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AlgebraQuestion and Answers: Page 34

Question Number 210081 Answers: 0 Comments: 0

Reduce [(3,(−2),4,7),(2,1,0,(−3)),(2,8,(−8),2) ] into echelon form

$${Reduce}\:\: \\ $$$$ \\ $$$$\:\:\:\begin{bmatrix}{\mathrm{3}}&{−\mathrm{2}}&{\mathrm{4}}&{\mathrm{7}}\\{\mathrm{2}}&{\mathrm{1}}&{\mathrm{0}}&{−\mathrm{3}}\\{\mathrm{2}}&{\mathrm{8}}&{−\mathrm{8}}&{\mathrm{2}}\end{bmatrix}\:\:\:\:{into}\:{echelon}\:{form} \\ $$$$ \\ $$

Question Number 210080 Answers: 1 Comments: 4

Given that det [(a,b,c),(d,e,f),(g,h,i) ]=n find det [((d+2a),(e+2b),(f+2c)),((2a),(2b),(2c)),((4g),(4h),(4i)) ]

$${Given}\:{that}\:\:{det}\:\begin{bmatrix}{{a}}&{{b}}&{{c}}\\{{d}}&{{e}}&{{f}}\\{{g}}&{{h}}&{{i}}\end{bmatrix}={n} \\ $$$$ \\ $$$${find}\:{det}\begin{bmatrix}{{d}+\mathrm{2}{a}}&{{e}+\mathrm{2}{b}}&{{f}+\mathrm{2}{c}}\\{\mathrm{2}{a}}&{\mathrm{2}{b}}&{\mathrm{2}{c}}\\{\mathrm{4}{g}}&{\mathrm{4}{h}}&{\mathrm{4}{i}}\end{bmatrix} \\ $$$$ \\ $$

Question Number 210079 Answers: 0 Comments: 0

Find directional derivatives(D_v )of f(x,y,z)=3xy^3 −2xz^2 in the direction of the v=2i−3j+6k. then Evaluate directional derivatives at the point (3,1,−2)

$${Find}\:{directional}\:{derivatives}\left({D}_{{v}} \right){of}\:\: \\ $$$${f}\left({x},{y},{z}\right)=\mathrm{3}{xy}^{\mathrm{3}} −\mathrm{2}{xz}^{\mathrm{2}} \:\:{in}\:{the}\:{direction}\:{of}\:{the} \\ $$$${v}=\mathrm{2}{i}−\mathrm{3}{j}+\mathrm{6}{k}. \\ $$$${then}\:{Evaluate}\:{directional}\:{derivatives}\: \\ $$$${at}\:{the}\:{point}\:\left(\mathrm{3},\mathrm{1},−\mathrm{2}\right) \\ $$

Question Number 210078 Answers: 1 Comments: 0

Find the directional derivative of f(x,y)=4x^3 −3x^2 y^2 in the direction given by the angle θ=(π/3) and also Evaluate directional derivatives at the point (1,2)

$${Find}\:{the}\:{directional}\:{derivative}\:{of} \\ $$$${f}\left({x},{y}\right)=\mathrm{4}{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} {y}^{\mathrm{2}} \:\:\:{in}\:{the}\:{direction}\:{given} \\ $$$${by}\:{the}\:{angle}\:\theta=\frac{\pi}{\mathrm{3}}\: \\ $$$${and}\:{also}\:{Evaluate}\:{directional}\:{derivatives} \\ $$$${at}\:{the}\:{point}\:\left(\mathrm{1},\mathrm{2}\right) \\ $$

Question Number 210072 Answers: 2 Comments: 0

Question Number 210036 Answers: 4 Comments: 0

Question Number 210034 Answers: 1 Comments: 4

Question Number 210011 Answers: 0 Comments: 0

Find: ∫_0 ^( 1) ((ln (cos (((πx)/2))))/(x^2 + x)) dx = ?

$$\mathrm{Find}:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\:\frac{\mathrm{ln}\:\left(\mathrm{cos}\:\left(\frac{\pi\mathrm{x}}{\mathrm{2}}\right)\right)}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}}\:\mathrm{dx}\:\:=\:\:? \\ $$

Question Number 209986 Answers: 1 Comments: 0

Solve ax^3 −bx(√x) +c=0 (a, b, c)∈R^3 and x∈R (the value of x for a=1, b=9,c=8)

$$\mathrm{Solve}\: \\ $$$$\:\boldsymbol{\mathrm{ax}}^{\mathrm{3}} −\boldsymbol{\mathrm{bx}}\sqrt{\boldsymbol{\mathrm{x}}}\:+\boldsymbol{\mathrm{c}}=\mathrm{0}\:\:\:\:\: \\ $$$$\:\left(\boldsymbol{\mathrm{a}},\:\boldsymbol{\mathrm{b}},\:\boldsymbol{\mathrm{c}}\right)\in\mathbb{R}^{\mathrm{3}} \:\:\:\:\mathrm{and}\:\boldsymbol{\mathrm{x}}\in\mathbb{R} \\ $$$$\left(\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\boldsymbol{{x}}\:\boldsymbol{{for}}\:\boldsymbol{{a}}=\mathrm{1},\:\:\boldsymbol{{b}}=\mathrm{9},\boldsymbol{{c}}=\mathrm{8}\right) \\ $$

Question Number 209980 Answers: 0 Comments: 7

determiner h ? CD=20 AB=30 h1=25

$$\mathrm{determiner}\:\mathrm{h}\:? \\ $$$$\boldsymbol{\mathrm{CD}}=\mathrm{20}\:\:\:\:\boldsymbol{\mathrm{AB}}=\mathrm{30} \\ $$$$\boldsymbol{\mathrm{h}}\mathrm{1}=\mathrm{25} \\ $$$$ \\ $$

