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Question Number 78948 Answers: 1 Comments: 7

Prove by mathematical induction that. n^4 + 4n^2 + 11 is divisible by 16

$$\mathrm{Prove}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction}\:\mathrm{that}. \\ $$$$\:\:\:\mathrm{n}^{\mathrm{4}} \:+\:\mathrm{4n}^{\mathrm{2}} \:+\:\mathrm{11}\:\:\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{16} \\ $$

Question Number 78946 Answers: 1 Comments: 2

solve cosx−(√3)sinx=1

$$\mathrm{solve} \\ $$$$\mathrm{cos}{x}−\sqrt{\mathrm{3}}{sinx}=\mathrm{1} \\ $$

Question Number 78944 Answers: 0 Comments: 1

Hello sirs i need your help to solve tan2x≥(√3) in [0;2π]. i want that you explain me if possible how we make graphic to determinate.

$$\mathrm{Hello}\:\mathrm{sirs}\:\mathrm{i}\:\mathrm{need}\:\mathrm{your}\:\mathrm{help}\:\mathrm{to}\:\mathrm{solve} \\ $$$$\mathrm{tan2}{x}\geqslant\sqrt{\mathrm{3}}\:\mathrm{in}\:\left[\mathrm{0};\mathrm{2}\pi\right]. \\ $$$$\mathrm{i}\:\mathrm{want}\:\mathrm{that}\:\mathrm{you}\:\mathrm{explain}\:\mathrm{me}\:\mathrm{if}\: \\ $$$$\mathrm{possible}\:\mathrm{how}\:\mathrm{we}\:\mathrm{make}\:\mathrm{graphic}\:\mathrm{to} \\ $$$$\mathrm{determinate}. \\ $$

Question Number 78941 Answers: 2 Comments: 0

Q.find the sum S=(2^3 /(2!))+(3^3 /(3!))+(4^3 /(4!))+.... then find Σ_(n=1) ^∞ (n^4 /(n!))

$${Q}.{find}\:{the}\:{sum} \\ $$$${S}=\frac{\mathrm{2}^{\mathrm{3}} }{\mathrm{2}!}+\frac{\mathrm{3}^{\mathrm{3}} }{\mathrm{3}!}+\frac{\mathrm{4}^{\mathrm{3}} }{\mathrm{4}!}+.... \\ $$$${then}\:{find}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}^{\mathrm{4}} }{{n}!} \\ $$

Question Number 78937 Answers: 1 Comments: 5

Question Number 78933 Answers: 0 Comments: 4

Question Number 78931 Answers: 1 Comments: 8

if x+(1/x)=a find x^n +(1/x^n )=?

$${if}\:{x}+\frac{\mathrm{1}}{{x}}={a} \\ $$$${find}\:{x}^{{n}} +\frac{\mathrm{1}}{{x}^{{n}} }=? \\ $$

Question Number 78897 Answers: 1 Comments: 11

Question Number 78894 Answers: 0 Comments: 1

if U=x^3 +y^3 +6 sinz+11 then u_z (1,0,pi) is

$${if}\:{U}={x}^{\mathrm{3}} +{y}^{\mathrm{3}} +\mathrm{6}\:{sinz}+\mathrm{11}\:{then}\:{u}_{{z}} \left(\mathrm{1},\mathrm{0},{pi}\right)\:{is} \\ $$

Question Number 78890 Answers: 0 Comments: 2

the local maximum value of f(x)=x^4 +32x

$${the}\:{local}\:{maximum}\:{value}\:{of}\:{f}\left({x}\right)={x}^{\mathrm{4}} +\mathrm{32}{x} \\ $$

Question Number 78889 Answers: 1 Comments: 0

the angle between the planes r^→ .(2i^→ +2j^→ +2k^→ )=4 and 4x−2y+2z=15 is

$${the}\:{angle}\:{between}\:{the}\:{planes}\:{r}^{\rightarrow} .\left(\mathrm{2}{i}^{\rightarrow} +\mathrm{2}{j}^{\rightarrow} +\mathrm{2}{k}^{\rightarrow} \right)=\mathrm{4}\:{and}\:\mathrm{4}{x}−\mathrm{2}{y}+\mathrm{2}{z}=\mathrm{15}\:{is} \\ $$

Question Number 78888 Answers: 1 Comments: 1

The roots of the equation (x−a)(x−b)=abx^2 are always

$$\mathrm{The}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\left({x}−{a}\right)\left({x}−{b}\right)={abx}^{\mathrm{2}} \:\mathrm{are}\:\mathrm{always} \\ $$

Question Number 78887 Answers: 0 Comments: 2

if teta=tan^(−1) (7) then sec teta is

$${if}\:{teta}=\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{7}\right)\:{then}\:\mathrm{sec}\:{teta}\:{is} \\ $$

Question Number 78885 Answers: 1 Comments: 0

The number of real numbers in [0,2pi] satisfying sin^(−1) x−2sin^2 x+1=0 is

$${The}\:{number}\:{of}\:{real}\:{numbers}\:{in}\:\left[\mathrm{0},\mathrm{2pi}\right]\:\mathrm{satisfying}\:\mathrm{sin}^{−\mathrm{1}} \mathrm{x}−\mathrm{2sin}^{\mathrm{2}} {x}+\mathrm{1}=\mathrm{0}\:{is} \\ $$

Question Number 78878 Answers: 1 Comments: 0

x^3 y′′′ − 3x^2 y′′+6xy′ −6y=x^4 ln(x),x>0

$${x}^{\mathrm{3}} \:{y}'''\:−\:\mathrm{3}{x}^{\mathrm{2}} {y}''+\mathrm{6}{xy}'\:−\mathrm{6}{y}={x}^{\mathrm{4}} \:{ln}\left({x}\right),{x}>\mathrm{0} \\ $$

