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AllQuestion and Answers: Page 302

Question Number 188619 Answers: 0 Comments: 1

Question Number 188615 Answers: 1 Comments: 0

Question Number 188591 Answers: 4 Comments: 3

Question Number 188590 Answers: 4 Comments: 0

Question Number 188589 Answers: 0 Comments: 1

Question Number 188587 Answers: 0 Comments: 0

Question Number 188575 Answers: 4 Comments: 0

Question Number 188572 Answers: 0 Comments: 3

Question Number 188569 Answers: 3 Comments: 0

Question Number 188568 Answers: 2 Comments: 0

Question Number 188564 Answers: 1 Comments: 0

1×2+2×3+3×4+...............+24×25 = ?

$$\mathrm{1}×\mathrm{2}+\mathrm{2}×\mathrm{3}+\mathrm{3}×\mathrm{4}+...............+\mathrm{24}×\mathrm{25}\:=\:? \\ $$

Question Number 188560 Answers: 2 Comments: 0

Question Number 188557 Answers: 1 Comments: 0

∫(√(x(√(x^2 +1))))dx

$$\int\sqrt{\boldsymbol{{x}}\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{1}}}\boldsymbol{{dx}} \\ $$

Question Number 188552 Answers: 0 Comments: 1

Question Number 188549 Answers: 0 Comments: 3

Q188442 please solve by programing for a cylinder

$$\mathrm{Q188442}\:\:\:\:\:\:\:\:\:\:\:{please}\:{solve}\:{by}\:{programing} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{for}\:\:{a}\:\:{cylinder} \\ $$

Question Number 188545 Answers: 1 Comments: 0

Question Number 188544 Answers: 1 Comments: 0

Question Number 188543 Answers: 0 Comments: 0

Question Number 188521 Answers: 1 Comments: 2

Question Number 188520 Answers: 1 Comments: 0

Question Number 188515 Answers: 1 Comments: 0

in AB^Δ C : a=3 , b=6 , c=7 find the value of : E = (a+b )cos(C) + (b+c)cos(A)+ (a+c )cos(B)=?

$$ \\ $$$$\:\:\:\:\:{in}\:\:{A}\overset{\Delta} {{B}C}\:\::\:\:\:{a}=\mathrm{3}\:\:,\:\:{b}=\mathrm{6}\:\:,\:\:{c}=\mathrm{7} \\ $$$$\:\:\: \\ $$$$\: \\ $$$$\:\:\:\:{find}\:\:{the}\:{value}\:\:{of}\:: \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:{E}\:=\:\left({a}+{b}\:\right){cos}\left({C}\right)\:+\:\left({b}+{c}\right){cos}\left({A}\right)+\:\left({a}+{c}\:\right){cos}\left({B}\right)=?\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\: \\ $$

Question Number 188512 Answers: 0 Comments: 0

x^3 +y^3 +z^3 −3xyz= (x+y+z) (x^2 +y^2 +z^2 −xy−yz−zx) if x+y+z = 0, then x^3 +y^3 +z^3 −3xyz = 0×(x^2 +y^2 +z^2 −xy−yz−zx) = 0

$${x}^{\mathrm{3}} +\boldsymbol{{y}}^{\mathrm{3}} +\boldsymbol{{z}}^{\mathrm{3}} −\mathrm{3}\boldsymbol{{xyz}}= \\ $$$$\left(\boldsymbol{{x}}+\boldsymbol{{y}}+\boldsymbol{{z}}\right)\:\left(\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} +\boldsymbol{{z}}^{\mathrm{2}} −\boldsymbol{{xy}}−\boldsymbol{{yz}}−\boldsymbol{{zx}}\right) \\ $$$$\boldsymbol{{if}}\:\boldsymbol{{x}}+\boldsymbol{{y}}+\boldsymbol{{z}}\:=\:\mathrm{0},\:{then} \\ $$$${x}^{\mathrm{3}} +\boldsymbol{{y}}^{\mathrm{3}} +\boldsymbol{{z}}^{\mathrm{3}} −\mathrm{3}\boldsymbol{{xyz}} \\ $$$$=\:\mathrm{0}×\left(\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} +\boldsymbol{{z}}^{\mathrm{2}} −\boldsymbol{{xy}}−\boldsymbol{{yz}}−\boldsymbol{{zx}}\right) \\ $$$$=\:\mathrm{0} \\ $$

Question Number 188511 Answers: 0 Comments: 0

evaluate ∫_0 ^π (dx/(a+bcosx )) , a > 0 and deduce that ∫_0 ^π (dx/((a+bcos x)^2 )) = ((πa)/((a^2 −b^2 )^(3/2) )) ; a^2 >b^2 and ∫_0 ^π ((cos x dx)/((a+bcos x)^2 )) = ((−πb)/((a^2 −b^2 )^(3/2) )) ; a^2 >b^2

$$\:\:\:{evaluate} \\ $$$$\int_{\mathrm{0}} ^{\pi} \frac{{dx}}{{a}+{b}\mathrm{cos}{x}\:}\:\:\:\:\:\:,\:\:\:{a}\:>\:\mathrm{0} \\ $$$$\:\:\:{and}\:{deduce}\:{that} \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\pi} \frac{{dx}}{\left({a}+{b}\mathrm{cos}\:{x}\right)^{\mathrm{2}} }\:\:=\:\:\:\frac{\pi{a}}{\left({a}^{\mathrm{2}} −{b}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} }\:\:;\:\:{a}^{\mathrm{2}} >{b}^{\mathrm{2}} \\ $$$${and}\:\:\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{cos}\:{x}\:{dx}}{\left({a}+{b}\mathrm{cos}\:{x}\right)^{\mathrm{2}} }\:\:=\:\frac{−\pi{b}}{\left({a}^{\mathrm{2}} −{b}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} }\:\:;\:\:{a}^{\mathrm{2}} >{b}^{\mathrm{2}} \\ $$

Question Number 188508 Answers: 2 Comments: 0

Question Number 188507 Answers: 0 Comments: 0

Question Number 188551 Answers: 1 Comments: 0

you randomly select a 5 digit number. what′s the probability that this number has exactly 3 different digits?

$${you}\:{randomly}\:{select}\:{a}\:\mathrm{5}\:{digit}\:{number}. \\ $$$${what}'{s}\:{the}\:{probability}\:{that}\:{this}\:{number} \\ $$$${has}\:{exactly}\:\mathrm{3}\:{different}\:{digits}? \\ $$

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