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Question Number 171922 Answers: 0 Comments: 2

if α and β are the positive roots of the eqn x^2 +px+q=0, find the sum M=(α)^(1/4) +(β)^(1/4)

$${if}\:\alpha\:{and}\:\beta\:{are}\:{the}\:{positive}\:{roots}\:{of}\:{the}\:{eqn} \\ $$$${x}^{\mathrm{2}} +{px}+{q}=\mathrm{0},\:{find}\:{the}\:{sum}\:{M}=\sqrt[{\mathrm{4}}]{\alpha}\:+\sqrt[{\mathrm{4}}]{\beta} \\ $$

Question Number 171921 Answers: 1 Comments: 0

(((x^2 −9))^(1/3) /( ((x+3))^(1/3) ))=3, find x

$$\frac{\sqrt[{\mathrm{3}}]{{x}^{\mathrm{2}} −\mathrm{9}}}{\:\sqrt[{\mathrm{3}}]{{x}+\mathrm{3}}}=\mathrm{3},\:{find}\:{x} \\ $$

Question Number 171919 Answers: 0 Comments: 0

if a+b+c=2196 (a)^(1/3) +b+c=2076 a+(b)^(1/3) +c=1860 a+b+(c)^(1/3) =480, determine the value of a^(2/3) +b^(2/3) +c^(2/3) , if a,b,c are all integer.

$${if} \\ $$$${a}+{b}+{c}=\mathrm{2196} \\ $$$$\sqrt[{\mathrm{3}}]{{a}}\:+{b}+{c}=\mathrm{2076} \\ $$$${a}+\sqrt[{\mathrm{3}}]{{b}}\:+{c}=\mathrm{1860} \\ $$$${a}+{b}+\sqrt[{\mathrm{3}}]{{c}}\:=\mathrm{480},\:{determine}\:{the}\:{value}\:{of} \\ $$$${a}^{\frac{\mathrm{2}}{\mathrm{3}}} +{b}^{\frac{\mathrm{2}}{\mathrm{3}}} +{c}^{\frac{\mathrm{2}}{\mathrm{3}}} ,\:{if}\:{a},{b},{c}\:{are}\:{all}\:{integer}. \\ $$

Question Number 171910 Answers: 3 Comments: 0

∫ (dx/(9 − 4x^2 )) using the trigonometric substitution.

$$\int\:\frac{\mathrm{dx}}{\mathrm{9}\:\:\:−\:\:\:\mathrm{4x}^{\mathrm{2}} } \\ $$$$\mathrm{using}\:\mathrm{the}\:\mathrm{trigonometric}\:\mathrm{substitution}. \\ $$

Question Number 171908 Answers: 0 Comments: 4

Question Number 171906 Answers: 0 Comments: 0

a fource f facts on a body of mass (t+2)kg and it′s momentum was (t^2 +6t+8) kg . m/ sec what is the average power in the first 3 seconds

$${a}\:{fource}\:{f}\:{facts}\:{on}\:{a}\:{body}\:{of}\:{mass} \\ $$$$\left({t}+\mathrm{2}\right){kg}\:{and}\:{it}'{s}\:{momentum}\:{was} \\ $$$$\left({t}^{\mathrm{2}} +\mathrm{6}{t}+\mathrm{8}\right)\:{kg}\:.\:{m}/\:{sec} \\ $$$$\:{what}\:{is}\:{the}\:{average}\:{power}\:{in}\:{the} \\ $$$${first}\:\mathrm{3}\:{seconds} \\ $$

Question Number 171883 Answers: 0 Comments: 0

The function f(x)=ax^2 +bx+c has gradient function 4x+2 and stationary value 1. Find the values of a,b and c.

$$\mathrm{The}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}\:\mathrm{has}\:\mathrm{gradient} \\ $$$$\mathrm{function}\:\mathrm{4x}+\mathrm{2}\:\mathrm{and}\:\mathrm{stationary}\:\mathrm{value}\:\mathrm{1}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:{a},{b}\:\mathrm{and}\:{c}. \\ $$

