Answer:
slope:3
y intercept:1
equation:y=3x+1
Step-by-step explanation:
After understanding the problem, formulate equations to determine the unknown. Let x be the price of one book. Equating Alana&Petra's expense with Angus' would be
5x + 4x +5 = 19x - 10
The 5 in the left side is needed because Angus' expense is $5 more. Also, the 10 on the right side represents the $10 discount. Solving the equation,
19x = 9x = 5+10
10x = 15
x = $1.5
Therefore, the book costs $1.5.
Answer: -51 my friend
Step-by-step explanation:
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
