Answer:
3xz5+2x+4y−2z
Step-by-step explanation:
2x−5y+3z5x+9y−2z
=2x+−5y+3xz5+9y+−2z
Combine Like Terms:
=2x+−5y+3xz5+9y+−2z
=(3xz5)+(2x)+(−5y+9y)+(−2z)
=3xz5+2x+4y+−2z
Answer:
k=13.8
Step-by-step explanation:
Given function:
- 2.5k+47.4=81.9
- to find k..
<u><em>Subtract final and middle value:</em></u>
<em><u>Divide by 2.5:</u></em>
Therefore, k=13.8..
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
Answer:
The answers are x < -65, x > 85, x < 180, x<= -13, and x >=25.
Step-by-step explanation:
For the first three, there's an open circle so the sign for the inequality would be < or > but for the last two, there's a closed circle so the sign for the inequality would be <= or >=, the ones with a line underneath. For 1, 3, and 4, the line goes to the left, showing that x is a number less than the point so it would have <, the less than sign. For 2 and 5, the line goes to the right, showing that x is a number greater than the point so it would have >, the greater than sign.
There's a trick to figuring out the right sign. If the line is pointing to the left, the inequality would be x < __, and the sign is pointng to the left. If the line is pointing to the right, the inequality would be x > __, and the sign is pointng to the right. This only works is x is on the left side of the inequality.
