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Question Number 110897 Answers: 3 Comments: 0

(1)4x−4 ≤ ∣x^2 −3x+2 ∣ find the solution set (2) ((1+cos ((α/2))−sin ((α/2)))/(1−cos ((α/2))−sin ((α/2))))=?

$$\left(\mathrm{1}\right)\mathrm{4x}−\mathrm{4}\:\leqslant\:\mid\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{2}\:\mid\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{set}\: \\ $$$$\left(\mathrm{2}\right)\:\frac{\mathrm{1}+\mathrm{cos}\:\left(\frac{\alpha}{\mathrm{2}}\right)−\mathrm{sin}\:\left(\frac{\alpha}{\mathrm{2}}\right)}{\mathrm{1}−\mathrm{cos}\:\left(\frac{\alpha}{\mathrm{2}}\right)−\mathrm{sin}\:\left(\frac{\alpha}{\mathrm{2}}\right)}=? \\ $$

Question Number 110895 Answers: 3 Comments: 0

How many ways can 2018 be expressed as the sum of two squares?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{2018}\:\mathrm{be} \\ $$$$\mathrm{expressed}\:\mathrm{as}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{two}\:\mathrm{squares}? \\ $$

Question Number 110879 Answers: 0 Comments: 1

Question Number 110875 Answers: 4 Comments: 0

(1)∫_e ^e^e ((ln (x).ln (ln (x)))/x) dx ? (2)lim_(x→π/4) ((cosec^2 x−2)/(cot x−1)) (3) Given { ((xy=((16y−9x)/(45)))),(((4/( (√x)))−(3/( (√y))) = 5)) :} ⇒find 9(√(xy))

$$\left(\mathrm{1}\right)\underset{\mathrm{e}} {\overset{\mathrm{e}^{\mathrm{e}} } {\int}}\:\frac{\mathrm{ln}\:\left(\mathrm{x}\right).\mathrm{ln}\:\left(\mathrm{ln}\:\left(\mathrm{x}\right)\right)}{\mathrm{x}}\:\mathrm{dx}\:? \\ $$$$\left(\mathrm{2}\right)\underset{{x}\rightarrow\pi/\mathrm{4}} {\mathrm{lim}}\:\frac{\mathrm{cosec}\:^{\mathrm{2}} \mathrm{x}−\mathrm{2}}{\mathrm{cot}\:\mathrm{x}−\mathrm{1}} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Given}\:\begin{cases}{\mathrm{xy}=\frac{\mathrm{16y}−\mathrm{9x}}{\mathrm{45}}}\\{\frac{\mathrm{4}}{\:\sqrt{\mathrm{x}}}−\frac{\mathrm{3}}{\:\sqrt{\mathrm{y}}}\:=\:\mathrm{5}}\end{cases} \\ $$$$\Rightarrow\mathrm{find}\:\mathrm{9}\sqrt{\mathrm{xy}} \\ $$

Question Number 110869 Answers: 1 Comments: 0

Question Number 110868 Answers: 0 Comments: 0

x^2 +y^2 =z Level sets and surface plot using Geogebra

$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={z} \\ $$$${Level}\:{sets}\:{and}\:{surface}\:{plot} \\ $$$${using}\:{Geogebra} \\ $$$$ \\ $$

Question Number 110865 Answers: 0 Comments: 0

Plotting of x^2

$${Plotting}\:{of} \\ $$$${x}^{\mathrm{2}} \\ $$

Question Number 110861 Answers: 2 Comments: 0

Question Number 110860 Answers: 1 Comments: 0

Question Number 110858 Answers: 0 Comments: 0

evaluate ∫_0 ^1 ((xln(1+x))/(1+x^2 ))dx ∫_0 ^1 ((ln(1+x^2 ))/(1+x))dx ∫_0 ^∞ (√(1+x^6 ))dx

$${evaluate} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}\mathrm{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}}{dx} \\ $$$$\int_{\mathrm{0}} ^{\infty} \sqrt{\mathrm{1}+{x}^{\mathrm{6}} }{dx} \\ $$

Question Number 110857 Answers: 0 Comments: 0

solve ∫_0 ^∞ ((sin^3 x)/x^2 )dx

$${solve} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}^{\mathrm{3}} {x}}{{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 110856 Answers: 2 Comments: 0

find x in x^2 =5^x^2 −19

$${find}\:{x}\:{in}\: \\ $$$${x}^{\mathrm{2}} =\mathrm{5}^{{x}^{\mathrm{2}} } −\mathrm{19} \\ $$

Question Number 110843 Answers: 2 Comments: 0

(x+1)^((x+1)) =(√2) find all values of x (Please step by step)

$$\left({x}+\mathrm{1}\right)^{\left({x}+\mathrm{1}\right)} =\sqrt{\mathrm{2}}\:\:\:\:\:\:{find}\:{all}\:{values}\:{of}\:{x} \\ $$$$\left({Please}\:{step}\:{by}\:{step}\right) \\ $$

