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AlgebraQuestion and Answers: Page 251

Question Number 104297 Answers: 1 Comments: 0

((3a^2 b^3 c)/(5b^4 c))+((6xy^3 z^(16) )/(10x^2 y^2 z^(10) )) = ? Can you solve this?

$$\frac{\mathrm{3}{a}^{\mathrm{2}} {b}^{\mathrm{3}} {c}}{\mathrm{5}{b}^{\mathrm{4}} {c}}+\frac{\mathrm{6}{xy}^{\mathrm{3}} {z}^{\mathrm{16}} }{\mathrm{10}{x}^{\mathrm{2}} {y}^{\mathrm{2}} {z}^{\mathrm{10}} }\:=\:? \\ $$$$\boldsymbol{\mathrm{Can}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{this}}? \\ $$

Question Number 104294 Answers: 1 Comments: 0

1. ((1(1/2)+2(6/7))/(2(2/3)−3(4/5)))=? 2. 4×Π×Π=? 3. Transfer into fractions: 5.8^. 9^. , 9.6^. , 78.57^. 8^.

$$\mathrm{1}.\:\:\frac{\mathrm{1}\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{2}\frac{\mathrm{6}}{\mathrm{7}}}{\mathrm{2}\frac{\mathrm{2}}{\mathrm{3}}−\mathrm{3}\frac{\mathrm{4}}{\mathrm{5}}}=? \\ $$$$\mathrm{2}.\:\:\mathrm{4}×\Pi×\Pi=? \\ $$$$\mathrm{3}.\:\:\boldsymbol{\mathrm{Transfer}}\:\boldsymbol{\mathrm{into}}\:\boldsymbol{\mathrm{fractions}}: \\ $$$$\:\:\:\:\:\:\mathrm{5}.\overset{.} {\mathrm{8}}\overset{.} {\mathrm{9}},\:\mathrm{9}.\overset{.} {\mathrm{6}},\:\mathrm{78}.\mathrm{5}\overset{.} {\mathrm{7}}\overset{.} {\mathrm{8}} \\ $$

Question Number 104278 Answers: 1 Comments: 0

x−(−(−x+(−x+x)))= ?

$${x}−\left(−\left(−{x}+\left(−{x}+{x}\right)\right)\right)=\:? \\ $$

Question Number 104260 Answers: 0 Comments: 1

You bought 3g rice, 5g flour in a market. At first you had 500 rupees. Now you have 300 rupees. How much rupees you wasted? Suppose you distribute the 300 rupees among your 4 sons. Now how much rupees does your one son get?

$$\mathrm{You}\:\mathrm{bought}\:\mathrm{3g}\:\mathrm{rice},\:\mathrm{5g}\:\mathrm{flour}\:\mathrm{in}\:\mathrm{a} \\ $$$$\mathrm{market}.\:\mathrm{At}\:\mathrm{first}\:\mathrm{you}\:\mathrm{had}\:\mathrm{500}\:\mathrm{rupees}. \\ $$$$\mathrm{Now}\:\mathrm{you}\:\mathrm{have}\:\mathrm{300}\:\mathrm{rupees}.\:\mathrm{How}\:\mathrm{much} \\ $$$$\mathrm{rupees}\:\mathrm{you}\:\mathrm{wasted}?\:\mathrm{Suppose}\:\mathrm{you} \\ $$$$\mathrm{distribute}\:\mathrm{the}\:\mathrm{300}\:\mathrm{rupees}\:\mathrm{among} \\ $$$$\mathrm{your}\:\mathrm{4}\:\mathrm{sons}.\:\mathrm{Now}\:\mathrm{how}\:\mathrm{much}\:\mathrm{rupees} \\ $$$$\mathrm{does}\:\mathrm{your}\:\mathrm{one}\:\mathrm{son}\:\mathrm{get}? \\ $$

Question Number 104253 Answers: 1 Comments: 1

When a∗b= ((a+b)/(a−b)) then what is the answer of 2∗3×9∗10 ?

