Triangle A is a right triangle and has the dimensions 6, 8, 10. Triangle B is similar to Triangle A and has a hypotenuse of 35. Find the remaining dimensions of Triangle B.
x/35 = 6/10 x = 35*(6/10) x = 21 y/35 = 8/10 y = 35*(8/10) y = 28
A 15ft tall light post has fallen onto the wall of a building during a storm. The base of the light post is originally 8ft away. The post begins to slide away form the wall at a rate of 0.25 ft/sec. How quickly is the top of the pole sliding down the wall 5 seconds after it began moving?
h' = ? h^2 + b^2 = l^2 h^2 + b^2 = 15^2 use implicit differentiation 2hh' + 2bb' = 0 use d=r*t to find b and h at 5 seconds d=0.25*5=1.25ft b=8+1.25=9.25ft h=sqrt(15^2-9.25^2)=11.81ft Plug in values 2*11.8*h'= -2*9.25*0.25 h'=-0.196 ft/sec
Solve the following for x: 10^(x-2) = ((e^x)^5)*(e^(6-3x))
10^(x-2)=(e^5x)*(e^(6-3x)) 10^(x-2)=e^(6-3x+5x) 10^(x-2)=e^(6+2x) x-2=log(e^(6+2x)) x-2=(6+2x)log(e) x-2=6log(e) + 2xlog(e) x-2xlog(e) = 6log(e) + 2 x(1 - 2log(e)) = 6log(e) + 2 x=((6*log(e))=2)/(1-(2*log(e)))