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**JClarke****Member**- Registered: 2007-04-12
- Posts: 1

Ahhhh, I have a test tomorrow and I'm having a lot of trouble figuring out these questions, can you please help?

(1) Find two numbers whose difference is 10 and whose product is a minimum.

(2) Determine the maximum area of a triangle, in square centimetres, if the sum of its base and height is 10 cm.

(3) Find the value of q so that quadratic equation y=-3(x+2)^2 + q passes through this point.

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**JClarke****Member**- Registered: 2007-04-12
- Posts: 1

Even if you can only help me with one question, I'm in big trouble!!!

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

(1) Let the numbers be *x* and *x*+10. Then their product is y = *x*(*x*+10). Now apply calculus.

(2) If the base is *x*, the height is 10−*x*. The area is *y* = ½*x*(10−*x*). Apply calculus again.

(3) What point?

*Last edited by JaneFairfax (2007-04-12 16:59:07)*

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,684

1) x(x+10) = x²+10x, the derivative is 2x+10, set it to zero (for a minimum or maximum) and you get x = -5. The product is -25, which I would hazard a guess is the minimum.

That is easiest for me, but you could also solve it using Completing the Square:

x²+10x => (x+5)² - 25, and that indicates the point (-5,-25) as a vertex (turning point).

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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