,0)∫(0.2x .dx)
Integrating, we have;
W1 = [0.2x²/2] at boundary of 30 and 0
W1 = 0.1(30²)
W1 = 90 J
work done in lifting the sand is given as;
W2 = (30,0)∫(F .dx)
F = mx + c
Where, c = 30 - 15 = 15
m = (30 - 15)/(30 - 0)
m = 15/30 = 0.5
So,
F = 0.5x + 15
Thus,
W2 = (30,0)∫(0.5x + 15 .dx)
Integrating, we have;
W2 = (0.5x²/2) + 15x at boundary of 30 and 0
So,
W2 = (0.5 × 30²)/2) + 15(30)
W2 = 225 + 450
W2 = 675 J
Therefore,
work done lifting the bucket (sand and rope) to the top of the building,
W = 90 + 675
W = 765 J