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A tugboat is travelling from Asaba to Onitsha across the River Niger with a resultant velocity of 20 knots. If the river flows at 12 knots, the direction of motion of the boat relative to the direction of water flow is?

Question Number 180926 Answers: 0 Comments: 9

For this problem, we define the fractional part of x∈R_(≥0) as {x} = x − ⌊x⌋ where ⌊x⌋ is the integer part of x, i.e the greatest integer less than or equal to x. (a) Draw the function {x} in a cordinate system for 0≤x≤3 (b) Find the area A_n , under the graph of {x} between 0 and n∈N as given by A_n =∫_0 ^n {x}dx. M.m

$$\mathrm{For}\:\mathrm{this}\:\mathrm{problem},\:\mathrm{we}\:\mathrm{define}\:\mathrm{the}\: \\ $$$$\mathrm{fractional}\:\mathrm{part}\:\mathrm{of}\:\mathrm{x}\in\mathbb{R}_{\geqslant\mathrm{0}} \:\mathrm{as} \\ $$$$\left\{\mathrm{x}\right\}\:=\:\mathrm{x}\:−\:\lfloor\mathrm{x}\rfloor \\ $$$$\mathrm{where}\:\lfloor\mathrm{x}\rfloor\:\mathrm{is}\:\mathrm{the}\:\mathrm{integer}\:\mathrm{part}\:\mathrm{of}\:\mathrm{x},\:\mathrm{i}.\mathrm{e} \\ $$$$\mathrm{the}\:\mathrm{greatest}\:\mathrm{integer}\:\mathrm{less}\:\mathrm{than}\:\mathrm{or}\:\mathrm{equal} \\ $$$$\mathrm{to}\:\mathrm{x}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Draw}\:\mathrm{the}\:\mathrm{function}\:\left\{\mathrm{x}\right\}\:\mathrm{in}\:\mathrm{a}\:\mathrm{cordinate} \\ $$$$\mathrm{system}\:\mathrm{for}\:\mathrm{0}\leqslant\mathrm{x}\leqslant\mathrm{3} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{A}_{\mathrm{n}} \:,\:\mathrm{under}\:\mathrm{the}\:\mathrm{graph} \\ $$$$\mathrm{of}\:\left\{\mathrm{x}\right\}\:\mathrm{between}\:\mathrm{0}\:\mathrm{and}\:\mathrm{n}\in\mathbb{N}\:\mathrm{as}\:\mathrm{given}\:\mathrm{by} \\ $$$$\mathrm{A}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\mathrm{n}} \left\{\mathrm{x}\right\}\mathrm{dx}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 180886 Answers: 1 Comments: 0

Question Number 180867 Answers: 1 Comments: 0

Question Number 180866 Answers: 1 Comments: 0

Question Number 180858 Answers: 1 Comments: 0

Question Number 180839 Answers: 1 Comments: 0

Find the derivatives f^′ (x) of the following function with respect to x: f(x)=Sin(π^(Sinx) +π^(Cosx) ). Mastermind

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{derivatives}\:\mathrm{f}^{'} \left(\mathrm{x}\right)\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{function}\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to}\:\mathrm{x}: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{Sin}\left(\pi^{\mathrm{Sinx}} +\pi^{\mathrm{Cosx}} \right). \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 180838 Answers: 0 Comments: 1

Find all x∈R that are solutions to this question: 0=(1−x−x^2 −...)∙(2−x−x^2 −...) Mastermind

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{x}\in\mathbb{R}\:\mathrm{that}\:\mathrm{are}\:\mathrm{solutions}\:\mathrm{to}\:\mathrm{this} \\ $$$$\mathrm{question}:\: \\ $$$$\mathrm{0}=\left(\mathrm{1}−\mathrm{x}−\mathrm{x}^{\mathrm{2}} −...\right)\centerdot\left(\mathrm{2}−\mathrm{x}−\mathrm{x}^{\mathrm{2}} −...\right) \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

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