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AlgebraQuestion and Answers: Page 356

Question Number 9324    Answers: 1   Comments: 0

if x=((a(1−r^n ))/(1−r)) make r the subject of the formula

$${if}\:\:{x}=\frac{{a}\left(\mathrm{1}−{r}^{{n}} \right)}{\mathrm{1}−{r}}\:{make}\:{r}\:{the}\: \\ $$$${subject}\:{of}\:{the}\:{formula} \\ $$

Question Number 9323    Answers: 0   Comments: 1

if x=((a(1−r^n ))/(1−r)) make r the subject of the formula

$${if}\:\:{x}=\frac{{a}\left(\mathrm{1}−{r}^{{n}} \right)}{\mathrm{1}−{r}}\:{make}\:{r}\:{the}\: \\ $$$${subject}\:{of}\:{the}\:{formula} \\ $$

Question Number 9312    Answers: 0   Comments: 6

Solve simultaneously xy + x + y = 23 ....... (i) xz + x + z = 41 ........ (ii) yz + y + z = 27 ........ (iii)

$$\mathrm{Solve}\:\mathrm{simultaneously} \\ $$$$\mathrm{xy}\:+\:\mathrm{x}\:+\:\mathrm{y}\:=\:\mathrm{23}\:\:\:\:.......\:\left(\mathrm{i}\right) \\ $$$$\mathrm{xz}\:+\:\mathrm{x}\:+\:\mathrm{z}\:=\:\mathrm{41}\:\:\:\:........\:\left(\mathrm{ii}\right) \\ $$$$\mathrm{yz}\:+\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{27}\:\:\:\:\:........\:\left(\mathrm{iii}\right) \\ $$

Question Number 9279    Answers: 3   Comments: 0

evalute the value of Σ_(m=2 ) ^5 m^4

$$\mathrm{evalute}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\overset{\mathrm{5}} {\sum}_{\mathrm{m}=\mathrm{2}\:} \mathrm{m}^{\mathrm{4}} \\ $$

Question Number 9278    Answers: 0   Comments: 1

represent in sigma notation −1+4−9+16..................

$$\mathrm{represent}\:\mathrm{in}\:\mathrm{sigma}\:\mathrm{notation}\: \\ $$$$−\mathrm{1}+\mathrm{4}−\mathrm{9}+\mathrm{16}.................. \\ $$

Question Number 9236    Answers: 2   Comments: 0

Solve simultaneously (x/(y + 1_ )) + (y/(x + 1)) = (5/3) ............. (i) x^2 + y^2 = 2 ........... (ii)

$$\mathrm{Solve}\:\:\mathrm{simultaneously} \\ $$$$\frac{\mathrm{x}}{\mathrm{y}\:+\:\mathrm{1}_{\:} }\:+\:\frac{\mathrm{y}}{\mathrm{x}\:+\:\mathrm{1}}\:=\:\frac{\mathrm{5}}{\mathrm{3}}\:\:\:\:.............\:\left(\mathrm{i}\right) \\ $$$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{2}\:\:\:\:\:\:\:\:...........\:\left(\mathrm{ii}\right) \\ $$

Question Number 9229    Answers: 0   Comments: 0

2^(3x + 1) − 3.2^(2x) + 2^(x + 1) = 2x Find x

$$\mathrm{2}^{\mathrm{3x}\:+\:\mathrm{1}} \:−\:\mathrm{3}.\mathrm{2}^{\mathrm{2x}} \:+\:\mathrm{2}^{\mathrm{x}\:+\:\mathrm{1}} \:=\:\mathrm{2x} \\ $$$$\mathrm{Find}\:\mathrm{x} \\ $$

