Answer:
1. What are the amplitude and period of the sine function that indicates the positioning of the band members as they start performing?
Answer: The amplitude is 80 ft and the period is 60 ft.
2. Edna, seated in the stands, faces Darla and notices that the sine curve starts rising from the left edge of the field. What is the equation for the sine function representing the arrangement of band members at the beginning of their performance?
Answer: y = 80cos(x*π/30)+80
3. When the band starts playing, the members move away from the edges, and the sine curve changes to start decreasing at the far left. Darla remains in her position. Now the sine curve is half as tall as it originally was. What is the equation for the updated sine curve depicting the band members' positions?
Answer: y = 40cos(x*π/30)+80
4. Finally, the entire band shifts closer to the edge of the football field, causing the sine curve to now position itself in the lower half of the field from Edna’s perspective. What is the equation for this sine curve reflecting the band members' positions after these adjustments?
Answer: y = 40cos(x*π/30)+40
Step-by-step explanation:
The increase in production is found by calculating 180 - 150 = 30 tons. The percentage rise is computed by taking 30 divided by 150, which equals 0.2 or a 20% rise.
Let X be the amount of 90% alloy and Y be the amount of 70% alloy. The equations are: x + y = 60 0.9x + 0.7y = 0.85 * 60 By substituting, we have: 0.9x + 0.7(60 - x) = 0.85 * 60 This simplifies to: (0.9 - 0.7)x = (0.85 - 0.7)*60 Solving for x yields: x = (0.85 - 0.7)*60/(0.9 - 0.7) x = 45 ounces For Y, we find: y = 60 - 45 y = 15 ounces
Answer:- 1. True. A compass serves the purpose of drawing circles and arcs in geometric constructions.
2. False. A standard geometric construction necessitates the use of a straightedge, compass, and pencil, among other tools, to accurately draw a geometric figure.
3. True. Geometric constructions are crafted using a compass and straightedge.
4. True. Protractors assist in geometric constructions for measuring angles, while rulers are employed to gauge segment lengths.
Answer:
The exact population of Vermont in 2008 could have been around 618,000
Step-by-step explanation:
* Here's how rounding to the nearest ten thousand works:
- Numbers ending with the last four digits between 0001 and 4999 are rounded down to the nearest lower multiple of ten thousand
- Example: 83,525 rounds down to 80,000.
- If the last four digits are 5000 or above, round up to the next higher ten thousand
- Example: 58,988 rounds up to 60,000
* Applying this rule to the problem given:
Since the rounded population is 620,000 to the nearest ten thousand, the actual population could be any value with the last four digits from 0001 to 4999 (like 618,000) or from 5000 upwards (like 624,000).
Therefore, 618,000 might represent the actual population of Vermont in 2008