Question Number 78877 Answers: 1 Comments: 6

if ((sin(A))/(sin(B)))=((sin(D))/(sin(C))) and A+B=C+D then prove that A+B=180 C+D=180

$${if}\:\:\:\frac{{sin}\left({A}\right)}{{sin}\left({B}\right)}=\frac{{sin}\left({D}\right)}{{sin}\left({C}\right)} \\ $$$${and}\:{A}+{B}={C}+{D} \\ $$$$ \\ $$$${then}\:{prove}\:{that}\:\: \\ $$$${A}+{B}=\mathrm{180} \\ $$$${C}+{D}=\mathrm{180} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 78880 Answers: 1 Comments: 0

x + (1/x) = 3 , x ∈ R (x^(2020) + (1/x^(2020) )) mod (10) = y y^2 − 1 = ?

$${x}\:+\:\frac{\mathrm{1}}{{x}}\:\:=\:\:\mathrm{3}\:\:\:,\:\:\:\:{x}\:\in\:\mathbb{R} \\ $$$$\left({x}^{\mathrm{2020}} \:+\:\frac{\mathrm{1}}{{x}^{\mathrm{2020}} }\right)\:\:{mod}\:\left(\mathrm{10}\right)\:\:=\:\:{y} \\ $$$${y}^{\mathrm{2}} \:−\:\mathrm{1}\:\:=\:\:? \\ $$

Question Number 78865 Answers: 2 Comments: 5

lim_(x→0) ((((1+(√(1+x^3 )) ))^(1/3) −(2)^(1/3) )/(2x^3 ))

$$ \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }\:}\:−\sqrt[{\mathrm{3}}]{\mathrm{2}}}{\mathrm{2x}^{\mathrm{3}} } \\ $$

Question Number 78857 Answers: 1 Comments: 5

with a,b∈R prove that ((a+(√3)bi))^(1/3) +((a−(√3)bi))^(1/3) has always real value and find this value (or a way how to find). examples: a=15, b=((28)/9) ⇒ result=5 a=6, b=((35)/9) ⇒ result=4 a=−24, b=((80)/9) ⇒ result=4

$${with}\:{a},{b}\in{R}\:{prove}\:{that} \\ $$$$\sqrt[{\mathrm{3}}]{{a}+\sqrt{\mathrm{3}}{bi}}+\sqrt[{\mathrm{3}}]{{a}−\sqrt{\mathrm{3}}{bi}} \\ $$$${has}\:{always}\:{real}\:{value}\:{and}\:{find}\:{this} \\ $$$${value}\:\left({or}\:{a}\:{way}\:{how}\:{to}\:{find}\right). \\ $$$${examples}: \\ $$$${a}=\mathrm{15},\:{b}=\frac{\mathrm{28}}{\mathrm{9}}\:\:\Rightarrow\:{result}=\mathrm{5} \\ $$$${a}=\mathrm{6},\:{b}=\frac{\mathrm{35}}{\mathrm{9}}\:\:\Rightarrow\:{result}=\mathrm{4} \\ $$$${a}=−\mathrm{24},\:{b}=\frac{\mathrm{80}}{\mathrm{9}}\:\:\Rightarrow\:{result}=\mathrm{4} \\ $$

Question Number 78853 Answers: 4 Comments: 0

∫_0 ^(π/2) ∫_0 ^(π/2) ((sin(x)+sin(y))/(x+y))dxdy?

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\left(\mathrm{x}\right)+\mathrm{sin}\left(\mathrm{y}\right)}{\mathrm{x}+\mathrm{y}}\mathrm{dxdy}? \\ $$

Question Number 78851 Answers: 0 Comments: 1

Question Number 78829 Answers: 0 Comments: 8

given f(x)=f(x+4) ∀x∈R and ∫_5 ^7 f(x)dx=p . what is ∫_2 ^(10) f(x)dx?

$$\mathrm{given}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}+\mathrm{4}\right)\:\forall\mathrm{x}\in\mathbb{R} \\ $$$$\mathrm{and}\:\underset{\mathrm{5}} {\overset{\mathrm{7}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=\mathrm{p}\:.\:\mathrm{what}\:\mathrm{is}\: \\ $$$$\underset{\mathrm{2}} {\overset{\mathrm{10}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}? \\ $$$$ \\ $$

Question Number 78828 Answers: 0 Comments: 3

lim_(x→∞) (2+sin x).lnx = ?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{2}+\mathrm{sin}\:{x}\right).{lnx}\:=\:? \\ $$

Question Number 78827 Answers: 0 Comments: 2

what is inverse function of y= ((5x^5 −3x^3 +x)/(4x^4 −2x^2 +1))

$$\mathrm{what}\:\mathrm{is}\:\mathrm{inverse}\:\:\mathrm{function} \\ $$$$\mathrm{of}\:\mathrm{y}=\:\frac{\mathrm{5x}^{\mathrm{5}} −\mathrm{3x}^{\mathrm{3}} +\mathrm{x}}{\mathrm{4x}^{\mathrm{4}} −\mathrm{2x}^{\mathrm{2}} +\mathrm{1}} \\ $$

Question Number 78815 Answers: 1 Comments: 0

show that sin((2π)/5)=sin((3π)/5)

$$\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{sin}\frac{\mathrm{2}\pi}{\mathrm{5}}=\mathrm{sin}\frac{\mathrm{3}\pi}{\mathrm{5}} \\ $$

Question Number 78814 Answers: 1 Comments: 1

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