maths! help ! 15點!

2010-08-31 9:19 pm

1.solve tanθcosθ=0 for 0°≤θ≤90°

2.is cosθ>sinθ for 0°≤θ<45°? state the reason.

3.Rex measures the angle of elevation of the building from A to be 35°.He then walks 10m to point B and the angle of elevation from B becomes 40°.Find the height of the building for the man~

3.A ship sails from A to B in the direction 120° for 10km.After that, the ship sails from B to C in the direction 020° for another 10km.
a)What is the distance between A and C?
b)In what direction should the ship sail from C back to A?

4.A boat sarts at A and sails 30km in direction of N48°E to B.After that , it sails to C where C is due south of A. The sailor on the boat finds that the compass bearing of point B is N25°E from C. What is the distance between A and C?

5. x=4 ax+1/3<bx-4/2 Find 2 possible sets of the values of a and b.

6.Find 2 possible values of x that satisfy both inequalities x/4 +3≥x and x-2/-5>1.

7.the 8th power of a number is less than 10 times of the 5th power of that number.Find the no.

8.For the inequality 5 x 10^-x>0.0000488, suggest the value of x.

9.When a no. is increased by x% (x≠0),and then decreased by x%,explain why the result is not equal to the original no.

10.FInd 2 integers whose values lie between √10 and √50.

11. consider the expression (√a+√b)^2, where a and b are not perfect squares .Find 2 possible sets of the values of a and b such that the value of the expression is a rational no.

回答 (1)

Hello

2010-09-01 1:22 am

✔ 最佳答案

1.tanθcosθ=0
tanθ=0 or cosθ=0
θ=0° or θ=90°
θ=0° or 90°(rej.)
θ=0° 2.
Yes
∵cosθ=sin(90°-θ)
sin(90°-θ)>sinθ
∴cosθ>sinθ for 0°≤θ<45°3.
let y cm be the height of the building
tan35°=y/A0
A0=(y/tan35°)m

tan40°=y/B0
B0=(y/tan40°)m

A0-B0=10
(y/tan35°)-(y/tan40°)=10
y(1/tan35°-1/tan40°)=10
y=42.3m(corr. to 3 sig. fig.)4.

圖片參考：http://imgcld.yimg.com/8/n/HA00510450/o/701008310081213873368860.jpg

sin48°=BY/30
BY=22.29 km
cos48°=AY/30
AY=20.07 km
tan25°=BY/CY
=22.29/CY
CY=47.81 kmAC=CY-AY
=47.81-20.07
=27.7(correct to the nearest 0.1 km.)5.
x=4,ax+1/3<bx-4/2
4a+1/3<4b-4/2
8a+2 <12b-12
8a+14<12b or 8a<12b-14
8a+14/12<b or a<12b-14/82 possible sets of the values of a=4 or5
and b=6 or 76.
x/4 +3≧x
x/4≧x-3
x≧4x-12
-3x≧-12
x≦4 x-2 /-5>1
x-2<-5
x<-3
therefore,2 possible values of x = -5 or -77.
let the number is x
x^8<10x^5
x^3<10
x<2.15...
x must be a positive integer
then x=1 or 28.
5x10^-x > 0.0000488
10^-x>0.0000488 /5
10^-x>9.76 × 10^-6
log-x>log-5.01055018
x<5.010550189.
let the number is y
y(1+x%)(1-x%)
=y[1-(x%)^2] which is not equal to y.
∴the result is not equal to the original no.10.
√10=3.162......√50=7.071......
∴the integers can be 4 to 7 (you can choose 2)11.2. (√a + √b)^2 is rational if √(ab) is a perfect square.
so a = 2 and b = 8 ( √ ab = √ 16 = 4)
a = 3 and b = 27 (√ ab = √ 81 = 9)

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