Answer:
Step-by-step explanation:
Given
Points:
Required
Determine the equation of line that is perpendicular to the given points and that pass through 
First, we need to determine the slope, m of FG
Where
--- 
--- 
The question says the line is perpendicular to FG.
Next, we determine the slope (m2) of the perpendicular line using:
The equation of the line is then calculated as:
Where
Multiply through by 2
Add x to both sides
Hence, the line of the equation is
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
A) tomatoes : chicken broth = 9:15 or 3:5
Tomatoes : spinach = 9:9 = 1:1
Spinach : chicken broth = 9:15 = 3:5
b) tomatoes : chicken broth = 4.5:7.5 = still 3:5
Tomatoes to spinach is still 1:1
Spinach : chicken broth 4.5:7.5 still = 3:5
Dividing all quantities by 2 doesn’t change the ratio.
