# Thread: Need Help In These word problems

1. ## Need Help In These word problems

Let Me know if u have any problem reading it.

Ok so for question 9 i got this
a:0 show swimming distance is given by relationd d=wsecx
cos x=w/d
d=w/cosx
d=wsecx

B
if l=2w determine the range of values that x may take on given that P can anywhere along the length of pool. so i tried these

cosx=w/d will not work
sinx=2w/d will not work
tanx=2w/w
tanx=2 inverse therefore
0<x<1.07, is this right?

D) I think i know how to do once i figured out c?
E) same as D

For question 10, im just confused any hints is appreciated

2. ## Soln. to question 10 (a,b and d).

(10a) line d // horizontal. Hence x = angle on the top right in the triangle, since alternate angles are equal.

2/d =tanx
2/tanx=d
2cotx=d

(10b)

d=2/tanx
d=2/tan(pi/3)
d=1.15 metres

(10d)

Refer to the diagram in the question. When x approaches 0, then the window would get full sunlight (no shade). When x approaches pi/2, i.e. 90 degrees, then the window will get no sunlight (full shade). I hope this is correct.

Originally Posted by jepal

Let Me know if u have any problem reading it.

Ok so for question 9 i got this
a:0 show swimming distance is given by relationd d=wsecx
cos x=w/d
d=w/cosx
d=wsecx

B
if l=2w determine the range of values that x may take on given that P can anywhere along the length of pool. so i tried these

cosx=w/d will not work
sinx=2w/d will not work
tanx=2w/w
tanx=2 inverse therefore
0<x<1.07, is this right?

D) I think i know how to do once i figured out c?
E) same as D

For question 10, im just confused any hints is appreciated

actually range of x you have selected is correct it is 0≤x≤ArcTan(2)
values of d varies from w≤d≤√3 *w
graph of d=w*sec(x) is some thing similar to this

then the most interesting part of this problem comes
take total distance along which the lifeguard has to swim is P
then,
P = LP + PS
P = [ 2*w - w*tan(x) ] + w*sec(x)

we can easily see if he runs along length and width he has to run about 3*w distance if he follows the diagonal length he has to swim only √3 *w

you can observe it below ,

you can see P decreases with x .

4. thank u!