Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1171

Question Number 98057    Answers: 2   Comments: 0

The number of real solutions of 3^x +4^x =5^x is ____.

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{real}\:\mathrm{solutions}\:\mathrm{of} \\ $$$$\mathrm{3}^{{x}} +\mathrm{4}^{{x}} =\mathrm{5}^{{x}} \:\mathrm{is}\:\_\_\_\_. \\ $$

Question Number 98056    Answers: 0   Comments: 3

The number of real roots of the quadratic equation (x−4)^2 +(x−5)^2 +(x−6)^2 =0 is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{real}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{quadratic} \\ $$$$\mathrm{equation}\:\left({x}−\mathrm{4}\right)^{\mathrm{2}} +\left({x}−\mathrm{5}\right)^{\mathrm{2}} +\left({x}−\mathrm{6}\right)^{\mathrm{2}} =\mathrm{0}\:\mathrm{is} \\ $$

Question Number 98039    Answers: 1   Comments: 0

10000×((10)/(100))×((20)/(100))×((30)/(100))=

$$\mathrm{10000}×\frac{\mathrm{10}}{\mathrm{100}}×\frac{\mathrm{20}}{\mathrm{100}}×\frac{\mathrm{30}}{\mathrm{100}}= \\ $$$$ \\ $$

Question Number 98035    Answers: 0   Comments: 4

Question Number 98030    Answers: 0   Comments: 1

Question Number 98027    Answers: 0   Comments: 1

One card is randomly selected from a pack of 52 playing cards. Determine the probability that is a picture card.

$$\mathrm{One}\:\mathrm{card}\:\mathrm{is}\:\mathrm{randomly}\:\mathrm{selected} \\ $$$$\mathrm{from}\:\mathrm{a}\:\mathrm{pack}\:\mathrm{of}\:\mathrm{52}\:\mathrm{playing}\:\mathrm{cards}. \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\: \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{picture}\:\mathrm{card}.\: \\ $$

Question Number 98022    Answers: 1   Comments: 0

Derive the relation between an Arithmetic Mean and a Geometric Mean ((x_1 x_2 ...x_n ))^(1/n) ≤((x_1 +x_2 +∙∙∙+x_n )/n) ∀n∈N^∗ , ∀(x_1 ,x_2 ,...x_n )∈(R_+ ^∗ )^n

$$\mathcal{D}\mathrm{erive}\:\mathrm{the}\:\mathrm{relation}\:\mathrm{between}\:\mathrm{an}\:\mathcal{A}\mathrm{rithmetic}\:\mathcal{M}\mathrm{ean} \\ $$$$\mathrm{and}\:\mathrm{a}\:\mathcal{G}\mathrm{eometric}\:\mathcal{M}\mathrm{ean} \\ $$$$\sqrt[{\mathrm{n}}]{\mathrm{x}_{\mathrm{1}} \mathrm{x}_{\mathrm{2}} ...\mathrm{x}_{\mathrm{n}} }\leqslant\frac{\mathrm{x}_{\mathrm{1}} +\mathrm{x}_{\mathrm{2}} +\centerdot\centerdot\centerdot+\mathrm{x}_{\mathrm{n}} }{\mathrm{n}}\:\forall\mathrm{n}\in\mathbb{N}^{\ast} ,\:\forall\left(\mathrm{x}_{\mathrm{1}} ,\mathrm{x}_{\mathrm{2}} ,...\mathrm{x}_{\mathrm{n}} \right)\in\left(\mathbb{R}_{+} ^{\ast} \right)^{\mathrm{n}} \\ $$

Question Number 98020    Answers: 1   Comments: 0

What is the area of the region bounded by x^2 +y^2 ≤ 9 ; x+y ≤ 3 and y ≤ x

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{region}\:\mathrm{bounded} \\ $$$$\mathrm{by}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:\leqslant\:\mathrm{9}\:;\:\mathrm{x}+\mathrm{y}\:\leqslant\:\mathrm{3}\:\mathrm{and}\:\mathrm{y}\:\leqslant\:\mathrm{x}\: \\ $$

