Question and Answers Forum

AllQuestion and Answers: Page 235

Question Number 198423 Answers: 2 Comments: 0

show that ((1+sin∅)/(cos∅)) =((cos∅)/(1−sin∅)) Pls help

$$\mathrm{show}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}+\mathrm{sin}\varnothing}{\mathrm{cos}\varnothing}\:=\frac{\mathrm{cos}\varnothing}{\mathrm{1}−\mathrm{sin}\varnothing} \\ $$$$\mathrm{Pls}\:\mathrm{help} \\ $$$$ \\ $$

Question Number 198421 Answers: 1 Comments: 3

Question Number 198420 Answers: 1 Comments: 0

Question Number 198419 Answers: 0 Comments: 0

Please Help... ∫∫_S x^2 dydz+y^2 dzdx+2z(xy−x−y)dxdy where S is the surface of the cube. 0≤x≤1, 0≤y≤1, 0≤z≤1

$$\:\:{Please}\:{Help}... \\ $$$$\:\:\int\underset{{S}} {\int}{x}^{\mathrm{2}} {dydz}+{y}^{\mathrm{2}} {dzdx}+\mathrm{2}{z}\left({xy}−{x}−{y}\right){dxdy}\:{where} \\ $$$$\:\:\:{S}\:{is}\:{the}\:{surface}\:{of}\:{the}\:{cube}.\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1},\:\mathrm{0}\leqslant{y}\leqslant\mathrm{1}, \\ $$$$\:\:\:\:\mathrm{0}\leqslant{z}\leqslant\mathrm{1} \\ $$$$ \\ $$

Question Number 198418 Answers: 1 Comments: 0

20^(22) −1 = ... (mod 1000)

$$\:\mathrm{20}^{\mathrm{22}} −\mathrm{1}\:=\:...\:\left(\mathrm{mod}\:\mathrm{1000}\right) \\ $$$$ \\ $$

Question Number 198414 Answers: 0 Comments: 0

(3/8)(3h−p)^2 +3ph=(3h^2 −1) and (((3h−p)^3 )/(16))+p(3h^2 −1)=h^3 −h−c Find p and h in terms of 0<c<(2/(3(√3)))∙

$$\frac{\mathrm{3}}{\mathrm{8}}\left(\mathrm{3}{h}−{p}\right)^{\mathrm{2}} +\mathrm{3}{ph}=\left(\mathrm{3}{h}^{\mathrm{2}} −\mathrm{1}\right) \\ $$$${and} \\ $$$$\frac{\left(\mathrm{3}{h}−{p}\right)^{\mathrm{3}} }{\mathrm{16}}+{p}\left(\mathrm{3}{h}^{\mathrm{2}} −\mathrm{1}\right)={h}^{\mathrm{3}} −{h}−{c} \\ $$$${Find}\:\:{p}\:{and}\:{h}\:\:{in}\:{terms}\:{of}\:\mathrm{0}<{c}<\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}}\centerdot \\ $$

Question Number 198413 Answers: 1 Comments: 1

Question Number 198403 Answers: 1 Comments: 0

Question Number 198400 Answers: 3 Comments: 0

20^(11) −1 = ...(mod 1000)

$$\:\:\mathrm{20}^{\mathrm{11}} −\mathrm{1}\:=\:...\left(\mathrm{mod}\:\mathrm{1000}\right) \\ $$

Question Number 198395 Answers: 0 Comments: 4

Question Number 198391 Answers: 2 Comments: 1

Question Number 198426 Answers: 0 Comments: 0

Question Number 198380 Answers: 0 Comments: 2

Question Number 198377 Answers: 1 Comments: 0

Question Number 198373 Answers: 0 Comments: 0

Question Number 198372 Answers: 1 Comments: 1

(1/(1×5)) + (1/(4×8)) + (1/(7×11)) +(1/(10×14)) + …=?

$$\:\:\:\frac{\mathrm{1}}{\mathrm{1}×\mathrm{5}}\:+\:\frac{\mathrm{1}}{\mathrm{4}×\mathrm{8}}\:+\:\frac{\mathrm{1}}{\mathrm{7}×\mathrm{11}}\:+\frac{\mathrm{1}}{\mathrm{10}×\mathrm{14}}\:+\:\ldots=? \\ $$

