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Question Number 12267    Answers: 2   Comments: 0

Find the nth term of the sequence 1) (1/3) , (1/(15)) , (1/(35)) , (1/(63)) , (1/(99)) 2) (1/2), (1/6), (1/(12)), (1/(20)), (1/(30))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sequence} \\ $$$$\left.\mathrm{1}\right)\:\:\:\frac{\mathrm{1}}{\mathrm{3}}\:,\:\frac{\mathrm{1}}{\mathrm{15}}\:,\:\frac{\mathrm{1}}{\mathrm{35}}\:,\:\frac{\mathrm{1}}{\mathrm{63}}\:,\:\frac{\mathrm{1}}{\mathrm{99}} \\ $$$$\left.\mathrm{2}\right)\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}},\:\frac{\mathrm{1}}{\mathrm{6}},\:\frac{\mathrm{1}}{\mathrm{12}},\:\frac{\mathrm{1}}{\mathrm{20}},\:\frac{\mathrm{1}}{\mathrm{30}} \\ $$

Question Number 12265    Answers: 0   Comments: 2

Determinant method can be used to solve the system below?, if yes solve by determinant method and if no solve by another method x+y−z=8 2x+y−2z=3 (give clear reason for your answer)

$${Determinant}\:{method}\:{can}\:{be}\:{used}\:{to}\:{solve} \\ $$$${the}\:{system}\:{below}?,\:\mathrm{if}\:\mathrm{yes}\:\mathrm{solve}\:\mathrm{by}\:\mathrm{determinant}\:\mathrm{method}\:\mathrm{and} \\ $$$$\:\mathrm{if}\:\mathrm{no}\:\mathrm{solve}\:\mathrm{by}\:\mathrm{another}\:\mathrm{method} \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$$${x}+{y}−{z}=\mathrm{8} \\ $$$$\mathrm{2}{x}+{y}−\mathrm{2}{z}=\mathrm{3} \\ $$$$\left({give}\:{clear}\:{reason}\:{for}\:{your}\:{answer}\right) \\ $$

Question Number 12148    Answers: 0   Comments: 13

Question Number 12131    Answers: 0   Comments: 0

a cube has a rib ABCD.EFGH, the midle point P on BF so that BP = PF, and the midle point Q on FG so that FQ = QG how long projection point C to APQH field ?

$${a}\:{cube}\:{has}\:{a}\:{rib}\:{ABCD}.{EFGH},\:{the}\:{midle}\:{point}\:{P}\:\:{on}\:{BF}\:{so}\:{that}\:{BP}\:=\:{PF}, \\ $$$${and}\:{the}\:{midle}\:{point}\:{Q}\:{on}\:{FG}\:{so}\:{that}\:{FQ}\:=\:{QG} \\ $$$${how}\:{long}\:{projection}\:{point}\:{C}\:{to}\:{APQH}\:{field}\:? \\ $$

Question Number 12045    Answers: 1   Comments: 0

how much matrices of integers number A= [(a,b),(c,d) ]if A^2 =I and b=c

$${how}\:{much}\:{matrices}\:{of}\:{integers}\:{number} \\ $$$${A}=\begin{bmatrix}{{a}}&{{b}}\\{{c}}&{{d}}\end{bmatrix}{if}\:{A}^{\mathrm{2}} ={I}\:{and}\:{b}={c} \\ $$

Question Number 12019    Answers: 1   Comments: 0

Question Number 12013    Answers: 1   Comments: 0

The slope of a curve is, 7x + 3 and it passes through the point (2, 4), Find the equation of the point

$$\mathrm{The}\:\mathrm{slope}\:\mathrm{of}\:\mathrm{a}\:\mathrm{curve}\:\mathrm{is},\:\mathrm{7x}\:+\:\mathrm{3}\:\:\mathrm{and}\:\mathrm{it}\:\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{2},\:\mathrm{4}\right), \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{point} \\ $$

Question Number 12008    Answers: 1   Comments: 1

Question Number 11991    Answers: 0   Comments: 0

show that: ((2n)/(2n+1))=1−(1/(2n+1)) via power series, and other methods

$$\mathrm{show}\:\mathrm{that}: \\ $$$$\frac{\mathrm{2}{n}}{\mathrm{2}{n}+\mathrm{1}}=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{1}} \\ $$$$\mathrm{via}\:\mathrm{power}\:\mathrm{series},\:\mathrm{and}\:\mathrm{other}\:\mathrm{methods} \\ $$

Question Number 11969    Answers: 2   Comments: 0

A gas occupies 30 dm^3 at s t p, what volume will it occupy at 91°C and 380 mmHg

$$\mathrm{A}\:\mathrm{gas}\:\mathrm{occupies}\:\mathrm{30}\:\mathrm{dm}^{\mathrm{3}} \:\mathrm{at}\:\mathrm{s}\:\mathrm{t}\:\mathrm{p},\:\:\mathrm{what}\:\mathrm{volume}\:\mathrm{will}\:\mathrm{it}\:\mathrm{occupy}\:\mathrm{at}\:\mathrm{91}°\mathrm{C}\: \\ $$$$\mathrm{and}\:\mathrm{380}\:\mathrm{mmHg} \\ $$

Question Number 11935    Answers: 3   Comments: 0

((7!)/(6!))+((8!)/(7!))+((9!)/(8!))+...((n!)/((n−1)!))=84 ⇒n=?

$$\frac{\mathrm{7}!}{\mathrm{6}!}+\frac{\mathrm{8}!}{\mathrm{7}!}+\frac{\mathrm{9}!}{\mathrm{8}!}+...\frac{\mathrm{n}!}{\left(\mathrm{n}−\mathrm{1}\right)!}=\mathrm{84}\:\Rightarrow\mathrm{n}=? \\ $$

