The answer to (-5)-3 is -8. I may be wrong but I did the work.
Answer:
4/7 = 8/14
Step-by-step explanation:
Force 1, F1 = 90, angle 30°
Force 2, F2 = 50, angle 160°
F1 = 90 cos(30) i + 90 sin (30) j
F2 = 50 cos (160) i + 50 sin (160) j
F1 = 90*0.866 i + 90*0.5 j
F2 = 50*(- 0.940) i + 50*0.342 j
F1 = 77.94 i + 45 j
F2 = -47 i +17.10 j
Resultant force, Fr = F1 + F2
Fr = [77.94 - 47.00] i +[45 +17.10]j = 30.94 i + 62.10 j
Magnitude = √[30.94 ^2 + 62.10^2] = 69.38 pounds
Direction = arctan[62.10/30.94] = 63.52 °
<span>let x = the original no. of students
then
(x+10) = the actual no. that went on the trip
:
= the original cost per student
and
= the actual cost
:
Original cost - actual cost = $12.50
- = 12.50
multiply equation by x(x+10)
x(x+10)* - x(x+10)* = 12.50x(x+10)
Cancel the denominators
1500(x+10) - 1500x = 12.5x(x+10)
1500x + 15000 - 1500x = 12.5x^2 + 125x
Combine on the right to form a quadratic equation
0 = 12.5x^2 + 125x - 15000
Simplify, divide equation by 12.5
x^2 + 10x - 1200 = 0
You can use the quadratic formula; a=1; b=10; c=-1200, but this will factor to
(x + 40(x - 30) = 0
The positive solution is what we want here
x = 30 students in the original group
Check this by finding the cost per student for each scenario
1500/30 = $50.00; original cost
1500/40 = $37.50; actual cost
---------------------
saving: $12.50</span>
He least common multiple would be 8 times 7.