Question Number 198367 Answers: 0 Comments: 7

if f(x) = ((x^2 −(b+1)x+b)/(x^2 −(a+1)x+a)) (a≠b & a,b ∈ R ∼ {1}) can take all values except two values α & β such that α+β = 0 then ∣((a^3 +b^3 −8)/(ab))∣ = ??

$$\:\:\mathrm{if}\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{{x}^{\mathrm{2}} −\left({b}+\mathrm{1}\right){x}+{b}}{{x}^{\mathrm{2}} −\left({a}+\mathrm{1}\right){x}+{a}}\:\:\left({a}\neq{b}\:\&\:{a},{b}\:\in\:\mathbb{R}\:\sim\:\left\{\mathrm{1}\right\}\right) \\ $$$$\:\:\mathrm{can}\:\mathrm{take}\:\mathrm{all}\:\mathrm{values}\:\mathrm{except}\:\mathrm{two}\:\mathrm{values}\:\alpha\:\&\:\beta \\ $$$$\:\:\mathrm{such}\:\mathrm{that}\:\alpha+\beta\:=\:\mathrm{0}\:\:\mathrm{then}\:\mid\frac{\mathrm{a}^{\mathrm{3}} +\mathrm{b}^{\mathrm{3}} −\mathrm{8}}{\mathrm{ab}}\mid\:\:=\:\:?? \\ $$

Question Number 198363 Answers: 2 Comments: 0

Question Number 198357 Answers: 0 Comments: 0

let a∈R, z∈C resolve (z+1)^n =e^(iπna) deduce that P_n =Π_(k=0) ^(n−1) sin(a+((kπ)/n))

$$\boldsymbol{{let}}\:\:\boldsymbol{{a}}\in\mathbb{R},\:\boldsymbol{{z}}\in\mathbb{C} \\ $$$$\boldsymbol{{resolve}}\: \\ $$$$\left(\boldsymbol{{z}}+\mathrm{1}\right)^{\boldsymbol{{n}}} =\boldsymbol{{e}}^{\boldsymbol{{i}}\pi\boldsymbol{{na}}} \\ $$$$\boldsymbol{{deduce}}\:\boldsymbol{{that}}\:\boldsymbol{{P}}_{\boldsymbol{{n}}} =\underset{{k}=\mathrm{0}} {\overset{\boldsymbol{{n}}−\mathrm{1}} {\prod}}\boldsymbol{{sin}}\left(\boldsymbol{{a}}+\frac{\boldsymbol{{k}}\pi}{\boldsymbol{{n}}}\right) \\ $$

Question Number 198355 Answers: 0 Comments: 2

solve the EDP 1− x(∂f/∂x)−y(∂f/∂y)=0 2− x(∂f/∂x)−(∂f/∂y)=(z^2 /x) 3− x^2 (∂^2 f/∂x^2 )−y^2 (∂^2 f/∂y^2 )=0

$${solve}\:{the}\:{EDP} \\ $$$$\mathrm{1}−\:\:\:{x}\frac{\partial{f}}{\partial{x}}−{y}\frac{\partial{f}}{\partial{y}}=\mathrm{0} \\ $$$$\mathrm{2}−\:\:\:{x}\frac{\partial{f}}{\partial{x}}−\frac{\partial{f}}{\partial{y}}=\frac{{z}^{\mathrm{2}} }{{x}} \\ $$$$ \\ $$$$\mathrm{3}−\:\:{x}^{\mathrm{2}} \frac{\partial^{\mathrm{2}} {f}}{\partial{x}^{\mathrm{2}} }−{y}^{\mathrm{2}} \frac{\partial^{\mathrm{2}} {f}}{\partial{y}^{\mathrm{2}} }=\mathrm{0} \\ $$