$$\mathrm{When}\:{a}\ast{b}=\:\frac{{a}+{b}}{{a}−{b}}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{answer}\:\mathrm{of}\:\mathrm{2}\ast\mathrm{3}×\mathrm{9}\ast\mathrm{10}\:? \\ $$

Question Number 104251 Answers: 1 Comments: 0

If x=8 and y=5 then what is the answer of ((x+y+6)/(x^2 −y^3 )) ?

$$\mathrm{If}\:{x}=\mathrm{8}\:\mathrm{and}\:{y}=\mathrm{5}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{answer}\:\mathrm{of}\:\:\frac{{x}+{y}+\mathrm{6}}{{x}^{\mathrm{2}} −{y}^{\mathrm{3}} }\:? \\ $$

Question Number 104246 Answers: 3 Comments: 0

(1−(1/3))(1−(1/4))(1−(1/5))....(1−(1/(99))) =?

$$\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{5}}\right)....\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{99}}\right)\:=? \\ $$

Question Number 104243 Answers: 2 Comments: 0

prove that π=2×(2/(√2))×(2/(√(2+(√2))))×(2/(√(2+(√(2+(√2))))))×.....

$${prove}\:{that} \\ $$$$\pi=\mathrm{2}×\frac{\mathrm{2}}{\sqrt{\mathrm{2}}}×\frac{\mathrm{2}}{\sqrt{\mathrm{2}+\sqrt{\mathrm{2}}}}×\frac{\mathrm{2}}{\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}}}}}×..... \\ $$

Question Number 104270 Answers: 1 Comments: 0

sgn(∣x∣)=?

$${sgn}\left(\mid{x}\mid\right)=? \\ $$

Question Number 104235 Answers: 1 Comments: 0

If you are given a triangle with side length 15 , 20 and 25. what is the triangle′s shortest altitude?

$${If}\:{you}\:{are}\:{given}\:{a}\:{triangle} \\ $$$${with}\:{side}\:{length}\:\mathrm{15}\:,\:\mathrm{20}\:{and} \\ $$$$\mathrm{25}.\:{what}\:{is}\:{the}\:{triangle}'{s} \\ $$$${shortest}\:{altitude}? \\ $$

Question Number 104201 Answers: 0 Comments: 0

If a^2 + b^2 + c^2 = 1 and b + ic = (1 + a)z, then show that ((a + ib)/(i + c)) = ((1 + iz)/(1 − iz))

$$\mathrm{If}\:\:\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} \:\:=\:\:\mathrm{1}\:\:\:\:\:\mathrm{and}\:\:\:\:\:\:\mathrm{b}\:\:+\:\:\mathrm{ic}\:\:=\:\:\left(\mathrm{1}\:\:+\:\:\mathrm{a}\right)\mathrm{z}, \\ $$$$\mathrm{then}\:\mathrm{show}\:\mathrm{that}\:\:\:\:\:\:\frac{\mathrm{a}\:\:+\:\:\mathrm{ib}}{\mathrm{i}\:\:+\:\:\mathrm{c}}\:\:\:=\:\:\:\frac{\mathrm{1}\:\:+\:\:\mathrm{iz}}{\mathrm{1}\:\:−\:\:\mathrm{iz}} \\ $$

Question Number 104190 Answers: 3 Comments: 1

integers x,y satisfy 2x+15y=2019. find the minimum of ∣y−x∣.

$${integers}\:{x},{y}\:{satisfy}\:\mathrm{2}{x}+\mathrm{15}{y}=\mathrm{2019}. \\ $$$${find}\:{the}\:{minimum}\:{of}\:\mid{y}−{x}\mid. \\ $$

