Anonymous
Anonymous asked in 科學及數學數學 · 8 years ago

# 緊急, 數學高手請幫幫手

1. In the mysterious lost city of Mim, the length of daylight (in hours) on the

Use this model to compare how the number of hours of daylight is increasing on March 16 and June 2 (assume that this is a standard year, not a leap year).

2. A Norman window has the shape of a semicircle atop a rectangle so that the diameterof the semicircle is equal to the width of the rectangle. What is the area of the largestpossible Norman window with a perimeter of 48 feet?

Rating
• Kevin
Lv 7
8 years ago

It is better to use the negation and the fact P(AUB) = P(A) + P(B) - P(A∩B) in this question

No restriction:

Number of all possible arrangements = 7P7 = 5040

V is at its original position:

Number of possible arrangements = 6P6 = 720

T is at its original position:

Number of possible arrangements = 6P6 = 720

V and T are both at their original position:

Number of possible arrangements = 5P5 = 120

Applying P(AUB) = P(A) + P(B) - P(A∩B),

Either V or T is at its original position:

Number of possible arrangements = 720+720-120 = 1320

Using the negation,

Number of possible arrangements = 5040-1320 = 3720Another method:

T is at the first place:

V can be at any other place, number of possible arrangements = 6P6 = 720

T is at the 2,3,5,6,7th place(5P1):

V can be at any other place except the first, number of possible arrangements = 5P1*5P1*5P5 = 3000

adding all cases and get 720+3000 = 3720