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June 15th 2008, 06:20 AM
santatrue

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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 $pie$ /1000 rad/s.Determine the rate of change of the third side when the angle between the first two sides is pie/4
June 15th 2008, 06:25 AM
kalagota

Quote:

Originally Posted by santatrue

[FONT='Cambria','serif']1.Determine the maximum area of a triangle that has a hypotenuse of 5 m.[/font]

[FONT='Cambria','serif']2.[FONT='Cambria','serif']Determine the local maxima and local minima of the function sinx^3 +cosx^3 [FONT='Cambria','serif'] for (0,2pie)[/font][/font][/font]
[FONT='Cambria','serif'][FONT='Cambria','serif']Two sides [/font]
[FONT='Cambria','serif']Two sides 3. Two sides of a triangle have lengths of 1 m and 2 m. The angle between them is increasing at $pie$ /1000 rad/s.Determine[/font]
[FONT='Cambria','serif']Determine the rate of change of the third side when the angle between the first two sides is pie/4[/font]
[/font]

these are applications of first and second derivative tests.. why don't you give us what you have done so far and we'll check it for you..
June 15th 2008, 07:45 AM
santatrue

Quote:

Originally Posted by kalagota

these are applications of first and second derivative tests.. why don't you give us what you have done so far and we'll check it for you..

of course i tried my best but cannot get to any answer

would be great if you could help me instead of taunting me for my incapablity
June 15th 2008, 07:48 AM
Moo

Hi

Quote:

Originally Posted by santatrue

of course i tried my best but cannot get to any answer

would be great if you could help me instead of taunting me for my incapablity

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 22:):)th post ^^
June 15th 2008, 09:07 AM
santatrue

Quote:

Originally Posted by Moo

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 22:):)th post ^^

sorry but i m still unable to continue after that

i need many help even for the other questions
June 15th 2008, 09:19 AM
topsquark

Quote:

Originally Posted by santatrue

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

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
$a^2 + b^2 = 25$

$b = \sqrt{25 - a^2}$

The area of this triangle is
$A = \frac{1}{2}ab = \frac{1}{2}a \sqrt{25 - a^2}$

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

-Dan