Answer:
The nearest time is 15 years or 180 months
Answer:
x² - 2x - 8
Step-by-step explanation:
The notation (f·g)(x) means to multiply the two functions. Use the distributive property to simplify.
(f·g)(x) = (x+2)(x-4) = x² + 2x - 4x - 8 = x² - 2x - 8
37
Line up the data, separate into quarters
Take the highest number in the 3rd quarter from the lowest in the 2nd
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= 3
b= 4
=3.14(a^2 + ab)
substitute the given a & b values in expression
=3.14((3)^2 + (3*4))
multiply inside parentheses
=3.14(9 + 12)
add inside parentheses
=3.14(21)
multiply
=65.94
ANSWER: 65.94
Hope this helps! :)
