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#1 2007-03-15 12:09:37

ali
Member
Registered: 2007-03-01
Posts: 5

Sooo....confused! Help aSaP!

1. The graphs of the equations 3ax-4by=5 and 7ax-3by=-1 intersect at the point (-2,5). Find the value of ab.



2.  Given that x-y=8 [Hint: Square both sides of the equation] and y=6/x, find the value of x^2+y^2.




3 LAST BUT NOT LEAST!

Snoopy decided to fly his Sopwith Camel looking for the Red Baron. The rate of his plane in still air is 300km/h. After flying 900km with a tail wind, he gets a call to return to base. On the return trip, flying against the same wind, he traveled two-thirds of the distance back to the base when he had to make an emergency landing to refuel. If he flew the same amount of time against the wind aswith the wind, how many km/hr was the wind blowing? [Reminder, Time=distance/rate and the rate of the wind must be taken into account in both directions.]



thnx<3

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#2 2007-03-15 12:32:31

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Sooo....confused! Help aSaP!

1. Substitute x = −2 and y = 5 into the two equations. Then you get two simultaneous equations in a and b instead of in x and y. So just solve for a and b.

2. Squaring both sides of the first equation, x[sup]2[/sup] − 2xy + y[sup]2[/sup] = 64. From the second equation, xy = 6. Substitute this into the squared equation and find x[sup]2[/sup]+y[sup]2[/sup]. (Note: You do not need to find x and y, just x[sup]2[/sup]+y[sup]2[/sup].)

3. Let the wind speed be v km/h.
When flying with the wind, the speed of the plane was 300+v.
The time taken to fly 900 km at this speed was t[sub]1[/sub] = 900⁄(300+v). (Remember: time = distance ∕ speed.)
When flying against the wind, the speed of the plane was 300−v.
The time taken to fly 600 km at this speed was t[sub]2[/sub] = 600⁄(300−v).
Now put t[sub]1[/sub] = t[sub]2[/sub] and you can solve for v. smile

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