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Question Number 224637 Answers: 0 Comments: 0

Question Number 224635 Answers: 1 Comments: 0

Prove that: sin(54°) = (((√5) + 1)/4)

$$\mathrm{Prove}\:\mathrm{that}:\:\:\:\mathrm{sin}\left(\mathrm{54}°\right)\:=\:\:\frac{\sqrt{\mathrm{5}}\:+\:\mathrm{1}}{\mathrm{4}} \\ $$

Question Number 224629 Answers: 4 Comments: 0

Question Number 224614 Answers: 1 Comments: 0

A binary operation ∗ is defined on a set real numbers, R by x∗y = 2x + 2y −((xy)/3) . find: (i) The inverse of x under the operation ∗ (ii) Truth set when m∗7=−2∗m

$${A}\:{binary}\:{operation}\:\ast\:{is}\:{defined}\:{on}\:{a}\:{set} \\ $$$${real}\:{numbers},\:{R}\:{by} \\ $$$${x}\ast{y}\:=\:\mathrm{2}{x}\:+\:\mathrm{2}{y}\:−\frac{{xy}}{\mathrm{3}}\:. \\ $$$${find}: \\ $$$$\left({i}\right)\:{The}\:{inverse}\:{of}\:{x}\:{under}\:{the}\:{operation}\:\ast \\ $$$$\left({ii}\right)\:{Truth}\:{set}\:{when}\:{m}\ast\mathrm{7}=−\mathrm{2}\ast{m} \\ $$

Question Number 224591 Answers: 1 Comments: 0

p is a prime number prove that if p^2 +8 is prime ⇒ ⇒ p^3 +4 is also prime

$$\mathrm{p}\:{is}\:{a}\:{prime}\:{number} \\ $$$${prove}\:{that}\:{if}\:\mathrm{p}^{\mathrm{2}} +\mathrm{8}\:{is}\:{prime}\:\Rightarrow \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:{p}^{\mathrm{3}} +\mathrm{4}\:{is}\:{also}\:{prime} \\ $$

Question Number 224570 Answers: 2 Comments: 0

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Question Number 224539 Answers: 3 Comments: 0

a^x =m, a^y =n ,a^2 =(m^y n^x )^z prove xyz=1

$${a}^{{x}} ={m},\:{a}^{{y}} ={n}\:,{a}^{\mathrm{2}} =\left({m}^{{y}} {n}^{{x}} \right)^{{z}} \\ $$$${prove}\:{xyz}=\mathrm{1} \\ $$

Question Number 224538 Answers: 2 Comments: 0

32^(4r^2 −8) =1 then find r=?

$$\mathrm{32}^{\mathrm{4r}^{\mathrm{2}} −\mathrm{8}} =\mathrm{1}\:\:\:\:\mathrm{then}\:\mathrm{find}\:\mathrm{r}=? \\ $$

Question Number 224455 Answers: 1 Comments: 0

If a,b,c ≠ 0 what is the difference between the maximum snd minimum value of S = 1 + ((∣a∣)/a) + ((2∣b∣)/b) + ((3∣ab∣)/(ab)) − ((4∣c∣)/c) ?

$${If}\:{a},{b},{c}\:\neq\:\mathrm{0}\:{what}\:{is}\:{the}\:{difference} \\ $$$${between}\:{the}\:{maximum}\:{snd}\:{minimum}\: \\ $$$${value}\:{of} \\ $$$${S}\:=\:\mathrm{1}\:+\:\frac{\mid{a}\mid}{{a}}\:+\:\frac{\mathrm{2}\mid{b}\mid}{{b}}\:+\:\frac{\mathrm{3}\mid{ab}\mid}{{ab}}\:−\:\frac{\mathrm{4}\mid{c}\mid}{{c}}\:? \\ $$

Question Number 224453 Answers: 0 Comments: 6

Question Number 224392 Answers: 2 Comments: 0

−∞<a<b<∞ and 0<λ<1 x_1 = a , x_2 = b x_(n+2) = λx_n + (1−λ)x_(n+1) ∀ n ∈ N find x_(n ) = ?

$$\:\:\:\:\:\:\:−\infty<{a}<{b}<\infty\:\:{and}\:\mathrm{0}<\lambda<\mathrm{1}\:\: \\ $$$$\:\:\:\:\:\:\:{x}_{\mathrm{1}} \:=\:{a}\:,\:{x}_{\mathrm{2}} \:=\:{b} \\ $$$$\:\:\:\:\:\:\:\:{x}_{{n}+\mathrm{2}} \:=\:\lambda{x}_{{n}} \:+\:\left(\mathrm{1}−\lambda\right){x}_{{n}+\mathrm{1}} \:\:\forall\:{n}\:\in\:\mathbb{N} \\ $$$$\:\:\mathrm{find}\:\:{x}_{{n}\:} \:=\:?\: \\ $$$$\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 224381 Answers: 0 Comments: 0