Question Number 209976 Answers: 0 Comments: 1

Question Number 209974 Answers: 0 Comments: 0

Question Number 209972 Answers: 1 Comments: 0

Question Number 209929 Answers: 0 Comments: 0

Question Number 209918 Answers: 1 Comments: 0

Find: ∫_0 ^( ∞) (({x}^([x]) )/([x] + 1)) dx = ? {x} → fractional part [x] → full part

$$\mathrm{Find}:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\left\{\mathrm{x}\right\}^{\left[\boldsymbol{\mathrm{x}}\right]} }{\left[\mathrm{x}\right]\:+\:\mathrm{1}}\:\mathrm{dx}\:=\:? \\ $$$$\left\{\mathrm{x}\right\}\:\rightarrow\:\mathrm{fractional}\:\mathrm{part} \\ $$$$\left[\mathrm{x}\right]\:\:\:\rightarrow\:\mathrm{full}\:\mathrm{part} \\ $$

Question Number 209876 Answers: 1 Comments: 0

1,6 = (((2x)^2 )/((3−2x)^2 ∙ (2−x))) find: x = ?

$$\mathrm{1},\mathrm{6}\:\:=\:\:\frac{\left(\mathrm{2x}\right)^{\mathrm{2}} }{\left(\mathrm{3}−\mathrm{2x}\right)^{\mathrm{2}} \:\centerdot\:\left(\mathrm{2}−\mathrm{x}\right)}\:\:\:\mathrm{find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$

Question Number 209872 Answers: 1 Comments: 0

Solve for x∈R: x^3 −3x^2 +2=(√(x+1))

$$\mathrm{Solve}\:\mathrm{for}\:{x}\in\mathbb{R}: \\ $$$${x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}=\sqrt{{x}+\mathrm{1}} \\ $$

Question Number 209852 Answers: 1 Comments: 0

Find: Σ_(n=1) ^∞ arctan ((2/n^2 )) = ?

$$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\mathrm{arctan}\:\left(\frac{\mathrm{2}}{\mathrm{n}^{\mathrm{2}} }\right)\:=\:? \\ $$

Question Number 209837 Answers: 2 Comments: 0

if the series Σ_(n=1) ^∞ (1/n^2 ) converges to k . find the convergence value of Σ_(n=1) ^∞ (1/((2n+1)^2 ))

$$ \\ $$$${if}\:{the}\:{series}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:{converges}\:{to}\:{k}\:.\:\:{find}\:\:{the}\:{convergence}\:{value}\:{of}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 209812 Answers: 0 Comments: 0

Question Number 209768 Answers: 1 Comments: 0

Express tan(3) in surd form

$$\boldsymbol{{Express}}\:\boldsymbol{{tan}}\left(\mathrm{3}\right)\:\boldsymbol{{in}}\:\boldsymbol{{surd}}\:\boldsymbol{{form}} \\ $$

Question Number 209735 Answers: 3 Comments: 0

tan(3x) + tan(5x) = 2 Find: x = ?

$$\mathrm{tan}\left(\mathrm{3x}\right)\:\:+\:\:\mathrm{tan}\left(\mathrm{5x}\right)\:\:=\:\:\mathrm{2} \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$

Question Number 209719 Answers: 1 Comments: 0

If: 7^(243) = a...bc^(−) Find: b∙c = ?

$$\mathrm{If}: \\ $$$$\mathrm{7}^{\mathrm{243}} \:\:=\:\:\overline {\mathrm{a}...\mathrm{bc}} \\ $$$$\mathrm{Find}: \\ $$$$\mathrm{b}\centerdot\mathrm{c}\:=\:? \\ $$

Question Number 209706 Answers: 2 Comments: 0

find the sum of sin^2 1°+sin^2 2°+...+sin^2 60°=?

$${find}\:{the}\:{sum}\:{of}\: \\ $$$$\mathrm{sin}^{\mathrm{2}} \:\mathrm{1}°+\mathrm{sin}^{\mathrm{2}} \:\mathrm{2}°+...+\mathrm{sin}^{\mathrm{2}} \:\mathrm{60}°=? \\ $$

Question Number 209695 Answers: 1 Comments: 0

If: (a + b)∙(√2) = 7∙(a−b−4) Find: (2a + b) = ?

$$\mathrm{If}: \\ $$$$\left(\mathrm{a}\:+\:\mathrm{b}\right)\centerdot\sqrt{\mathrm{2}}\:=\:\mathrm{7}\centerdot\left(\mathrm{a}−\mathrm{b}−\mathrm{4}\right) \\ $$$$\mathrm{Find}: \\ $$$$\left(\mathrm{2a}\:+\:\mathrm{b}\right)\:=\:? \\ $$

Question Number 209694 Answers: 1 Comments: 0

x^2 +xy+y^2 =α^2 y^2 +yz+z^2 =β^2 z^2 +zx+x^2 =α^2 +β^2 Find x+y+z for x, y, z ∈R^+

$${x}^{\mathrm{2}} +{xy}+{y}^{\mathrm{2}} =\alpha^{\mathrm{2}} \\ $$$${y}^{\mathrm{2}} +{yz}+{z}^{\mathrm{2}} =\beta^{\mathrm{2}} \\ $$$${z}^{\mathrm{2}} +{zx}+{x}^{\mathrm{2}} =\alpha^{\mathrm{2}} +\beta^{\mathrm{2}} \\ $$$$\mathrm{Find}\:{x}+{y}+{z}\:\mathrm{for}\:{x},\:{y},\:{z}\:\in\mathbb{R}^{+} \\ $$

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