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Draw a diagram to illustrate the problem as shown in the figure below.
Euclid is placed at the origin at (0,0).
Apollonius is 12 m north and 9 m east of Euclid, so its coordinate is (9,12).
Pythagoras is at the arbitrary position (x,y) so that is is at distance d from Euclid and 2d from Apollonius.
From the distance formula, obtain
d² = x² + y² (1)
(2d)² = (x-9)² + (y-12)²
or
4d² = (x-9)² + (y-12)² (2)
Substitute (1) into (2).
4(x² + y²) = x² - 18x + 81 + y² - 24y + 144
3x² + 3y² + 18x + 24y = 225
Divide by 3.
x² + 6x + y² + 8y = 75
Create perfect squares.
(x+3)² - 9 + (y+4)² - 16 = 75
(x+3)² + (y+4)² = 10²
Answer:
The path of Pythagoras is a circle of radius 10 m, centered at (-3, -4).
Euclid is placed at the origin at (0,0).
Apollonius is 12 m north and 9 m east of Euclid, so its coordinate is (9,12).
Pythagoras is at the arbitrary position (x,y) so that is is at distance d from Euclid and 2d from Apollonius.
From the distance formula, obtain
d² = x² + y² (1)
(2d)² = (x-9)² + (y-12)²
or
4d² = (x-9)² + (y-12)² (2)
Substitute (1) into (2).
4(x² + y²) = x² - 18x + 81 + y² - 24y + 144
3x² + 3y² + 18x + 24y = 225
Divide by 3.
x² + 6x + y² + 8y = 75
Create perfect squares.
(x+3)² - 9 + (y+4)² - 16 = 75
(x+3)² + (y+4)² = 10²
Answer:
The path of Pythagoras is a circle of radius 10 m, centered at (-3, -4).
Answer:
a) : t=13 seconds
: t<13 seconds
b) At α= 0.01, one-tailed critical value is -2.33
c) Test statistic is −2,98
d) since -2.98<-2.33, we can reject the null hypothesis. There is significant evidence that mean pit stop time for the pit crew is less than 13 seconds at α= 0.01.
Step-by-step explanation:
according to the web search, the question is missing some words, one part should be like this:
"A pit crew claims that its mean pit stop time ( for 4 new tires and fuel) is less than 13 seconds."
Let t be the mean pit stop time of the pit crew.
: t=13 seconds
: t<13 seconds
At α= 0.01, one-tailed critical value is -2.33
Test statistic can be calculated using the equation:
where
- X is the sample mean pit stop time (12.9 sec)
- M is the mean pit stop time assumed under null hypothesis (13 sec)
- s is the population standard deviation (0.19 sec.)
- N is the sample size (32)
Then ≈ −2,98
since -2.98<-2.33, we can reject the null hypothesis. There is significant evidence that mean pit stop time for the pit crew is less than 13 seconds at α= 0.01.