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Example of optimization , A piece of pipe is carried down a hallway i.e 10 ...

A piece of pipe is carried down a hallway i.e 10 feet wide.  At the ending of the hallway the there is a right-angled turn & the hallway narrows down to 8 feet wide. What is the lo

Discount, outdoor grill- regular price:$360 discount:33 1/3%

outdoor grill- regular price:$360 discount:33 1/3%

Nonhomogeneous systems, We now require addressing nonhomogeneous systems in...

We now require addressing nonhomogeneous systems in brief. Both of the methods which we looked at back in the second order differential equations section can also be used now.  Sin

Additionally functions in substitution rule, Substitution Rule Mostly ...

Substitution Rule Mostly integrals are fairly simple and most of the substitutions are quite simple. The problems arise in correctly getting the integral set up for the substi

Focal chord of the parabola, show that the circle described on any focal c...

show that the circle described on any focal chord of the parabola touches the directrix

Calculus with vector functions - three dimensional space, Calculus with Vec...

Calculus with Vector Functions In this part we need to talk concisely on derivatives, limits and integrals of vector functions. Like you will see, these behave in a quite pred

Law of cosines - vector, Theorem a → • b → = ||a → || ||b → || cos• ...

Theorem a → • b → = ||a → || ||b → || cos• Proof Let us give a modified version of the diagram above. The three vectors above make the triangle AOB and note tha

Rational exponents, Now we have to start looking at more complicated expone...

Now we have to start looking at more complicated exponents. In this section we are going to be evaluating rational exponents. i.e. exponents in the form

Cirlce Division, How can i calculate arc length for dividing a circle into ...

How can i calculate arc length for dividing a circle into 10 parts

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