Answer:
45.40
Step-by-step explanation:
First of all, the shape of rope is not a parabola but a catenary, and all catenaries are similar, defined by:
y=acoshxa
You just have to figure out where the origin is (see picture). The hight of the lowest point on the rope is 20 and the pole is 50 meters high. So the end point must be a+(50−20) above the x-axis. In other words (d/2,a+30) must be a point on the catenary:
a+30=acoshd2a(1)
The lenght of the catenary is given by the following formula (which can be proved easily):
s=asinhx2a−asinhx1a
where x1,x2 are x-cooridanates of ending points. In our case:
80=2asinhd2a
40=asinhd2a(2)
You have to solve the system of two equations, (1) and (2), with two unknowns (a,d). It's fairly straightforward.
Square (1) and (2) and subtract. You will get:
(a+30)2−402=a2
Calculate a from this equation, replace that value into (1) or (2) to evaluate d.
My calculation:
a=353≈11.67
d=703arccosh257≈45.40
I uploaded the answer to a file hosting. Here's link:
bit.
ly/3a8Nt8n
Okay. So in order to solve this problem, we really have to try out each answer and divide it by 9. A is not correct, because it does not divide evenly. B works, but let's check the others. C and D do not work, but E also works as well. If you can have two answers, 504 and 882 are both exactly divisible by 9. The answers are B: 504 and E: 882.
The answer is £150.
This could be calculated using proportion. If £1 is €1.2, how many £ is €180:
£1 : €1.2 = x : <span>€180
</span>x = £1 ÷ €1.2 × <span>€180</span>
x = £150
