Solution:
(6y^2-9y+4)-(-7y^2+5y+1)
Distribute to get rid of ( )
6y^2-9y+4+7y^2-5y-1
Combine like terms
13y^2-14y+3
Answer:
24 + 30 = 54 pancakes flipped in 2 minutes :)
Step-by-step explanation:
damon = 5 pancakes in 20 seconds
we do 20 x 3 and 5 x 3 to find how many pancakes he can flip in a minute
15 pancakes and a minute, we then multiply them by 2 to get the amount for 2 minutes
30 pancakes flipped in 2 minutes
Hailey = 2 pancakes in 10 seconds. to make it an equal amount of pancakes per second with damon, i will multiply them by 2 to have 4 pancakes in 20 seconds
we will then do 4 x 3 and 20 x 3 to find out how many pancakes per minute
then we multiply by 2 for 2 minutes
Answer:
2,598,960
Step-by-step explanation:
It is a combination because order doesn't matter. You wouldn't want to call A-K-Q-J-10 of hearts a different combination than 10-J-Q-K-A.
52 C 5 = 2,598,960
Answer:
Step-by-step explanation:
Here is a list of possible outcomes.
Penny nickel
Heads heads
Heads tails
tails Heads
tails tails
Since there are four ways the two coins can land, the chances of getting tails - tails is 1 chance in 4.
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