Question Number 171873 Answers: 1 Comments: 2

solve: ((x+(√(x^2 −1)))/(x−(√(x^2 −1)))) −((x−(√(x^2 −1)))/(x+(√(x^2 −1)))) =8x(√(x^2 −3x+2))

$${solve}: \\ $$$$\frac{{x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:−\frac{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:\:=\mathrm{8}{x}\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}} \\ $$

Question Number 171872 Answers: 1 Comments: 0

Solve for real numbers: (1/(1 + tan^4 x)) + (1/(10)) = (2/(1 + 3 tan^2 x))

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{tan}^{\mathrm{4}} \:\mathrm{x}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{10}}\:\:=\:\:\frac{\mathrm{2}}{\mathrm{1}\:+\:\mathrm{3}\:\mathrm{tan}^{\mathrm{2}} \:\mathrm{x}} \\ $$

Question Number 171871 Answers: 1 Comments: 2

solve: ((x+(√(x^2 −1)))/(x−(√(x^2 −1)))) + ((x−(√(x^2 −1)))/(x+(√(x^2 −1)))) =98

$${solve}: \\ $$$$\frac{{x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:\:+\:\:\frac{{x}−\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:=\mathrm{98} \\ $$

Question Number 171870 Answers: 1 Comments: 0

if x is a real number,then (√(log_e ((4x−x^2 )/3) ))

$${if}\:{x}\:{is}\:{a}\:{real}\:{number},{then} \\ $$$$\sqrt{{log}_{{e}} \:\frac{\mathrm{4}{x}−{x}^{\mathrm{2}} }{\mathrm{3}}\:}\:\: \\ $$

Question Number 171869 Answers: 2 Comments: 0

find the square root of: (√((7x^2 +2(√(14)) x+2)/(x^2 −(1/2)x +(1/6))))

$${find}\:{the}\:{square}\:{root}\:{of}: \\ $$$$\sqrt{\frac{\mathrm{7}{x}^{\mathrm{2}} +\mathrm{2}\sqrt{\mathrm{14}}\:{x}+\mathrm{2}}{{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{2}}{x}\:+\frac{\mathrm{1}}{\mathrm{6}}}} \\ $$

Question Number 171868 Answers: 0 Comments: 2

solve: x^2 +y^2 =1997(x−y),find the positive integer solution.

$${solve}: \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{1997}\left({x}−{y}\right),{find}\:{the}\:{positive}\:{integer}\:{solution}. \\ $$

Question Number 171867 Answers: 1 Comments: 0

solve: x_4 ^2 =100100_2 , find x and leave answer in base 2.

$${solve}:\:{x}_{\mathrm{4}} ^{\mathrm{2}} =\mathrm{100100}_{\mathrm{2}} ,\:{find}\:{x}\:{and}\:{leave}\:{answer}\:{in}\:{base}\:\mathrm{2}. \\ $$

Question Number 171866 Answers: 0 Comments: 1

(√a)+(√b)=(√(2009)). find a and b.

$$\sqrt{{a}}+\sqrt{{b}}=\sqrt{\mathrm{2009}}.\:{find}\:{a}\:{and}\:{b}. \\ $$

Question Number 171861 Answers: 0 Comments: 8

if ax+by=5 ax^2 +by^2 =10 ax^3 +by^3 =50 ax^4 +by^4 =130 find 13(x+y−xy)−120(a+b)

$${if}\: \\ $$$${ax}+{by}=\mathrm{5} \\ $$$${ax}^{\mathrm{2}} +{by}^{\mathrm{2}} =\mathrm{10} \\ $$$${ax}^{\mathrm{3}} +{by}^{\mathrm{3}} =\mathrm{50} \\ $$$${ax}^{\mathrm{4}} +{by}^{\mathrm{4}} =\mathrm{130} \\ $$$${find}\:\mathrm{13}\left({x}+{y}−{xy}\right)−\mathrm{120}\left({a}+{b}\right) \\ $$