Question Number 104115 Answers: 1 Comments: 0

Question Number 104086 Answers: 1 Comments: 3

Solve: log_r 8 + log_3 p = 5 ..... (i) r + p = 11 ..... (ii)

$$\mathrm{Solve}:\:\:\:\:\:\:\mathrm{log}_{\mathrm{r}} \mathrm{8}\:\:\:+\:\:\:\mathrm{log}_{\mathrm{3}} \mathrm{p}\:\:\:=\:\:\mathrm{5}\:\:\:\:\:\:\:\:\:.....\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{r}\:\:\:+\:\:\mathrm{p}\:\:\:=\:\:\mathrm{11}\:\:\:\:\:\:\:\:\:.....\:\left(\mathrm{ii}\right) \\ $$

Question Number 104062 Answers: 3 Comments: 4

{ (((x/y) + (y/x) = ((13)/6))),((x+y = 5)) :} find the solution

$$\begin{cases}{\frac{{x}}{{y}}\:+\:\frac{{y}}{{x}}\:=\:\frac{\mathrm{13}}{\mathrm{6}}}\\{{x}+{y}\:=\:\mathrm{5}}\end{cases} \\ $$$${find}\:{the}\:{solution} \\ $$

Question Number 104037 Answers: 4 Comments: 0

(1) { ((x^3 +y^6 = 91)),((x+y^2 = 7 )) :} find x−y^6 . (2) 2a+(2/a) = 8 ⇒ ((a^6 +1)/a^3 ) ?

$$\left(\mathrm{1}\right)\begin{cases}{{x}^{\mathrm{3}} +{y}^{\mathrm{6}} \:=\:\mathrm{91}}\\{{x}+{y}^{\mathrm{2}} \:=\:\mathrm{7}\:}\end{cases} \\ $$$${find}\:{x}−{y}^{\mathrm{6}} \:. \\ $$$$\left(\mathrm{2}\right)\:\mathrm{2}{a}+\frac{\mathrm{2}}{{a}}\:=\:\mathrm{8}\:\Rightarrow\:\frac{{a}^{\mathrm{6}} +\mathrm{1}}{{a}^{\mathrm{3}} }\:? \\ $$

Question Number 104023 Answers: 0 Comments: 1

Question Number 103983 Answers: 0 Comments: 0

If α and β are two unequal angle, which satisfy the equation, a cos(α) + b sin(β) = c, show that (i) sin(((α + β)/2)) sec(((α − β)/2)) = (b/c) (ii) tan((α/2)) tan((β/2)) = ((c − a)/(c + a))

$$\mathrm{If}\:\:\alpha\:\:\mathrm{and}\:\:\beta\:\:\mathrm{are}\:\mathrm{two}\:\mathrm{unequal}\:\mathrm{angle},\:\mathrm{which}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}, \\ $$$$\:\:\:\:\mathrm{a}\:\mathrm{cos}\left(\alpha\right)\:\:+\:\:\mathrm{b}\:\mathrm{sin}\left(\beta\right)\:\:=\:\:\mathrm{c},\:\:\:\:\mathrm{show}\:\mathrm{that} \\ $$$$\left(\mathrm{i}\right)\:\:\:\:\mathrm{sin}\left(\frac{\alpha\:\:+\:\beta}{\mathrm{2}}\right)\:\mathrm{sec}\left(\frac{\alpha\:\:−\:\:\beta}{\mathrm{2}}\right)\:\:=\:\:\frac{\mathrm{b}}{\mathrm{c}} \\ $$$$\left(\mathrm{ii}\right)\:\:\:\:\:\mathrm{tan}\left(\frac{\alpha}{\mathrm{2}}\right)\:\mathrm{tan}\left(\frac{\beta}{\mathrm{2}}\right)\:\:=\:\:\frac{\mathrm{c}\:\:−\:\:\mathrm{a}}{\mathrm{c}\:\:+\:\:\mathrm{a}} \\ $$

Question Number 103921 Answers: 1 Comments: 0

Prove that ∀ x ∈ R^ , ∣ cos x ∣ ≤ 1 − sin^2 x

$$\mathrm{Prove}\:\mathrm{that}\:\forall\:{x}\:\in\:\bar {\mathbb{R}}\:,\:\mid\:\mathrm{cos}\:{x}\:\mid\:\leqslant\:\mathrm{1}\:−\:\mathrm{sin}^{\mathrm{2}} \:{x} \\ $$

