數學雜題(HELP)八題

我只是個小學生﹐因此只識第一題﹐煩請見諒！
1)〔63.25×（25＋15）－52×15〕÷25
＝70kg
唔知有無計錯﹐不過條列式好sure！
希望可以幫到你！

1.
Weight of all girls = # of girls x Avg. wt of girls = 15 x 52 kg = 780 kg
Wt of all students = # of students x Avg. wt of students = 25 x 63.25 kg = 1581.25 kg
Wt of all boys = total wt of students - wt of all girls = 1581.25 kg - 780 kg = 801.25 kg
Average weight of boys = Wt of all boys/ no. of boys = 801.25 kg/(25 – 15) = 80.125 kg

2. cos^3+sin^2 cos
cos ^3 x + sin^2 x cos x
cos x(cos^2x + sin^2x)
cos x(1)
cos x

3. 2-cos^2 48°-cos^2 42°
2-cos^2 48°-sin^2 48°
2 + 1(cos^2 48°+ sin^2 48°)
2 + 1(1)
3

4. tan25°sin25°+cos^2 25°
Please check the original question.

5. tan(cos/1-sin + cos/1+sin)
What does cos/1 mean?

6. sin^4-cos^4≡1-2cos^2
sinx^4 x - cos^4 x≡1-2cos^2 x
(sin^2 x - cos^2 x) (1) ≡1 - 2cos^2 x
(1- cos^2 x - cos^2 x) (1) ≡1-2cos^2 x
1- 2cos^2 x ≡1 - 2cos^2 x

7. 考慮點A(1,3)及B(-2,y)
a)若線段AB的斜率為負值,求y的最小可能整數值。
B lies on the vertical line x = -2
For line AB to have negative value slope, B must a point whose y-coordinate greater than that of a point ((-2, 3) y >3
If y = 3, ie B(-2, 3), the slope AB = 0
If y >3, b(-2, >3), the slope AB < 0

b)利用(a)的結果,求以上情況中AB的長度。(如有需要,答案以根式表示)
Distance between A and B, = 3 unit distance AB > = 3

8. 假設A(3,4)、B(8,14)、C(4,12)及D(-1,2)組成一平行四邉形。
a)P、Q、R及S為平行四邉形上的点,分別以1:2的比內分AB、BC、CD及DA。
求 P、Q、R及S的坐標。
b)PQRS是否平行四邉形?

Slope of BC = (14 – 12)/(8 – 4) = 2/4 = 1/2
Slope of AD = (4 – 2)/(3 –(-2)) = 2/5
They don’t have the same slopes, so ABCD不是平行四邉形 as stated.
Please check the question.

You can still find the locations of P,Q, R, S by using the following formula:

The coordinates of point P(x, y) which divides the line joining points A(x1, y1) and B(x2, y2) in the ratio m:n are:
x-coordinate of P = (nx1 +mx2) / (m + n)
y-coordinate of P = (ny1 +my2) / (m + n)

Hence, P(14/3, 22/3), Q(20/3,40/3), R(2, 22/3) and S(-1/3, 8/3)

(b) PQRS is not a parallelogram. Slope SP is not equal to slope RQ

I leave the calculations to you. I run out of space. Yahoo limits me to enter 2000 words.