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Question Number 224331 Answers: 0 Comments: 0

a,b,c > 0 prove that Σ a^2 ≥ Σ ab + (1/8) Σ (∣a−c∣ + ∣b−c∣)^2

$$\mathrm{a},\mathrm{b},\mathrm{c}\:>\:\mathrm{0} \\ $$$$\mathrm{prove}\:\mathrm{that} \\ $$$$\Sigma\:\mathrm{a}^{\mathrm{2}} \:\geqslant\:\Sigma\:\mathrm{ab}\:+\:\frac{\mathrm{1}}{\mathrm{8}}\:\Sigma\:\left(\mid\mathrm{a}−\mathrm{c}\mid\:+\:\mid\mathrm{b}−\mathrm{c}\mid\right)^{\mathrm{2}} \\ $$

Question Number 224312 Answers: 1 Comments: 0

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(√x)+(√y)=7 (√(x+y))=5 Find (x,y).

$$\sqrt{\mathrm{x}}+\sqrt{\mathrm{y}}=\mathrm{7} \\ $$$$\sqrt{\mathrm{x}+\mathrm{y}}=\mathrm{5} \\ $$$$\mathrm{Find}\:\left(\mathrm{x},\mathrm{y}\right). \\ $$

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Question Number 224146 Answers: 1 Comments: 0

a = 12^(223) ∙ 7^(56) + 19^(25) what is the last digit of the number?

$$\boldsymbol{\mathrm{a}}\:=\:\mathrm{12}^{\mathrm{223}} \:\centerdot\:\mathrm{7}^{\mathrm{56}} \:+\:\mathrm{19}^{\mathrm{25}} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{the}\:\mathrm{number}? \\ $$

Question Number 224095 Answers: 1 Comments: 2

how to prove that x + 9 = x is not has solution because (x + 9)^2 = x^2 x^2 + 18x + 81 = x^2 18x = −81 x = − ((81)/(18)) = −(9/2)

$${how}\:{to}\:{prove}\:{that}\:\:{x}\:+\:\mathrm{9}\:=\:{x}\:{is}\:{not}\:{has}\:{solution} \\ $$$${because}\: \\ $$$$\left({x}\:+\:\mathrm{9}\right)^{\mathrm{2}} \:=\:{x}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} \:+\:\mathrm{18}{x}\:+\:\mathrm{81}\:=\:{x}^{\mathrm{2}} \\ $$$$\mathrm{18}{x}\:=\:−\mathrm{81} \\ $$$${x}\:=\:−\:\frac{\mathrm{81}}{\mathrm{18}}\:=\:−\frac{\mathrm{9}}{\mathrm{2}} \\ $$

Question Number 224080 Answers: 0 Comments: 0

Use choleski′s method to solve the following system of equation 4x_1 −2x_2 +2x_3 =6 4x_1 −3x_2 −2x_3 =−8 2x_1 +3x_2 −x_3 =5

$$\boldsymbol{{Use}}\:\boldsymbol{{choleski}}'\boldsymbol{{s}}\:\boldsymbol{{method}}\:\boldsymbol{{to}}\:\boldsymbol{{solve}}\:\boldsymbol{{the}}\:\boldsymbol{{following}}\:\boldsymbol{{system}} \\ $$$$\boldsymbol{{of}}\:\boldsymbol{{equation}} \\ $$$$\mathrm{4}\boldsymbol{{x}}_{\mathrm{1}} −\mathrm{2}\boldsymbol{{x}}_{\mathrm{2}} +\mathrm{2}\boldsymbol{{x}}_{\mathrm{3}} =\mathrm{6} \\ $$$$\mathrm{4}\boldsymbol{{x}}_{\mathrm{1}} −\mathrm{3}\boldsymbol{{x}}_{\mathrm{2}} −\mathrm{2}\boldsymbol{{x}}_{\mathrm{3}} =−\mathrm{8} \\ $$$$\mathrm{2}\boldsymbol{{x}}_{\mathrm{1}} +\mathrm{3}\boldsymbol{{x}}_{\mathrm{2}} −\boldsymbol{{x}}_{\mathrm{3}} =\mathrm{5} \\ $$