Question Number 103914 Answers: 2 Comments: 2

(2+(√3))^x^2 + (2−(√3))^x^2 = 4

$$\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{{x}^{\mathrm{2}} } \:+\:\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{{x}^{\mathrm{2}} } \:=\:\mathrm{4}\: \\ $$

Question Number 103888 Answers: 2 Comments: 0

find all such numbers: if we make its last digit, say k, as its first digit, the number becomes k times large as before. (□□...□k)→(k□□...□)=k×(□□...□k)

$${find}\:{all}\:{such}\:{numbers}: \\ $$$${if}\:{we}\:{make}\:{its}\:{last}\:{digit},\:{say}\:{k},\:{as}\:{its} \\ $$$${first}\:{digit},\:{the}\:{number}\:{becomes}\:{k} \\ $$$${times}\:{large}\:{as}\:{before}. \\ $$$$\left(\Box\Box...\Box{k}\right)\rightarrow\left({k}\Box\Box...\Box\right)={k}×\left(\Box\Box...\Box{k}\right) \\ $$

Question Number 103804 Answers: 0 Comments: 0

Solve for r ((h−p^2 )/(p−r))=(1/(2p)) , ((h−q)/(q^2 −r))= 2q (h−p^2 )^2 +(p−r)^2 =r^2 (h−q)^2 +(q^2 −r)^2 =r^2

$$\:\:\:\boldsymbol{{S}}{olve}\:{for}\:\boldsymbol{{r}} \\ $$$$\:\:\frac{\boldsymbol{{h}}−\boldsymbol{{p}}^{\mathrm{2}} }{\boldsymbol{{p}}−\boldsymbol{{r}}}=\frac{\mathrm{1}}{\mathrm{2}\boldsymbol{{p}}}\:\:\:\:,\:\:\:\:\frac{\boldsymbol{{h}}−\boldsymbol{{q}}}{\boldsymbol{{q}}^{\mathrm{2}} −\boldsymbol{{r}}}=\:\mathrm{2}\boldsymbol{{q}} \\ $$$$\left(\boldsymbol{{h}}−\boldsymbol{{p}}^{\mathrm{2}} \right)^{\mathrm{2}} +\left(\boldsymbol{{p}}−\boldsymbol{{r}}\right)^{\mathrm{2}} =\boldsymbol{{r}}^{\mathrm{2}} \\ $$$$\:\left(\boldsymbol{{h}}−\boldsymbol{{q}}\right)^{\mathrm{2}} +\left(\boldsymbol{{q}}^{\mathrm{2}} −\boldsymbol{{r}}\right)^{\mathrm{2}} =\boldsymbol{{r}}^{\mathrm{2}} \\ $$

Question Number 103736 Answers: 0 Comments: 0

Solve: a^2 + c^2 = 196 ... (i) b^2 + (c − a)^2 = 169 ... (ii) c^2 + (b − c)^2 = 225 ... (iii)

$$\mathrm{Solve}:\:\:\:\:\:\:\mathrm{a}^{\mathrm{2}} \:\:+\:\:\mathrm{c}^{\mathrm{2}} \:\:=\:\:\:\mathrm{196}\:\:\:\:\:\:...\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{b}^{\mathrm{2}} \:\:+\:\:\left(\mathrm{c}\:\:−\:\:\mathrm{a}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{169}\:\:\:\:\:...\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{c}^{\mathrm{2}} \:\:+\:\:\left(\mathrm{b}\:\:−\:\:\mathrm{c}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{225}\:\:\:\:\:...\:\left(\mathrm{iii}\right) \\ $$

Question Number 103685 Answers: 1 Comments: 0

Question Number 103647 Answers: 0 Comments: 0

Question Number 103603 Answers: 0 Comments: 1

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