12, Mathematics

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Determines the angles of depression, A pilot is flying over a straight leng...

A pilot is flying over a straight length of road. He determines the angles of depression of two mileposts, 5 miles apart, to be 32° and 48°. a) Find the distance of the plane f

Limit, limit x APProaches infinity (1+1/x)x=e

limit x APProaches infinity (1+1/x)x=e

Word Problem, a local pizza store offers medium two-topping pizzas delivere...

a local pizza store offers medium two-topping pizzas delivered for $6.00 per pizza plus a $1.50 delivery charge per order. on weekends, the store runs a game day special: if six or

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

Find the distance of the journey, A train covered a certain distance at a u...

A train covered a certain distance at a uniform speed.  If the train would have been 6km/hr faster, it would have taken 4hours less than the scheduled time.   And if the train were

Analyze the dynamic path - difference equation, One of the well-known class...

One of the well-known class of models that involve a simple difference equation are models of mean reversion. These models typically take the form yt+1 - yt = -a(yt - μ)where 0

Example of integrals involving trig functions, Example of Integrals Involvi...

Example of Integrals Involving Trig Functions Example: Estimate the following integral. ∫ sin 5 x dx Solution This integral no longer contains the cosine in it that

Prove that r is an equivalence relation, 1. Let S be the set of all nonzero...

1. Let S be the set of all nonzero real numbers. That is, S = R - {0}. Consider the relation R on S given by xRy iff xy > 0. (a) Prove that R is an equivalence relation on S, an

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