Question Number 9219    Answers: 0   Comments: 1

Show that: (a + b)[(1/a^2 ) + (1/b^2 )][(a^4 /b^2 ) + (b^4 /a^2 )] ≥ 8(√(ab))

$$\mathrm{Show}\:\mathrm{that}:\: \\ $$$$\left(\mathrm{a}\:+\:\mathrm{b}\right)\left[\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{b}^{\mathrm{2}} }\right]\left[\frac{\mathrm{a}^{\mathrm{4}} }{\mathrm{b}^{\mathrm{2}} }\:+\:\frac{\mathrm{b}^{\mathrm{4}} }{\mathrm{a}^{\mathrm{2}} }\right]\:\geqslant\:\mathrm{8}\sqrt{\mathrm{ab}} \\ $$

Question Number 9199    Answers: 0   Comments: 2

If r^2 = (x + ea)^2 + y^2 and s^2 = (x − ea)^2 + y^2 and r + s = 2a, Prove that: r = a + ex, s = a − ex, and that, x^2 (1 − e^2 ) + y^2 = a^2 (1 − e^2 )

$$\mathrm{If}\:\:\mathrm{r}^{\mathrm{2}} \:=\:\left(\mathrm{x}\:+\:\mathrm{ea}\right)^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{s}^{\mathrm{2}} \:=\:\left(\mathrm{x}\:−\:\mathrm{ea}\right)^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \\ $$$$\mathrm{and}\:\mathrm{r}\:+\:\mathrm{s}\:=\:\mathrm{2a},\:\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{r}\:=\:\mathrm{a}\:+\:\mathrm{ex},\:\:\mathrm{s}\:=\:\mathrm{a}\:−\:\mathrm{ex},\:\mathrm{and}\:\mathrm{that}, \\ $$$$\mathrm{x}^{\mathrm{2}} \left(\mathrm{1}\:−\:\mathrm{e}^{\mathrm{2}} \right)\:+\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{a}^{\mathrm{2}} \left(\mathrm{1}\:−\:\mathrm{e}^{\mathrm{2}} \right) \\ $$

Question Number 9141    Answers: 0   Comments: 5

Find the value of x if ((√(2 + (√3))))^x + ((√(2 − (√3))))^x = 4

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:\mathrm{if} \\ $$$$\left(\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{3}}}\right)^{\mathrm{x}} \:+\:\left(\sqrt{\mathrm{2}\:−\:\sqrt{\mathrm{3}}}\right)^{\mathrm{x}} \:=\:\mathrm{4} \\ $$

Question Number 9128    Answers: 2   Comments: 1

Question Number 9123    Answers: 0   Comments: 1

simplify (x^2 (x+1)^(−1/2) −(x+1)^(1/2) )/x^2

$$\mathrm{simplify} \\ $$$$\left(\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}+\mathrm{1}\right)^{−\mathrm{1}/\mathrm{2}} −\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{1}/\mathrm{2}} \right)/\mathrm{x}^{\mathrm{2}} \\ $$

Question Number 9119    Answers: 1   Comments: 0

If x = 5^(1/4) + 5^(−1/4) and y = 5^(1/4) − 5^(−1/4) Show that : 5^((x^2 + y^2 )^2 ) = 144

$$\mathrm{If}\:\:\mathrm{x}\:=\:\mathrm{5}^{\mathrm{1}/\mathrm{4}} \:+\:\mathrm{5}^{−\mathrm{1}/\mathrm{4}} \:\:\:\mathrm{and}\:\:\mathrm{y}\:=\:\mathrm{5}^{\mathrm{1}/\mathrm{4}} \:−\:\mathrm{5}^{−\mathrm{1}/\mathrm{4}} \\ $$$$\mathrm{Show}\:\mathrm{that}\::\:\mathrm{5}^{\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \right)^{\mathrm{2}} \:} =\:\mathrm{144} \\ $$

Question Number 9096    Answers: 1   Comments: 0

Question Number 9061    Answers: 2   Comments: 1

Question Number 9029    Answers: 2   Comments: 0

2cos(x+Π/4)=cos(x−Π/4)

$$ \\ $$$$\mathrm{2}{cos}\left({x}+\Pi/\mathrm{4}\right)={cos}\left({x}−\Pi/\mathrm{4}\right) \\ $$

