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Question Number 174507 Answers: 1 Comments: 0

Determine the numerical value of the following expression without the use of a calculator log[log(3)∙(log(2)∙((((√3)−2sin((π/3)))/(π^3 +1))+1))−log(2)log(3)+(−1)^(100) ] Mastermind

$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{numerical}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{following}\:\mathrm{expression}\:\mathrm{without}\:\mathrm{the}\:\mathrm{use} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{calculator} \\ $$$$\mathrm{log}\left[\mathrm{log}\left(\mathrm{3}\right)\centerdot\left(\mathrm{log}\left(\mathrm{2}\right)\centerdot\left(\frac{\sqrt{\mathrm{3}}−\mathrm{2sin}\left(\frac{\pi}{\mathrm{3}}\right)}{\pi^{\mathrm{3}} +\mathrm{1}}+\mathrm{1}\right)\right)−\mathrm{log}\left(\mathrm{2}\right)\mathrm{log}\left(\mathrm{3}\right)+\left(−\mathrm{1}\right)^{\mathrm{100}} \right] \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 174500 Answers: 1 Comments: 0

Find the values of the following infinite sum: 1+(3/π)+(3/π^2 )+(3/π^3 )+(3/π^4 )+(3/π^5 )+... Mastermind

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{infinite} \\ $$$$\mathrm{sum}: \\ $$$$\mathrm{1}+\frac{\mathrm{3}}{\pi}+\frac{\mathrm{3}}{\pi^{\mathrm{2}} }+\frac{\mathrm{3}}{\pi^{\mathrm{3}} }+\frac{\mathrm{3}}{\pi^{\mathrm{4}} }+\frac{\mathrm{3}}{\pi^{\mathrm{5}} }+... \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 174495 Answers: 2 Comments: 2

What are the roots of the function f(x)=(log(3^x )−2log(3))∙(x^2 −1) with x∈R? Mastermind

$$\mathrm{What}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\left(\mathrm{log}\left(\mathrm{3}^{\mathrm{x}} \right)−\mathrm{2log}\left(\mathrm{3}\right)\right)\centerdot\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)\:\mathrm{with} \\ $$$$\mathrm{x}\in\mathrm{R}? \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 174490 Answers: 0 Comments: 1

A die is rolled 57 times, what is the probability that the sum of its outcome is 100?

$$\mathrm{A}\:\mathrm{die}\:\mathrm{is}\:\mathrm{rolled}\:\mathrm{57}\:\mathrm{times},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{its}\:\mathrm{outcome} \\ $$$$\mathrm{is}\:\mathrm{100}? \\ $$

Question Number 174361 Answers: 0 Comments: 1

Question Number 175036 Answers: 1 Comments: 0

Solve the differential equation (xy^2 −1)dx−(x^2 y−1)dy=0

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\left(\mathrm{xy}^{\mathrm{2}} −\mathrm{1}\right)\mathrm{dx}−\left(\mathrm{x}^{\mathrm{2}} \mathrm{y}−\mathrm{1}\right)\mathrm{dy}=\mathrm{0} \\ $$

Question Number 176895 Answers: 2 Comments: 0

7C=log_2 (1/6)+log_3 27 Solve

$$\mathrm{7C}=\mathrm{log}_{\mathrm{2}} \frac{\mathrm{1}}{\mathrm{6}}+\mathrm{log}_{\mathrm{3}} \mathrm{27} \\ $$$$ \\ $$$$\mathrm{Solve} \\ $$

Question Number 174367 Answers: 0 Comments: 2

solve y^(10) ((dy/dx))+(y^(11) /((x−1)))=xy^(12)

$$\mathrm{solve} \\ $$$$\mathrm{y}^{\mathrm{10}} \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)+\frac{\mathrm{y}^{\mathrm{11}} }{\left(\mathrm{x}−\mathrm{1}\right)}=\mathrm{xy}^{\mathrm{12}} \\ $$

Question Number 174220 Answers: 1 Comments: 7

Question Number 181439 Answers: 1 Comments: 0

Question Number 173630 Answers: 0 Comments: 2

(x+4)^2 =x^((x+2)) Please Help...

$$\left({x}+\mathrm{4}\right)^{\mathrm{2}} ={x}^{\left({x}+\mathrm{2}\right)} \\ $$$${Please}\:\:{Help}... \\ $$

Question Number 173620 Answers: 2 Comments: 0

Question Number 173599 Answers: 0 Comments: 1

Find the area bounded by the graph y=x^2 and y=2−x^2 for 0≤x≤2.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{graph} \\ $$$$\mathrm{y}=\mathrm{x}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{y}=\mathrm{2}−\mathrm{x}^{\mathrm{2}} \:\mathrm{for}\:\mathrm{0}\leqslant\mathrm{x}\leqslant\mathrm{2}. \\ $$

Question Number 173245 Answers: 1 Comments: 0

The ends X and Y of an inextensible strings 27m long are fixed at two points on the same horizontal line which are 20 m apart. A particle of mass 7.5 kg is suspended from a point P on the string 12 m from X. (a) Illustrate this information in a diagram. (b) calculate, correct to two decimal places, <YXP and <XYP. (c) Find, correct to the nearest hundredth, the magnitudes of the tensions in the string. [take g=10 ms^(−2) ]

$$\mathrm{The}\:\mathrm{ends}\:\boldsymbol{\mathrm{X}}\:\mathrm{and}\:\boldsymbol{\mathrm{Y}}\:\mathrm{of}\:\mathrm{an}\:\mathrm{inextensible}\:\mathrm{strings}\:\mathrm{27m} \\ $$$$\mathrm{long}\:\mathrm{are}\:\mathrm{fixed}\:\mathrm{at}\:\mathrm{two}\:\mathrm{points}\:\mathrm{on}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{horizontal}\:\mathrm{line}\:\mathrm{which}\:\mathrm{are}\:\mathrm{20}\:\mathrm{m}\:\mathrm{apart}. \\ $$$$\mathrm{A}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{7}.\mathrm{5}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{suspended} \\ $$$$\mathrm{from}\:\mathrm{a}\:\mathrm{point}\:\boldsymbol{\mathrm{P}}\:\mathrm{on}\:\mathrm{the}\:\mathrm{string}\:\mathrm{12}\:\mathrm{m}\:\mathrm{from}\:\boldsymbol{\mathrm{X}}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Illustrate}\:\mathrm{this}\:\mathrm{information}\:\mathrm{in}\:\mathrm{a}\:\mathrm{diagram}. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{calculate},\:\mathrm{correct}\:\mathrm{to}\:\boldsymbol{\mathrm{two}}\:\mathrm{decimal} \\ $$$$\mathrm{places},\:<\mathrm{YXP}\:\mathrm{and}\:<\mathrm{XYP}. \\ $$$$\left(\mathrm{c}\right)\:\mathrm{Find},\:\mathrm{correct}\:\mathrm{to}\:\mathrm{the}\:\boldsymbol{\mathrm{nearest}}\:\mathrm{hundredth}, \\ $$$$\mathrm{the}\:\mathrm{magnitudes}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tensions}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{string}.\:\:\left[\mathrm{take}\:\boldsymbol{\mathrm{g}}=\mathrm{10}\:\mathrm{ms}^{−\mathrm{2}} \right] \\ $$

Question Number 172991 Answers: 2 Comments: 0