Question Number 11915    Answers: 2   Comments: 2

Question Number 11880    Answers: 0   Comments: 0

S_(ABCD) =3+2(√2) ∠BAO=∠MAO=22,5° ∠BCM=∠DCM S_(AOB) =?

$$\boldsymbol{\mathrm{S}}_{\boldsymbol{\mathrm{ABCD}}} =\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}} \\ $$$$\angle\boldsymbol{\mathrm{BAO}}=\angle\boldsymbol{\mathrm{MAO}}=\mathrm{22},\mathrm{5}° \\ $$$$\angle\boldsymbol{\mathrm{BCM}}=\angle\boldsymbol{\mathrm{DCM}} \\ $$$$\boldsymbol{\mathrm{S}}_{\boldsymbol{\mathrm{AOB}}} =? \\ $$

Question Number 11867    Answers: 0   Comments: 1

Question Number 11864    Answers: 2   Comments: 0

∫_7 ^(10) x^2 dx/x^2 −3x+2=

$$\underset{\mathrm{7}} {\overset{\mathrm{10}} {\int}}{x}^{\mathrm{2}} {dx}/{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}= \\ $$

Question Number 11827    Answers: 1   Comments: 0

∫x^2 dcosx=?

$$\int\mathrm{x}^{\mathrm{2}} \mathrm{dcosx}=? \\ $$

Question Number 11759    Answers: 1   Comments: 0

A quadrilateral with consecutive sides of lenght 7, 15, 15, and d is inscribed in a circle with its diameter d. Find the radius of circle

$$\mathrm{A}\:\mathrm{quadrilateral}\:\mathrm{with}\:\mathrm{consecutive}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{lenght}\:\mathrm{7},\:\mathrm{15},\:\mathrm{15},\:\mathrm{and}\:{d} \\ $$$$\mathrm{is}\:\mathrm{inscribed}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{its}\:\mathrm{diameter}\:{d}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{circle} \\ $$

Question Number 11740    Answers: 0   Comments: 0

Metal pellets of mass 0.1 kg are fired into an iron plate of large mass m and specific heat capacity c at a temperature of 15°C . 25% of the kinetic energy of the pellets is converted thermal energy and the plate temperature rises to 16°C. The average speed of the pellets before hitting the plate was ?

$$\mathrm{Metal}\:\mathrm{pellets}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{0}.\mathrm{1}\:\mathrm{kg}\:\mathrm{are}\:\mathrm{fired}\:\mathrm{into}\:\mathrm{an}\:\mathrm{iron}\:\mathrm{plate}\:\mathrm{of}\:\mathrm{large}\:\mathrm{mass}\:\mathrm{m} \\ $$$$\mathrm{and}\:\mathrm{specific}\:\mathrm{heat}\:\mathrm{capacity}\:\mathrm{c}\:\mathrm{at}\:\mathrm{a}\:\mathrm{temperature}\:\mathrm{of}\:\mathrm{15}°\mathrm{C}\:.\:\mathrm{25\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{kinetic} \\ $$$$\mathrm{energy}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pellets}\:\mathrm{is}\:\mathrm{converted}\:\mathrm{thermal}\:\mathrm{energy}\:\mathrm{and}\:\mathrm{the}\:\mathrm{plate}\:\mathrm{temperature} \\ $$$$\mathrm{rises}\:\mathrm{to}\:\mathrm{16}°\mathrm{C}.\:\mathrm{The}\:\mathrm{average}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pellets}\:\mathrm{before}\:\mathrm{hitting}\:\mathrm{the}\:\mathrm{plate}\:\mathrm{was}\:? \\ $$

Question Number 11781    Answers: 3   Comments: 0

sin(2θ) + 7cos(2θ) = 6 find θ

$$\mathrm{sin}\left(\mathrm{2}\theta\right)\:+\:\mathrm{7cos}\left(\mathrm{2}\theta\right)\:=\:\mathrm{6} \\ $$$$\mathrm{find}\:\theta \\ $$

Question Number 11632    Answers: 1   Comments: 0

Question Number 11594    Answers: 1   Comments: 0

please how can demonstred sin(2x)_ /cos(2x)=2sin(2x)

$${please}\:{how}\:{can}\:{demonstred}\: \\ $$$${sin}\left(\mathrm{2}{x}\underset{} {\right)}/{cos}\left(\mathrm{2}{x}\right)=\mathrm{2}{sin}\left(\mathrm{2}{x}\right) \\ $$

Question Number 11403    Answers: 0   Comments: 1

how can demonstred that cos(2x)−sin(2x)−1=−cos^2 x

$${how}\:{can}\:{demonstred}\:{that}\: \\ $$$${cos}\left(\mathrm{2}{x}\right)−{sin}\left(\mathrm{2}{x}\right)−\mathrm{1}=−{cos}^{\mathrm{2}} {x} \\ $$

Question Number 11344    Answers: 0   Comments: 1

n_c_n =((n!)/((n−n)!n!))

$${n}_{{c}_{{n}} } =\frac{{n}!}{\left({n}−{n}\right)!{n}!} \\ $$

Question Number 11343    Answers: 0   Comments: 1

n_c_n =((n1)/((n−n)))

$${n}_{\boldsymbol{\mathrm{c}}_{\boldsymbol{\mathrm{n}}} } =\frac{{n}\mathrm{1}}{\left({n}−{n}\right)} \\ $$

Question Number 11221    Answers: 0   Comments: 4

Question Number 11148    Answers: 1   Comments: 0

∫((x dx)/((x+1))^(1/3) )=....???

$$\int\frac{{x}\:{dx}}{\sqrt[{\mathrm{3}}]{{x}+\mathrm{1}}}=....??? \\ $$

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