Question 202383
1) Solve the following system. 
x^2 + y^2 = 25
2x + y = 10 
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Solve the 2nd equation for "y":
y = 10-2x
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Substitute that into the 1st equation and solve for "x":
x^2 + (10-2x)^2 = 25
x^2 + 100 - 40x + 4x^2 = 25
5x^2 - 40x + 75 = 0
x^2 - 8x + 15 = 0
x^2-5x-3x+15 = 0
x(x-5) -3(x-5) = 0
(x-5)(x-3) = 0
x = 3 or x = 5
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y=10-2x
If x = 3, then y = 10 - 6 = 4
If x = 5, then y = 10 -10 = 0

The solution set {(3,4),(5,0)} 
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2) Complete the following item based on the given information. 
The volume of a box(V) varies directly with its length(l).
 Using k for the constant of proportionality, express the relationship between V and l if V varies directly with l. 
V = kl
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3) Complete the following item based on the given information. 
The volume of a box(V) varies directly with its length(l).
V = kl
 If one of the boxes has a volume of 325 cubic inches and a length of 13 inches, what is the constant of proportionality for the group of boxes? 
k = 325/13 = 25
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4) Complete the following item based on the given information. 
The volume of a box(V) varies directly with its length(l). If a box in the group has a length of 25 inches and k = 15, what is its volume? 
V=kl
V=15*25
= 375 cubic inches
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5) Complete the following item based on the given information. 
The volume of a box(V) varies directly with its length(l). If a box in the group has a length of 30 inches, and the girth of 20 inches (perimeter of the side formed by the width and height), what is its height? Use k = 24. (Hint: Volume = length * width * height. Solve for length, and substitute into the equation for constant of proportionality.)
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V=kl
l = V/k
30 =V/24
V = 720 cu. in.
height = V/[length*width]
height = V/[30*width)
Comment: width seems to be unknown
__?__ inches or __?__ inches 

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Cheers,
Stan H.