Question Number 98018    Answers: 1   Comments: 0

the vector equations of two lines l_1 and l_2 are given by l_1 :r=5i−j+k+λ(−3i+2j) l_2 :r=2i+3j+2k+μ(2j+k) find thd position vdctor of intersection of thf linds l_1 and l_2 thd cartesian equatkon of the plane π, containing the lines l_(1 ) and l_2 the sine of the anhle between the plane π and the line, l_3 :r=i−5j−2k+s(2i+2j−k)

$${the}\:{vector}\:{equations}\:{of}\:{two}\:{lines}\:{l}_{\mathrm{1}} \:{and}\:{l}_{\mathrm{2}} \:{are}\:{given}\:{by} \\ $$$${l}_{\mathrm{1}} :{r}=\mathrm{5}{i}−{j}+{k}+\lambda\left(−\mathrm{3}{i}+\mathrm{2}{j}\right) \\ $$$${l}_{\mathrm{2}} :{r}=\mathrm{2}{i}+\mathrm{3}{j}+\mathrm{2}{k}+\mu\left(\mathrm{2}{j}+{k}\right) \\ $$$${find} \\ $$$${thd}\:{position}\:{vdctor}\:{of}\:{intersection}\:{of}\:{thf}\:{linds}\:{l}_{\mathrm{1}} \:{and}\:{l}_{\mathrm{2}} \: \\ $$$${thd}\:{cartesian}\:{equatkon}\:{of}\:{the}\:{plane}\:\pi,\:{containing}\:{the}\:{lines}\:{l}_{\mathrm{1}\:} {and}\:{l}_{\mathrm{2}} \\ $$$${the}\:{sine}\:{of}\:{the}\:{anhle}\:{between}\:{the}\:{plane}\:\pi\:{and}\:{the}\:{line},\:{l}_{\mathrm{3}} :{r}={i}−\mathrm{5}{j}−\mathrm{2}{k}+{s}\left(\mathrm{2}{i}+\mathrm{2}{j}−{k}\right) \\ $$

Question Number 98016    Answers: 1   Comments: 3

∫_0 ^1 ((ln^2 (x))/(x^2 +1)) dx ?

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{ln}^{\mathrm{2}} \left({x}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx}\:?\: \\ $$

Question Number 98008    Answers: 0   Comments: 1

Question Number 98004    Answers: 0   Comments: 1

lim_(n→∞) [sin(n)+4^n ×(3/n^2 )×((n+1)/(n^2 −4))]

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left[\mathrm{sin}\left(\mathrm{n}\right)+\mathrm{4}^{\mathrm{n}} ×\frac{\mathrm{3}}{\mathrm{n}^{\mathrm{2}} }×\frac{\mathrm{n}+\mathrm{1}}{\mathrm{n}^{\mathrm{2}} −\mathrm{4}}\right] \\ $$

Question Number 98003    Answers: 4   Comments: 0

prove that E=mc^2

$${prove}\:{that}\: \\ $$$${E}={mc}^{\mathrm{2}} \:\: \\ $$

Question Number 97994    Answers: 1   Comments: 0

find all the values of θ, in the interval 0≤θ≤2π for which sin 3θ−sin θ=(√(3cos 2θ))

$${find}\:{all}\:{the}\:{values}\:{of}\:\theta,\:{in}\:{the}\:{interval}\:\mathrm{0}\leqslant\theta\leqslant\mathrm{2}\pi \\ $$$${for}\:{which}\:\mathrm{sin}\:\mathrm{3}\theta−\mathrm{sin}\:\theta=\sqrt{\mathrm{3cos}\:\mathrm{2}\theta} \\ $$

Question Number 97990    Answers: 1   Comments: 0

find lim_(x→1^+ ) ∫_x ^x^2 ((lnt)/((t−1)^2 ))dt

$$\mathrm{find}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{1}^{+} } \:\:\int_{\mathrm{x}} ^{\mathrm{x}^{\mathrm{2}} } \:\:\frac{\mathrm{lnt}}{\left(\mathrm{t}−\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dt} \\ $$

