Q2
x^2 - 6x - 2y + 7 = 0
Complete the square on 'x'
(x-3)^2 -9 - 2y+7 = 0 Move y and stuff to the right side of the equation
(x-3)^2 = 2y +2 re-arrange to form
(x-3)^2 = 2 (y+1)
500 000 = PV (1.05)10 Solve for PV = amount to invest now
Sorry...I mislead you just a bit....the 'n' should be a supescript....I fixed it above....do you see it should be (1.05)n
Another way is to use the QUadratic Formula....
you got pretty far
1/4 (x^2-6x+9) - 11
1/4 (x^2-6x-35) use quadratic formula
a=1 b = -6 c = -35
\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
x=3±2sqrt(11) Then continue as Cphil did.......don't forget the 1/4 in front....
FV = PV (1+.05)n
FV = Future Value = 500 000 PV = Present Value = amount to invest now .05 = interest rate n = number of years=10
Can you take it from here? (this assumes a one time investment now)
Using the website calculator:
sqrt(3456) = 58.7877538267962744
A rate = 1 job /6 days = 1/6
B rate = 1 job /12 days = 1/12
1 job / (1 job /6days + 1 job/ 12 days)
1/(1/6 + 1/12) = ? days
can you do it from here???
Tan 40 = opp/adj = h / (20+x)
Tan 60 = opp/adj = h / x now you have two equations and two unkinowns
Do you think you can solve this system of equations for 'h' ?
time for commute to work = distance / rate = d/20
time for bike ride home = d/40
total distance = 2d
distance/total time = rate
2d/(d/20+d/40) = 2d/(2d/40 + d/40) = 2d/(3d/40) = 2 d * 40/3d = 80/3 = 80/3 km/hr = 26.67 km/hr average
Rate for pipe 1 1 tank/1hour = 1
Rate for pipe 2 1 tank/2 hours = 1/2
1 tank / (1 tank / hour - 1/2 tank/hour) = 1 tank /(1/2 tank/hour) = 2 hours (edited...misread the Q)