Question Number 224079 Answers: 0 Comments: 0

For the given function f(x),let x_0 =0,x_1 =0.6 and x_2 =0.9. construct the lagrange interpolating polynomials of degree. (1) at most 1 (2)at most 2 to approximate f(0.45) if (a) f(x)=cosx (b) f(x)=(√(1+x)) (c) f(x)=In(1+x) (d) f(x)=tanx

$$\boldsymbol{{For}}\:\boldsymbol{{the}}\:\boldsymbol{{given}}\:\boldsymbol{{function}}\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right),\boldsymbol{{let}}\:\boldsymbol{{x}}_{\mathrm{0}} =\mathrm{0},\boldsymbol{{x}}_{\mathrm{1}} =\mathrm{0}.\mathrm{6} \\ $$$$\boldsymbol{{and}}\:\boldsymbol{{x}}_{\mathrm{2}} =\mathrm{0}.\mathrm{9}.\:\boldsymbol{{construct}}\:\boldsymbol{{the}}\:\boldsymbol{{lagrange}}\:\boldsymbol{{interpolating}} \\ $$$$\boldsymbol{{polynomials}}\:\boldsymbol{{of}}\:\boldsymbol{{degree}}.\:\left(\mathrm{1}\right)\:\boldsymbol{{at}}\:\boldsymbol{{most}}\:\mathrm{1}\:\left(\mathrm{2}\right)\boldsymbol{{at}}\:\boldsymbol{{most}}\:\mathrm{2} \\ $$$$\boldsymbol{{to}}\:\boldsymbol{{approximate}}\:\boldsymbol{{f}}\left(\mathrm{0}.\mathrm{45}\right)\:\boldsymbol{{if}}\: \\ $$$$\left(\boldsymbol{{a}}\right)\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\boldsymbol{{cosx}}\:\:\left(\boldsymbol{{b}}\right)\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\sqrt{\mathrm{1}+\boldsymbol{{x}}}\:\left(\boldsymbol{{c}}\right)\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\boldsymbol{{In}}\left(\mathrm{1}+\boldsymbol{{x}}\right) \\ $$$$\left(\boldsymbol{{d}}\right)\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\boldsymbol{{tanx}} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 224078 Answers: 0 Comments: 0

Evaluate ∫^(𝛑/2) _0 sinxdx with h=(𝛑/(12)),correct to 5 decimal places,using (1)Trapezoidal rule (2)Newton−Cotes formula for n=4 (3)Simpson 3/8 −rule then find the truncation error in each case.

$$\boldsymbol{{Evaluate}}\:\underset{\mathrm{0}} {\int}^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \boldsymbol{{sinxdx}}\:\boldsymbol{{with}}\:\boldsymbol{{h}}=\frac{\boldsymbol{\pi}}{\mathrm{12}},\boldsymbol{{correct}}\:\boldsymbol{{to}} \\ $$$$\mathrm{5}\:\boldsymbol{{decimal}}\:\boldsymbol{{places}},\boldsymbol{{using}} \\ $$$$\left(\mathrm{1}\right)\boldsymbol{{Trapezoidal}}\:\boldsymbol{{rule}} \\ $$$$\left(\mathrm{2}\right)\boldsymbol{{Newton}}−\boldsymbol{{Cotes}}\:\boldsymbol{{formula}}\:\boldsymbol{{for}}\:\boldsymbol{{n}}=\mathrm{4} \\ $$$$\left(\mathrm{3}\right)\boldsymbol{{Simpson}}\:\mathrm{3}/\mathrm{8}\:−\boldsymbol{{rule}} \\ $$$$\boldsymbol{{then}}\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{truncation}}\:\boldsymbol{{error}}\:\boldsymbol{{in}}\:\boldsymbol{{each}}\:\boldsymbol{{case}}. \\ $$

Question Number 224076 Answers: 1 Comments: 0

D=(√((m−(n^2 /4))^2 +(e^m −n)^2 ))+(n^2 /4)(m,n∈R),D_(min) =?

$$ \\ $$$${D}=\sqrt{\left({m}−\frac{{n}^{\mathrm{2}} }{\mathrm{4}}\right)^{\mathrm{2}} +\left({e}^{{m}} −{n}\right)^{\mathrm{2}} }+\frac{{n}^{\mathrm{2}} }{\mathrm{4}}\left({m},{n}\in{R}\right),{D}_{\mathrm{min}} =? \\ $$

Question Number 224069 Answers: 1 Comments: 0

If x^(32) =2^x then solve for x.

$$\mathrm{If}\:\mathrm{x}^{\mathrm{32}} =\mathrm{2}^{\mathrm{x}} \:\mathrm{then}\:\mathrm{solve}\:\mathrm{for}\:\mathrm{x}. \\ $$

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