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lord [1]
2 years ago
14

Analyze the Conjecture::

Mathematics
1 answer:
Alexxandr [17]2 years ago
6 0

The distance the ball is thrown is given by cosine rule and the triangle

formed by a known location, the thrower and the destination.

Correct response:

  • <u>Hector throws the ball farther than Tre</u>
<h3>Methods used to obtain the correct response</h3>

The given dimensions are;

Dimension of the base diamond = 90 feet by 90 feet

Distance of pitcher's mound from home base = 60.5 feet

Horizontal distance from pitchers mound to right fielder = 95 feet

The distance between Tre and the 3rd base, d₁, is calculated using cosine rule as follows;

  • a² = b² + c² - 2·b·c·cos(A)

Where;

A = The angle formed by the line, <em>b</em>, from home base to the pitcher's mound and the line, <em>c</em>,  from home base to 3rd base.

a = Distance from the pitcher's mound to 3rd base = d₁

b = 60.5 feet

c = 90 feet

Therefore;

d₁² = 60.5² + 90² - 2 × 60.5 × 90 × cos(45°) = 11,760.25 - 10,890·cos(45°)

d₁ = √(11,760.25 - 10,890×cos(45°)) ≈ 63.717

  • The distance Tre throws the ball, d₁ ≈ 63.717 feet

Similarly, the distance Hector throws the ball, d₂, is calculated as follows;

d₂² = (90·√2 - 60.5)² + 95² - 2 × (90·√2 - 60.5) × 95 × cos(45°)

Which gives;

d₂ = √((90·√2 - 60.5)² + 95² - 2 × (90·√2 - 60.5) × 95 × cos(45°)) ≈ 67.18

  • The distance Hector throws the ball, d₂ ≈ 67.18 feet

Therefore;

  • The distance Hector throws the ball, d₂ ≈ 67.18 feet, is farther than the distance, d₁ ≈ 63.717 feet, Tre throws the ball

Learn more about the law of cosines here:

brainly.com/question/2491835

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Answer:

17:16

Step-by-step explanation:

Number of employees exceeded their sales quota = 17

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3 years ago
Ben drives 405 miles on 15 gallons. How many miles does Ben drive on one gallon?
wel

Answer:

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Step-by-step explanation:

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Hopefully I helped :)

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2 years ago
There were five teams entered in a competition. Each team consisted of either only boys or only girls. The number of team member
WINSTONCH [101]

Answer:

21.

Step-by-step explanation:

Since there were five teams entered in a competition, and each team consisted of either only boys or only girls, with the number of team members being 9, 15, 17, 19 and 21 members, if after one team of girls had been knocked out of the competition, the number of girls still competing was three times the number of boys, to determine how many girls were in the team that was eliminated, the following calculation must be performed:

9 + 15 + 17 + 19 = 60/4 = 15

9 + 15 + 17 + 21 = 62/4 = 15.5

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3 0
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Answer:

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Step-by-step explanation:

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Hope this helped :)

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