Question Number 9020    Answers: 2   Comments: 1

Question Number 9015    Answers: 0   Comments: 0

Question Number 9009    Answers: 1   Comments: 0

If : x = ((3y + 6z)/(7z − 2)) and y = (((1/2)z + 6y)/((3/2)z + 6y)) Find : x^3 + y^3

$$\mathrm{If}\::\:\:\mathrm{x}\:=\:\frac{\mathrm{3y}\:+\:\mathrm{6z}}{\mathrm{7z}\:−\:\mathrm{2}}\:\:\mathrm{and}\:\:\mathrm{y}\:=\:\frac{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{z}\:+\:\mathrm{6y}}{\frac{\mathrm{3}}{\mathrm{2}}\mathrm{z}\:+\:\mathrm{6y}} \\ $$$$\mathrm{Find}\::\:\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \\ $$

Question Number 9004    Answers: 1   Comments: 0

prove (1/2)∙(3/4)∙(5/6)∙∙∙∙∙((2n−1)/(2n))≤(1/(√(3n+1)))

$$\mathrm{prove} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\centerdot\frac{\mathrm{3}}{\mathrm{4}}\centerdot\frac{\mathrm{5}}{\mathrm{6}}\centerdot\centerdot\centerdot\centerdot\centerdot\frac{\mathrm{2n}−\mathrm{1}}{\mathrm{2n}}\leqslant\frac{\mathrm{1}}{\sqrt{\mathrm{3n}+\mathrm{1}}} \\ $$

Question Number 8998    Answers: 1   Comments: 0

If 2^x = 3^y = 6^(−z) find the value of : (1/x) + (1/y) + (1/z)

$$\mathrm{If}\:\:\mathrm{2}^{\mathrm{x}} \:=\:\mathrm{3}^{\mathrm{y}} \:=\:\mathrm{6}^{−\mathrm{z}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\::\:\:\frac{\mathrm{1}}{\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{y}}\:+\:\frac{\mathrm{1}}{\mathrm{z}} \\ $$

Question Number 8985    Answers: 1   Comments: 0

solve the value of x log_x 3=81

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$$$\mathrm{log}_{\mathrm{x}} \mathrm{3}=\mathrm{81} \\ $$

Question Number 8965    Answers: 0   Comments: 1

If xy − x = yz − 2y = xz + 3z = 3 and xyz > 0 What is the value of xyz ?

$${If} \\ $$$${xy}\:−\:{x}\:=\:{yz}\:−\:\mathrm{2}{y}\:=\:{xz}\:+\:\mathrm{3}{z}\:=\:\mathrm{3} \\ $$$${and} \\ $$$${xyz}\:>\:\mathrm{0} \\ $$$${What}\:{is}\:{the}\:{value}\:{of}\:{xyz}\:? \\ $$

Question Number 8956    Answers: 0   Comments: 1

prove that; log_(ab) x=((log_a x−log_b x)/(log_a x+log_b x))

$$\mathrm{prove}\:\mathrm{that}; \\ $$$$\mathrm{log}_{\mathrm{ab}} \mathrm{x}=\frac{\mathrm{log}_{\mathrm{a}} \mathrm{x}−\mathrm{log}_{\mathrm{b}} \mathrm{x}}{\mathrm{log}_{\mathrm{a}} \mathrm{x}+\mathrm{log}_{\mathrm{b}} \mathrm{x}} \\ $$

Question Number 8934    Answers: 1   Comments: 0

find the value of x. 3^(x+1) =2^(x+2)

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{x}. \\ $$$$\mathrm{3}^{\mathrm{x}+\mathrm{1}} =\mathrm{2}^{\mathrm{x}+\mathrm{2}} \\ $$

Question Number 8905    Answers: 1   Comments: 0

find the value of x 3^x =9x

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$$$\mathrm{3}^{\mathrm{x}} \:=\mathrm{9x} \\ $$

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