Question

Math in English有人能帮我解一下这个题么?要解题不要翻译.A fence 8 ft tall runs p

Answer 1

let the angle between the ladder and ground be x.

And let the length of the ladder be y.

Then y = (8 cot (x) + 4)/(cos (x)) = 4 (2/(sin (x)) + 1/(cos (x)))

y` = -8 cot (x) csc (x) + 4 sec (x) tan (x)

1.let y` > 0 :

then - 8 cot (x) csc (x) + 4 sec (x) tan (x) > 0

so after simplify we have tan (x) > Power[2,(3)^-1]

(Attention :For all x value here,

the value of all trigonometrical function are positive)

so 0.90 < x < [Pi]/2

2.let y` < 0

clearly we' ll get 0 < x < 0.90

so from case 1 and 2 we know that the length of ladder (y) will have

the least value when x = 0.90

that is y (0.90) = 16.65 which will be length of the shortest ladde