Question Number 110842 Answers: 0 Comments: 0

Question Number 110837 Answers: 0 Comments: 0

Question Number 110826 Answers: 0 Comments: 6

The probability that at least one of the events A and B occurs is 0.7 and they occur simultaneously with probability 0.2. Then P(A^− )+P(B^ ) =

$$\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{events}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{occurs}\:\mathrm{is}\:\mathrm{0}.\mathrm{7}\:\mathrm{and} \\ $$$$\mathrm{they}\:\mathrm{occur}\:\mathrm{simultaneously}\:\mathrm{with} \\ $$$$\mathrm{probability}\:\mathrm{0}.\mathrm{2}.\:\mathrm{Then}\:\mathrm{P}\left(\overset{−} {\mathrm{A}}\right)+\mathrm{P}\left(\bar {\mathrm{B}}\right)\:= \\ $$

Question Number 110848 Answers: 3 Comments: 3

Question Number 110815 Answers: 1 Comments: 0

Question Number 110810 Answers: 1 Comments: 1

m^4 +2m^3 +6m^2 +2m+5=0 find all roots of m?

$${m}^{\mathrm{4}} +\mathrm{2}{m}^{\mathrm{3}} +\mathrm{6}{m}^{\mathrm{2}} +\mathrm{2}{m}+\mathrm{5}=\mathrm{0} \\ $$$${find}\:{all}\:{roots}\:{of}\:{m}? \\ $$

Question Number 110809 Answers: 0 Comments: 3

lim_(x→∞) (√(x!))=?

$${li}\underset{{x}\rightarrow\infty} {{m}}\sqrt{{x}!}=? \\ $$

Question Number 110800 Answers: 0 Comments: 0

∫((sin(x))/(x^2 +1))dx

$$\int\frac{{sin}\left({x}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$

Question Number 110799 Answers: 0 Comments: 0

What is the he minimum value of (√(x^2 +1))+(√((y−x)^2 +25))+(√((z−y)^2 +4))+(√((9−z)^2 +16)) if (x, y and z) ∈ R

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{What}\:{is}\:{the}\:{he}\:{minimum}\:{value}\:{of}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}+\sqrt{\left({y}−{x}\right)^{\mathrm{2}} +\mathrm{25}}+\sqrt{\left({z}−{y}\right)^{\mathrm{2}} +\mathrm{4}}+\sqrt{\left(\mathrm{9}−{z}\right)^{\mathrm{2}} +\mathrm{16}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{if}\:\:\left({x},\:{y}\:{and}\:{z}\right)\:\in\:\mathbb{R}\: \\ $$

Question Number 110798 Answers: 0 Comments: 0

Use Laplace transform to solve ∂u/∂x +∂u/∂t=x x>0,t>0 u(0,t)=0,u(x,0)=0,t>0,x>0

$${Use}\:{Laplace}\:{transform}\:{to}\:{solve} \\ $$$$\partial{u}/\partial{x}\:+\partial{u}/\partial{t}={x} \\ $$$${x}>\mathrm{0},{t}>\mathrm{0} \\ $$$${u}\left(\mathrm{0},{t}\right)=\mathrm{0},{u}\left({x},\mathrm{0}\right)=\mathrm{0},{t}>\mathrm{0},{x}>\mathrm{0} \\ $$

Question Number 110797 Answers: 0 Comments: 2

If p^→ = ((a),(b) ) and q^→ = ((c),(d) ), Prove that the area bounded by p^→ ,q^→ and p^→ −q^(→ ) is (((ad−bc))/2). Hints: Use cosine rule and sine rule

$$\mathrm{If}\:\overset{\rightarrow} {{p}}=\begin{pmatrix}{{a}}\\{{b}}\end{pmatrix}\:\mathrm{and}\:\overset{\rightarrow} {{q}}=\begin{pmatrix}{{c}}\\{{d}}\end{pmatrix}, \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{area}\:\mathrm{bounded}\:\mathrm{by}\: \\ $$$$\overset{\rightarrow} {{p}},\overset{\rightarrow} {{q}}\:\mathrm{and}\:\overset{\rightarrow} {{p}}−\overset{\rightarrow\:} {{q}}\mathrm{is}\:\frac{\left({ad}−{bc}\right)}{\mathrm{2}}. \\ $$$$ \\ $$$$\mathrm{Hints}:\:\mathrm{Use}\:\mathrm{cosine}\:\mathrm{rule}\:\mathrm{and}\:\mathrm{sine}\:\mathrm{rule} \\ $$

Question Number 110783 Answers: 0 Comments: 2

Find the number of rational numbers r, 0<r<1, such that when r is written as fraction in lowest term. The numerator and demominator have a sum of 1000.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{rational}\:\mathrm{numbers} \\ $$$$\mathrm{r},\:\mathrm{0}<\mathrm{r}<\mathrm{1},\:\mathrm{such}\:\mathrm{that}\:\mathrm{when}\:\mathrm{r}\:\mathrm{is}\:\mathrm{written} \\ $$$$\mathrm{as}\:\mathrm{fraction}\:\mathrm{in}\:\mathrm{lowest}\:\mathrm{term}.\:\mathrm{The} \\ $$$$\mathrm{numerator}\:\mathrm{and}\:\mathrm{demominator}\:\mathrm{have}\:\mathrm{a} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{1000}. \\ $$

Question Number 110782 Answers: 2 Comments: 0

A triangle has area 15 and circumradius 12. Find the product of its heights.

$$\mathrm{A}\:\mathrm{triangle}\:\mathrm{has}\:\mathrm{area}\:\mathrm{15}\:\mathrm{and} \\ $$$$\mathrm{circumradius}\:\mathrm{12}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of} \\ $$$$\mathrm{its}\:\mathrm{heights}. \\ $$

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