Answer:
the slope for the first one is 0
the slope for the second one is 2
the slope for the third one is 3/8
Step-by-step explanation:
Answer:
The probability is 10/121
Step-by-step explanation:
In this question, we are tasked with calculating probability.
The probability to be calculated is that we have an ordered selection of picking a red marble after which we pick a yellow marble.
Firstly let us know the total number of marbles we have. That will be 4 + 5 + 2 = 11 marbles
Probability of picking a red marble will be 5/11 while the probability of picking a yellow marble will be 2/11
Now, the probability of picking a red marble before a yellow marble will be mathematically equal to; P(r) * P(y) = 5/11 * 2/11 = 10/121
Answer:
(-2, -3)
Step-by-step explanation:
solutions are all the points where the line intersects
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:
2
Step-by-step explanation:
2/2+6=7