Question Number 198352 Answers: 0 Comments: 1

Question Number 198339 Answers: 1 Comments: 0

Question Number 198326 Answers: 0 Comments: 0

express 𝚪(k−n) in pocchammer symbol

$$\boldsymbol{\mathrm{express}}\:\boldsymbol{\Gamma}\left(\boldsymbol{{k}}−\boldsymbol{{n}}\right)\:\boldsymbol{{in}}\:\boldsymbol{{pocchammer}}\:\boldsymbol{{symbol}} \\ $$

Question Number 198321 Answers: 2 Comments: 1

A certain preliminary science class contains 50 students all of whom take Mathematics. 18 study Chemistry, 17 study Biology, 24 study Physics. Of those taking three subjects, 5 study Physics and Chemistry, 7 study Physics and Biology and 6 study Chemistry and Biology while 2 take all four subjects. How many students study only Mathematics?

$${A}\:{certain}\:{preliminary}\:{science}\:{class} \\ $$$${contains}\:\mathrm{50}\:{students}\:{all}\:{of}\:{whom}\:{take} \\ $$$${Mathematics}.\:\mathrm{18}\:{study}\:{Chemistry},\:\mathrm{17} \\ $$$${study}\:{Biology},\:\mathrm{24}\:{study}\:{Physics}.\:{Of} \\ $$$${those}\:{taking}\:{three}\:{subjects},\:\mathrm{5}\:{study} \\ $$$${Physics}\:{and}\:{Chemistry},\:\mathrm{7}\:{study}\:{Physics} \\ $$$${and}\:{Biology}\:{and}\:\mathrm{6}\:{study}\:{Chemistry} \\ $$$${and}\:{Biology}\:{while}\:\mathrm{2}\:{take}\:{all}\:{four}\:{subjects}. \\ $$$${How}\:{many}\:{students}\:{study}\:{only}\:{Mathematics}? \\ $$

Question Number 198319 Answers: 1 Comments: 1

An analysis of 100 personal injury claims made upon a motor insurance company revealed that loss or injury in respect of an eye, an arm or leg occurred in 30, 50 and 70 cases, respectively. Claims involving the loss or injury to two of these number 44. How many claims involved loss or injury to all three. Assume that one or other of the three members was mentioned in each of the 100 claims.

$${An}\:{analysis}\:{of}\:\mathrm{100}\:{personal}\:{injury} \\ $$$${claims}\:{made}\:{upon}\:{a}\:{motor}\:{insurance} \\ $$$${company}\:{revealed}\:{that}\:{loss}\:{or}\:{injury} \\ $$$${in}\:{respect}\:{of}\:{an}\:{eye},\:{an}\:{arm}\:{or}\:{leg} \\ $$$${occurred}\:{in}\:\mathrm{30},\:\mathrm{50}\:{and}\:\mathrm{70}\:{cases},\:{respectively}. \\ $$$${Claims}\:{involving}\:{the}\:{loss}\:{or}\:{injury}\:{to} \\ $$$${two}\:{of}\:{these}\:{number}\:\mathrm{44}.\:{How}\:{many} \\ $$$${claims}\:{involved}\:{loss}\:{or}\:{injury}\:{to}\:{all} \\ $$$${three}.\:{Assume}\:{that}\:{one}\:{or}\:{other}\:{of} \\ $$$${the}\:{three}\:{members}\:{was}\:{mentioned}\:{in} \\ $$$${each}\:{of}\:{the}\:\mathrm{100}\:{claims}. \\ $$

Question Number 198314 Answers: 0 Comments: 0

Solve the EDP x^2 (∂^2 u/∂x^2 )−y^2 (∂^2 u/∂y^2 )=0

$${Solve}\:{the}\:{EDP} \\ $$$${x}^{\mathrm{2}} \frac{\partial^{\mathrm{2}} {u}}{\partial{x}^{\mathrm{2}} }−{y}^{\mathrm{2}} \frac{\partial^{\mathrm{2}} {u}}{\partial{y}^{\mathrm{2}} }=\mathrm{0} \\ $$

Pg 230 Pg 231 Pg 232 Pg 233 Pg 234 Pg 235 Pg 236 Pg 237 Pg 238 Pg 239

Contact: info@tinkutara.com