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- Jun 15th 2008, 06:20 AM #1

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## help

1.Determine the maximum area of a triangle that has a hypotenuse of 5 m.[/FONT][/COLOR]

2.Determine the local maxima and local minima of the function sinx^3 +cosx^3 for (0,2pie)

3. Two sides of a triangle have lengths of 1 m and 2 m. The angle between them is increasing at /1000 rad/s.Determine the rate of change of the third side when the angle between the first two sides is pie/4

- Jun 15th 2008, 06:25 AM #2

- Jun 15th 2008, 07:45 AM #3

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- Jun 15th 2008, 07:48 AM #4
Hi

I don't think he was taunting you o.O

For the first exercise, let x be one of the sides of the triangle.

Then, express the length of the third side with respect to the hypotenuse and x, using the Pythagorean theorem.

--> area=x*(third side)/2=...a function of x...

Edit : this is my 22th post ^^

- Jun 15th 2008, 09:07 AM #5

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- Jun 15th 2008, 09:19 AM #6
I'm assuming since we have the word "hypotenuse" we are dealing with a right triangle. So assume this right triangle has legs a and b. Then by the Pythagorean theorem we know that

The area of this triangle is

Use the first derivative to find the value of a that corresponds to the maximum area.

-Dan