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 #1
avatar+26396 
+15

The angle of elevation of the top of a tree is found to be 23° at one point and 76° at a point 49 feet nearer the tree. How high is the tree if both observation points and the base of the tree are on the same horizontal plane?

 

tan(23)=hxx=htan(23)tan(76)=hx49tan(76)=hhtan(23)49(htan(23)49)tan(76)=hhtan(76)tan(23)49tan(76)=hh(tan(76)tan(23)1)=49tan(76)h(tan(76)tan(23)tan(23))=49tan(76)h=49(tan(76)tan(23)tan(76)tan(23))h=49(4.010780933540.424474816214.010780933540.42447481621)h=49(1.702475499623.58630611733)h=490.47471561097h=23.2610649376 feet

 

 

The tree is 23.2610649376 feet high

 

laugh

19.01.2016
 #6
avatar+26396 
+40

A broken clock is set corectly at 12:00 noon. However, it registers only 20 minutes for each hour. In how many hours will it again register the correct time  ?

A)12

B)18  analog clock(12h)

C)24 

D)30

E)36  digital clock (12h)

 

1. Analog Clock:

 angular velocity real time: ω1=2π12 hangular velocity display time: ω2=2π36 hw2tw1t=n2π2π12 ht2π36 ht=n2π|:2π112 ht136 ht=nt(112 h136 h)=nt(36121236)=nt(241236)=nt(236)=nt(118)=nt=18n

 

next correct time, if n = 1, then t = 18 hours.

 

2. Digital Clock(24h):

angular velocity real time: ω1=2π24 hangular velocity display time: ω2=2π72 hw2tw1t=n2π2π24ht2π72 ht=n2π|:2π124 ht172 ht=nt(124 h172 h)=nt(72242472)=nt(482472)=nt(272)=nt(136)=nt=36n

 

next correct time, if n = 1, then t = 36 hours.

 

laugh

19.01.2016
 #2
avatar+26396 
+41

cos 2x / cos^2(x) * sin^2(x) (integrals) I want to know how to solve it

 

cos(2x)sin2(x)cos2(x)=cos(2x)[1cos2(x)]cos2(x)|sin2(x)=1cos2(x)=cos(2x)[1cos2(x)cos2(x)]=cos(2x)[1cos2(x)1]=cos(2x)cos2(x)cos(2x)|cos(2x)=cos2(x)sin2(x)=cos2(x)sin2(x)cos2(x)cos(2x)=1sin2(x)cos2(x)cos(2x)=11cos2(x)cos2(x)cos(2x)=1[1cos2(x)1]cos(2x)=21cos2(x)cos(2x)

 

cos(2x)sin2(x)cos2(x)=2 dx1cos2(x) dxcos(2x) dx

 

1.2 dx=2dx2 dx=2x

 

2.1cos2(x) dx=sin2(x)+cos2(x)cos2(x) dx=(tan2(x)+1) dx we need: y=tan(x)y=sin(x)cos(x)y=sin(x)cos(x)[cos(x)sin(x)sin(x)cos(x)]y=tan(x)[cot(x)+tan(x)]y=1+tan2(x) =(tan2(x)+1) dxwe substitute: u=tan(x)du=(1+tan2(x)) dx=(tan2(x)+1)du1+tan2(x)=du=u1cos2(x) dx=tan(x)

 

3.cos(2x) dxwe substitute: u=2xdu=2 dxcos(2x) dx=cos(u)du2=12cos(u) du=12sin(u)=12sin(2x)|sin(2x)=2sin(2x)cos(x)=122sin(2x)cos(x)cos(2x) dx=sin(x)cos(x)

 

cos(2x)sin2(x)cos2(x)=2 dx1cos2(x) dxcos(2x) dxcos(2x)sin2(x)cos2(x)=2xtan(x)sin(x)cos(x)+c

 

laugh

18.01.2016