Question Number 9254 by tawakalitu last updated on 25/Nov/16 Answered by mrW last updated on 26/Nov/16 $$\mathrm{2cos}\:\pi\mathrm{t}=\mathrm{x} \\ $$$$\mathrm{y}=\mathrm{1}−\mathrm{4cos}\:\mathrm{2}\pi\mathrm{t}=\mathrm{1}−\mathrm{4}\left(\mathrm{2cos}\:^{\mathrm{2}} \pi\mathrm{t}−\mathrm{1}\right) \\ $$$$\mathrm{y}=\mathrm{5}−\mathrm{2}\left(\mathrm{2cos}\:\pi\mathrm{t}\right)^{\mathrm{2}} \\ $$$$\mathrm{hence}\:\mathrm{y}=\mathrm{5}−\mathrm{2x}^{\mathrm{2}} \\…
Question Number 9230 by tawakalitu last updated on 24/Nov/16 $$\mathrm{Given}\:\mathrm{that}\: \\ $$$$\mathrm{a}\:=\:\mathrm{2i}\:−\:\mathrm{3j}\:+\:\mathrm{k},\:\mathrm{b}\:=\:\mathrm{4i}\:+\:\mathrm{j}\:−\:\mathrm{3k}, \\ $$$$\mathrm{c}\:=\:\mathrm{i}\:−\:\mathrm{3k} \\ $$$$\mathrm{Find}\:\:\left(\mathrm{a}\centerdot\mathrm{b}\right)\mathrm{c},\:\:\mathrm{a}\left(\mathrm{b}×\mathrm{c}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 140176 by EDWIN88 last updated on 05/May/21 $$\mathrm{Let}\:\mathrm{V}\:\mathrm{be}\:\mathrm{a}\:\mathrm{vector}\:\mathrm{space}\:\mathrm{of}\:\mathrm{polynomials} \\ $$$$\mathrm{p}\left(\mathrm{x}\right)=\:\mathrm{a}+\mathrm{bx}+\mathrm{cx}^{\mathrm{2}} \:\mathrm{with}\:\mathrm{real}\:\mathrm{coefficients} \\ $$$$\mathrm{a},\mathrm{b}\:\mathrm{and}\:\mathrm{c}.\:\mathrm{Define}\:\mathrm{an}\:\mathrm{inner}\:\mathrm{product}\:\mathrm{on}\:\mathrm{V} \\ $$$$\mathrm{by}\:\left(\mathrm{p},\mathrm{q}\right)=\frac{\mathrm{1}}{\mathrm{2}}\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\mathrm{p}\left(\mathrm{x}\right)\mathrm{q}\left(\mathrm{x}\right)\:\mathrm{dx}\:. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Find}\:\mathrm{a}\:\mathrm{orthonormal}\:\mathrm{basis}\:\mathrm{for}\:\mathrm{V}\:\mathrm{consisting} \\ $$$$\mathrm{of}\:\mathrm{polynomials}\:\phi_{\mathrm{o}} \left(\mathrm{x}\right)\:,\:\phi_{\mathrm{1}} \left(\mathrm{x}\right)\:\mathrm{and}\:\phi_{\mathrm{2}}…
Question Number 9060 by tawakalitu last updated on 16/Nov/16 Answered by mrW last updated on 17/Nov/16 $$\left.{b}\right) \\ $$$$\mathrm{60}^{\mathrm{2}} =\mathrm{40}^{\mathrm{2}} +\mathrm{92}^{\mathrm{2}} −\mathrm{2}×\mathrm{40}×\mathrm{92}×\mathrm{cos}\:\alpha \\ $$$$\mathrm{cos}\:\alpha=\frac{\mathrm{40}^{\mathrm{2}} +\mathrm{92}^{\mathrm{2}}…
Question Number 74579 by malikmasood3535@gmail.com last updated on 26/Nov/19 $${find}\:{the}\:{gradient}\:{of}\:{scalar}\:{point}\:{function}\:{being}\:{expressed}\:{in}\:{term}\:{of}\:{scalar}\:{triple}\:{product}\:{as}\:{u}=\left(\bar {{a}},\bar {{b}},\bar {{c}}\right)=\bar {{a}}.\bar {{b}}×\bar {{c}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 9008 by Yozzias last updated on 12/Nov/16 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\epsilon_{\mathrm{ijk}} \epsilon_{\mathrm{ijk}} \delta_{\mathrm{mn}} \delta_{\mathrm{mn}} \:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 140053 by ajfour last updated on 03/May/21 Commented by ajfour last updated on 03/May/21 $${Find}\:{radius}\:{of}\:{largest}\:{sphere}\: \\ $$$${within}\:{the}\:{cuboid}\:{and}\:{between} \\ $$$${the}\:{shown}\:{triangular}\:{planes}. \\ $$ Commented by…
Question Number 139992 by ajfour last updated on 02/May/21 Commented by ajfour last updated on 03/May/21 $${Let}\:\:{role}\:{of}\:{new}\:{cross}\: \\ $$$${multiplication}\:{by}\:\hat {{k}} \\ $$$$\:{be}\:{to}\:{rotate}\:{the}\:{component} \\ $$$${of}\:{a}\:{vector}\:\bot\:{to}\:{z}\:{axis}\:{by}\:\mathrm{90}° \\…
Question Number 73940 by smartsmith459@gmail.com last updated on 16/Nov/19 Answered by Rio Michael last updated on 16/Nov/19 $$\left.{Q}\mathrm{4}\right)\:{is}\:{equivalent}\:{to}\:{solving}\: \\ $$$$\:\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:=\:{M}^{−\mathrm{1}} \begin{pmatrix}{\mathrm{1}}\\{\mathrm{23}}\end{pmatrix} \\ $$$${where}\:{M}\:=\:\begin{pmatrix}{\mathrm{3}}&{−\mathrm{4}}\\{\mathrm{7}}&{\mathrm{1}}\end{pmatrix} \\ $$$${M}^{−\mathrm{1}}…
Question Number 8390 by tawakalitu last updated on 09/Oct/16 Answered by fernandodantas1996 last updated on 12/Oct/16 $$ \\ $$$$\: \\ $$$$\left.\mathrm{i}\right)\:\overset{\rightarrow} {\mathrm{F}}+\overset{\rightarrow} {\mathrm{P}}\:=\:\mathrm{6i}\:+\:\mathrm{4j}\:−\:\mathrm{k}\:\Rightarrow\: \\ $$$$\Rightarrow\:\parallel\overset{\rightarrow}…