I assume c, because usually to get to the opposite you reflect the line or figure on the x axis
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
You just combine like terms so it'll be 5x^43
Answer:
0.35m + 25 = 42.50
Step-by-step explanation:
If you were to rent a truck for one day you will first have to pay a $25 fee for one day. This is represented by + 25 in the equation above.
Then for every mile you go you must pay $0.35, represented as 0.35m.
<em>As an example to make it easier if you had to pay 1 dollar per mile and you went 10 miles it would cost $10. This can be proved by 1m (m being the variable for number of miles) Plug in 10 for m and you can asee 1(10)=10, because obviously 1 times 10 is 10. </em>
Same premise with $0.35
Then both of those fees added up are equal to a total of $42.50.
To prove it can find the exact number of miles that need to be driven to cost a total of $42.50 just follow steps bellow.
1. 0.35m + 25 - 25 = 42.50 - 25
Subtracting the inital fee since it is part of the total, and if you add/subtract/multiply/divide on one side you must do to the other.
2. 0.35m/0.35 = 17.50/0.35
You divide because m is being multiplied with 0.35 and to undo the multiplication you divide. Doing the same to both sides.
3. m = 50
Plug in 50 to "m" in the equation above and if both sides are equal the answer is valid.
The nearest number to 15.04 it 15
