Answer:
Part A: From 0 to 2 seconds, the height of the water balloon increases from 60 to 75 feet, therefore the water balloon's height is increasing during the interval [0,2]
Part B: From 2 to 4 seconds, the height of the water balloon stays the same at 75 feet, therefore the water balloon's height is the same during the interval [2,4] From 10 to 12 seconds, the height of the water balloon stays the same at 0 feet, therefore the water balloon's height is the same during the interval [10,12] From 12 to 14 seconds, the height of the water balloon stays the same at 0 feet, therefore the water balloon's height is the same during the interval [12,14]
Part C: The interval, [4,6] of the domain is when the water ballon's height decreases the fastest. The interval [4,6] decreases by 35 feet. The two other intervals that decrease are [6,8] and [8,10] which both have the same slope. They decrease by 20 feet. Therefore, this helps us conclude that the interval [4,6] decreases the fastest because 35 feet is a more significant decrease than 20 feet.
Part D: I predict that the height of the water balloon at 16 seconds is 0 feet. This is because at 10-14 seconds, the water balloon's height is 0 feet. In read-world situations, if the water balloon is on the ground which is 0 feet, it stays on the ground due to gravity.
Step-by-step explanation:
I hope this helps! I also do not know if it is all correct but I did research and everything so hopefully it is correct! Good luck!
Answer:
the correct choice is A. At the gas station
Step-by-step explanation:
Lucy starts at home and travels 3 miles south to the post office. From the post office, she travels 4 miles east to the gas station. As it is known south and east directions form right angle. Since the entire trip forms a triangle, this triangle is right with right angle at the post office.
Call the vertices of this triangle P - post office, G - gas station, H - home. Then HP and PG are legs of this triangle and GH is hypotenuse.
From the given data:
HP=3;
PG=4;
GH=5;
∠P=90°.
The smallest angle is opposite to the smallest side. The smallest side is leg HP, so the smallest angle is G that is the angle at gas station.
Answer:
4 inches per second
Step-by-step explanation:
Speed = distance/time
Given
Distance = 20 feet
12 inches = 1 foot
X inches = 20 feet
X = 20 x 12 = 240 inches
Time = 1 minute = 60 secs
Therefore
Speed = 240/60
= 4 inches per second
Answer:
- Fantasy: 3 barrels
- Ecstasy: 1 barrel
Step-by-step explanation:
<u>Given</u>
Fantasy uses 4 lb of nuts, 3 lb of chocolate, for a profit of $50
Ecstasy uses 4 lb of nuts, 1 lb of chocolate, for a profit of $40
In stock are 16 lb of nuts, 10 lb of chocolate
<u>Find</u>
amount of each to maximize profit
<u>Solution</u>
Let x and y represent barrels of Fantasy and Ecstasy, respectively. Then the limitations on production are ...
4x +4y ≤ 16 . . . lb of nuts
3x +y ≤ 10 . . . . lb of chocolate
We want to maximize
50x +40y
The graph shows the feasible region. Its vertices are ...
(0, 4), (3, 1), (3.33, 0)
Profit is maximized at $190 when production is 3 barrels of Fantasy and 1 barrel of Ecstasy.
Answer:
15.43 ft
Step-by-step explanation:
To solve this question, one should use the concept of similar triangles.
The pole's shadow and the distance to the ground (x) form a similar triangle to the distance of the plumb bob from the base and the length of the plumb bob, respectively. Note that we do not need to know the measurements of the third side of the triangles to solve the problem. Therefore, the distance of the top of the pole to the ground is:
The distance of the top of the pole to the ground is 15.43 ft.