Question Number 171860 Answers: 0 Comments: 0

solve: ((4x^2 )/([1−(√(1+2x))]^2 ))<2x+9

$${solve}: \\ $$$$\frac{\mathrm{4}{x}^{\mathrm{2}} }{\left[\mathrm{1}−\sqrt{\mathrm{1}+\mathrm{2}{x}}\right]^{\mathrm{2}} }<\mathrm{2}{x}+\mathrm{9} \\ $$

Question Number 171858 Answers: 0 Comments: 0

solve: find the value of x and y between 0^(° ) and180^° which satisfy the simultaneous eqn sin(x+y)=((√2)/2) cos2x=−(1/2)

$${solve}: \\ $$$${find}\:{the}\:{value}\:{of}\:{x}\:{and}\:{y}\:{between}\:\mathrm{0}^{°\:} {and}\mathrm{180}^{°} \:{which}\:{satisfy}\:{the}\:{simultaneous}\:{eqn} \\ $$$${sin}\left({x}+{y}\right)=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\ $$$${cos}\mathrm{2}{x}=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 171854 Answers: 1 Comments: 0

solve: (3(√2))^n =3

$${solve}: \\ $$$$\left(\mathrm{3}\sqrt{\mathrm{2}}\right)^{{n}} =\mathrm{3} \\ $$

Question Number 171849 Answers: 1 Comments: 1

solve: 3^(2x+y) =12 2^(x−y) =4

$${solve}: \\ $$$$\mathrm{3}^{\mathrm{2}{x}+{y}} =\mathrm{12} \\ $$$$\mathrm{2}^{{x}−{y}} =\mathrm{4} \\ $$

Question Number 171847 Answers: 1 Comments: 1

solve: log_x 10+log_x^2 10=6

$${solve}: \\ $$$${log}_{{x}} \mathrm{10}+{log}_{{x}^{\mathrm{2}} } \mathrm{10}=\mathrm{6} \\ $$

Question Number 171846 Answers: 0 Comments: 2

solve: x^9 −2x^5 −3x=0

$${solve}: \\ $$$${x}^{\mathrm{9}} −\mathrm{2}{x}^{\mathrm{5}} −\mathrm{3}{x}=\mathrm{0} \\ $$

Question Number 171845 Answers: 0 Comments: 0

n_c_(r+1) + n_c_r =n+1_c_(r .solve for n and r.)

$${n}_{{c}_{{r}+\mathrm{1}} } +\:{n}_{{c}_{{r}} } ={n}+\mathrm{1}_{{c}_{{r}\:\:.{solve}\:{for}\:\:{n}\:{and}\:{r}.} } \\ $$

Question Number 171844 Answers: 1 Comments: 0

solve: x^5 −5x^4 +9x^3 −9x^2 +5x−1=0

$${solve}: \\ $$$${x}^{\mathrm{5}} −\mathrm{5}{x}^{\mathrm{4}} +\mathrm{9}{x}^{\mathrm{3}} −\mathrm{9}{x}^{\mathrm{2}} +\mathrm{5}{x}−\mathrm{1}=\mathrm{0} \\ $$

Question Number 171843 Answers: 0 Comments: 0

find a: (2:3:4:5)a=5:6:7:8

$${find}\:{a}: \\ $$$$\left(\mathrm{2}:\mathrm{3}:\mathrm{4}:\mathrm{5}\right){a}=\mathrm{5}:\mathrm{6}:\mathrm{7}:\mathrm{8} \\ $$

Question Number 171841 Answers: 1 Comments: 0

solve: 2^((5x−20)) =1!

$${solve}: \\ $$$$\mathrm{2}^{\left(\mathrm{5}{x}−\mathrm{20}\right)} =\mathrm{1}! \\ $$

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