3 problems: ave. speed; values for A; value of x^2 + y^2

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Hockeyman

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1) A plane flys round trip from Yarmouth to Sydney. When the plane is flying into a headwind its speed is 300km/h, and its speed with a tail wind is 600km/h. What is the average speed for the round trip?

2) The points (1,2), (5,A), and (A,7) lie on a straight line. Find all possible vaules for A

3) You are given that xy=6 and x^2y + xy^2 + x + y = 63. Calculate the value of x^2 + y^2.
 
Re: 3 problems

\(\displaystyle \frac{{A - 2}}{{5 - 1}} = \frac{{7 - 2}}{{A - 1}} = \frac{{7 - A}}{{A - 5}}\)
Solve for A.
 
Re: 3 problems

when i solve for A i get -3 and 6, are these the possible values for A?
 
Re: 3 problems

You can use those values back into the equation and check.

for #3 - factorize the given expression - and find the value of (x+y)

from there find (x+y)^2 and hence find x^2 + y^2.
 
Re: 3 problems

Hockeyman said:
1) A plane flys round trip from Yarmouth to Sydney. When the plane is flying into a headwind its speed is 300km/h, and its speed with a tail wind is 600km/h. What is the average speed for the round trip?
Click to expand...

Let d = distance between Yarmouth and Sydney

Let t[sub:3syjumqn]1[/sub:3syjumqn] = time going into the headwind

Let t[sub:3syjumqn]2[/sub:3syjumqn] = time going with the tailwind

t[sub:3syjumqn]1[/sub:3syjumqn] = d / 300

t[sub:3syjumqn]2[/sub:3syjumqn] = d / 600

Average speed = total distance / total time

The total distance is 2d. The total time is t[sub:3syjumqn]1[/sub:3syjumqn] + t[sub:3syjumqn]2[/sub:3syjumqn]

Average speed = (2d) / (t[sub:3syjumqn]1[/sub:3syjumqn] + t[sub:3syjumqn]2[/sub:3syjumqn])

Average speed = (2d) / [(d/300) + d/600)]

Ok...you should be able to solve this now...if you're still having trouble, please repost, showing what you've done.
 
Re: 3 problems

Hockeyman said:
3) You are given that xy=6 and x^2y + xy^2 + x + y = 63. Calculate the value of x^2 + y^2.
Click to expand...

You can factor the left side by grouping:

x[sup:jaiavt8w]2[/sup:jaiavt8w]y + xy[sup:jaiavt8w]2[/sup:jaiavt8w] + x + y = 63

xy(x + y) + 1(x + y) = 63

(x + y)(xy + 1) = 63

NOW, you know that xy = 6. So,

(x + y)*(6 + 1) = 63

7(x + y) = 63

(x + y) = 9

Now, it should be relatively easy to find the value of x[sup:jaiavt8w]2[/sup:jaiavt8w] + y[sup:jaiavt8w]2[/sup:jaiavt8w]....

If you're still having trouble, please repost showing what you have done to try to solve this problem.
 
Re: 3 problems

For my answer i squared both sides and solved for x^2 + y^2 and ended up getting that x^2 + y^2 = 69?
 
Re: 3 problems

Hockeyman said:
For my answer i squared both sides and solved for x^2 + y^2 and ended up getting that x^2 + y^2 = 69?....Correct
Click to expand...
 
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