Simone has 32 erasers. She arranges the erasers into 5
1 answer:
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Answer: Boat A should travel 152.8° to reach B
Step-by-step explanation:
The diagram illustrating the scenario is shown in the attached photo. Triangle ABP is formed. A represents the position of boat A. B represents the position of boat B. P represents the position of the port.
We would determine AB by applying the law of cosines
AB² = AP² + BP² - 2AP×BPCosP
AB² = 20² + 25² - 2 × 20 × 25 × Cos45
AB² = 1025 - 707.10678 = 317.89322
AB = √317.89322 = 17.83
We would determine the bearing of B from A by finding angle A. We would apply the sine rule.
AB/SinP = AP/Sin A
17.83/Sin45 = 20/SinA
Cross multiplying, it becomes
17.83 × SinA = 20Sin45 = 14.14
SinA = 14.14/17.83 = 0.79
A = Sin^-1(0.79) = 52.2°
The total angle at A is 65 + 52.2 = 117.2°
The angle formed outside the third quadrant is 117.2 - 90 = 27.2°
Therefore, bearing B from A is
180 - 27/2 = 152.8°
Answer:
Kimberly and Mike had at first $100 each
Step-by-step explanation:
Assume that Kimberly and Mike each have $x
∵ Kimberly has $x
∵ Kimberly spent $50
- Find the reminder with Kimberly by subtracting 50 from x
∴ The money left with Kimberly = x - 50
∵ Mike has $x
∵ Mike spent $25
- Find the reminder with Mike by subtracting 25 from x
∴ The money left with Mike = x - 25
∵ Mike's money is 50% more than Kimberly's money
- That means Mike's money is more than Kimberly's money by
50% of Kimberly's money
∴ x - 25 = (x - 50) + 50%(x - 50)
∵ 50% = = 0.5
∴ x - 25 = (x - 50) + 0.5(x - 50)
- Simplify the right hand side
∴ x - 25 = x - 50 + 0.5x - 25
- Add the like terms in the right hand side
∴ x - 25 = 1.5x - 75
- Add 75 to both sides
∴ x + 50 = 1.5x
- Subtract x from both sides
∴ 50 = 0.5x
- Divide both sides by 0.5
∴ 100 = x
∵ x represents the amount of money that Kimberly and
Mike each had at first
∴ Kimberly and Mike had at first $100 each