Question Number 97988    Answers: 0   Comments: 0

calculate by recurrence A_n =∫_0 ^(π/4) (dx/(cos^n x))

$$\mathrm{calculate}\:\mathrm{by}\:\mathrm{recurrence}\:\mathrm{A}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\frac{\mathrm{dx}}{\mathrm{cos}^{\mathrm{n}} \mathrm{x}} \\ $$

Question Number 97987    Answers: 1   Comments: 0

find lim_(n→+∞) Σ_(k=1) ^n (√((n−k)/(n^3 −n^2 k)))

$$\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \sqrt{\frac{\mathrm{n}−\mathrm{k}}{\mathrm{n}^{\mathrm{3}} −\mathrm{n}^{\mathrm{2}} \mathrm{k}}} \\ $$

Question Number 97985    Answers: 2   Comments: 0

let S_n =Σ_(k=1) ^n (1/(√(n^2 +2kn))) find lim_(n→+∞) S_n

$$\mathrm{let}\:\mathrm{S}_{\mathrm{n}} =\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\frac{\mathrm{1}}{\sqrt{\mathrm{n}^{\mathrm{2}} +\mathrm{2kn}}} \\ $$$$\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\mathrm{S}_{\mathrm{n}} \\ $$

Question Number 97984    Answers: 2   Comments: 0

calculate Σ_(k=0) ^n (((−1)^k )/(2k+1)) C_n ^k

$$\mathrm{calculate}\:\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{k}} }{\mathrm{2k}+\mathrm{1}}\:\mathrm{C}_{\mathrm{n}} ^{\mathrm{k}} \\ $$

Question Number 97983    Answers: 0   Comments: 0

f continue on [0,1] and f(x)>0 on [0,1] prove that ∫_0 ^1 lnf(x)dx≤ln(∫_0 ^1 f(x)dx)

$$\mathrm{f}\:\mathrm{continue}\:\:\mathrm{on}\:\left[\mathrm{0},\mathrm{1}\right]\:\mathrm{and}\:\mathrm{f}\left(\mathrm{x}\right)>\mathrm{0}\:\mathrm{on}\:\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\mathrm{prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{lnf}\left(\mathrm{x}\right)\mathrm{dx}\leqslant\mathrm{ln}\left(\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\right) \\ $$

Question Number 97981    Answers: 1   Comments: 0

calculate lim_(x→1^+ ) ∫_(x−1) ^(x^2 −1) (dt/(ln(1+t)))

$$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{1}^{+} } \:\:\int_{\mathrm{x}−\mathrm{1}} ^{\mathrm{x}^{\mathrm{2}} −\mathrm{1}} \:\frac{\mathrm{dt}}{\mathrm{ln}\left(\mathrm{1}+\mathrm{t}\right)} \\ $$

Question Number 97979    Answers: 0   Comments: 0

find lim_(n→+∞) (C_(2n) ^n )^(1/n)

$$\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\left(\mathrm{C}_{\mathrm{2n}} ^{\mathrm{n}} \right)^{\frac{\mathrm{1}}{\mathrm{n}}} \\ $$

Question Number 97972    Answers: 3   Comments: 0

Prove that, (d/dx)(e^x ) = e^x

$$\:\:\:\:\mathrm{Prove}\:\mathrm{that}, \\ $$$$\:\:\:\:\:\frac{\boldsymbol{{d}}}{\boldsymbol{{dx}}}\left(\boldsymbol{{e}}^{\boldsymbol{{x}}} \right)\:=\:\boldsymbol{{e}}^{\boldsymbol{{x}}} \\ $$

Question Number 97968    Answers: 1   Comments: 1

$$ \\ $$

Question Number 99300    Answers: 1   Comments: 0

Find Σ_(n=1) ^∞ (1/((3n)!))=?

$$\mathrm{Find}\:\:\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{3}\boldsymbol{{n}}\right)!}=? \\ $$

Question Number 97963    Answers: 0   Comments: 0

  Pg 1166      Pg 1167      Pg 1168      Pg 1169      Pg 1170      Pg 1171      Pg 1172      Pg 1173      Pg 1174      Pg 1175   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com