Menu Close

Category: Algebra

If-A-20-and-B-25-Find-1-tanA-1-tanB-

Question Number 184475 by Shrinava last updated on 07/Jan/23 $$\mathrm{If}\:\:\:\mathrm{A}\:=\:\mathrm{20}°\:\:\:\mathrm{and}\:\:\:\mathrm{B}\:=\:\mathrm{25}° \\ $$$$\mathrm{Find}\:\:\:\left(\mathrm{1}\:+\:\mathrm{tanA}\right)\left(\mathrm{1}\:+\:\mathrm{tanB}\right) \\ $$ Answered by cortano1 last updated on 07/Jan/23 $$\:\mathrm{tan}\:\mathrm{45}\:=\:\frac{\mathrm{tan}\:\mathrm{20}°+\mathrm{tan}\:\mathrm{25}°}{\mathrm{1}−\mathrm{tan}\:\mathrm{20}°\:\mathrm{tan}\:\mathrm{25}°} \\ $$$$\Rightarrow\mathrm{1}−\mathrm{tan}\:\mathrm{20}°\:\mathrm{tan}\:\mathrm{25}°=\mathrm{tan}\:\mathrm{20}°+\mathrm{tan}\:\mathrm{25}° \\…

What-is-the-general-rule-for-factorising-a-b-c-n-

Question Number 118937 by harckinwunmy last updated on 20/Oct/20 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{general}\:\mathrm{rule}\: \\ $$$$\mathrm{for}\:\mathrm{factorising}\:\left(\mathrm{a}+\mathrm{b}+\mathrm{c}\right)^{\mathrm{n}} ? \\ $$ Answered by mathmax by abdo last updated on 20/Oct/20 $$\mathrm{i}\:\mathrm{think}\:\mathrm{the}\:\mathrm{question}\:\mathrm{is}\:\mathrm{developping}…

Let-x-denote-the-greatest-integer-x-Then-the-number-of-ordered-pair-x-y-where-x-and-y-are-positive-integers-less-than-30-such-that-x-2-2x-3-y-4-4y-5-7x-6-2

Question Number 118930 by Ar Brandon last updated on 20/Oct/20 $$\mathrm{Let}\:\left[{x}\right]\:\mathrm{denote}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{integer}\:\leqslant{x}.\:\mathrm{Then}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{ordered}\:\mathrm{pair}\:\left({x},\mathrm{y}\right),\:\mathrm{where}\:{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{are} \\ $$$$\mathrm{positive}\:\mathrm{integers}\:\mathrm{less}\:\mathrm{than}\:\mathrm{30}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\left[\frac{{x}}{\mathrm{2}}\right]+\left[\frac{\mathrm{2}{x}}{\mathrm{3}}\right]+\left[\frac{\mathrm{y}}{\mathrm{4}}\right]+\left[\frac{\mathrm{4y}}{\mathrm{5}}\right]=\frac{\mathrm{7}{x}}{\mathrm{6}}+\frac{\mathrm{21y}}{\mathrm{20}} \\ $$$$\mathrm{is} \\ $$$$\left(\mathrm{A}\right)\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{4} \\ $$ Answered by…

If-a-4-a-17-Find-a-4-a-

Question Number 184438 by Shrinava last updated on 06/Jan/23 $$\mathrm{If}\:\:\:\mathrm{a}\:−\:\frac{\mathrm{4}}{\:\sqrt{\mathrm{a}}}\:=\:\mathrm{17} \\ $$$$\mathrm{Find}\:\:\:\mathrm{a}\:−\:\mathrm{4}\:\sqrt{\mathrm{a}}\:=\:? \\ $$ Answered by Frix last updated on 06/Jan/23 $${a}−\frac{\mathrm{4}}{\:\sqrt{{a}}}=\mathrm{17} \\ $$$$\mathrm{Let}\:{t}=\sqrt{{a}}\:\Rightarrow\:{t}>\mathrm{0} \\…

Question-118896

Question Number 118896 by bobhans last updated on 20/Oct/20 Answered by benjo_mathlover last updated on 20/Oct/20 $$\:\rightarrow\begin{pmatrix}{\mathrm{2}\:\:\:\:\:{b}}\\{{b}\:\:\:\:\:\:\mathrm{2}}\end{pmatrix}\:\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:=\:\begin{pmatrix}{{ac}^{\mathrm{2}} +{c}}\\{\:\:{c}−\mathrm{1}}\end{pmatrix} \\ $$$$\rightarrow\:\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:=\:\frac{\mathrm{1}}{\mathrm{4}−{b}^{\mathrm{2}} }\:\begin{pmatrix}{\mathrm{2}\:\:\:−{b}}\\{−{b}\:\:\:\mathrm{2}}\end{pmatrix}\:\begin{pmatrix}{{ac}^{\mathrm{2}} +{c}}\\{\:\:\:{c}−\mathrm{1}}\end{pmatrix} \\ $$$$\rightarrow\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:=\:\frac{\mathrm{1}}{\mathrm{4}−{b}^{\mathrm{2}} }\:\begin{pmatrix}{\mathrm{2}{ac}^{\mathrm{2}}…

U-n-4-n-1-1-1-4-n-U-n-1-with-U-0-1-find-U-n-in-terms-of-n-question-Q173132-reposted-

Question Number 184401 by mr W last updated on 06/Jan/23 $${U}_{{n}} \:=\:\left(\frac{\left(−\mathrm{4}\right)^{{n}+\mathrm{1}} −\mathrm{1}}{\mathrm{1}−\left(−\mathrm{4}\right)^{{n}} }\right){U}_{{n}−\mathrm{1}} \:{with}\:{U}_{\mathrm{0}} =\mathrm{1} \\ $$$${find}\:{U}_{{n}\:} \:{in}\:{terms}\:{of}\:{n}\:\: \\ $$$$ \\ $$$$\left({question}\:{Q}\mathrm{173132}\:{reposted}\right) \\ $$…