Question and Answers Forum

To do normally his commercial activities in some place situated at 150km from him, a driver use a car. the consumption of gazoil in liters for 10 km is defined by: C(v)=((20)/v)+(v/(45)) where v is the speed of car. How should be the speed of car to reduce minimally the consumption of gazoil?

$$\mathrm{To}\:\mathrm{do}\:\mathrm{normally}\:\mathrm{his}\:\mathrm{commercial} \\ $$$$\mathrm{activities}\:\mathrm{in}\:\mathrm{some}\:\mathrm{place}\:\mathrm{situated}\:\mathrm{at}\:\mathrm{150km} \\ $$$$\mathrm{from}\:\mathrm{him},\:\mathrm{a}\:\mathrm{driver}\:\mathrm{use}\:\mathrm{a}\:\mathrm{car}.\:\mathrm{the}\:\mathrm{consumption} \\ $$$$\mathrm{of}\:\mathrm{gazoil}\:\mathrm{in}\:\mathrm{liters}\:\mathrm{for}\:\mathrm{10}\:\mathrm{km}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{by}: \\ $$$$\mathrm{C}\left(\mathrm{v}\right)=\frac{\mathrm{20}}{\mathrm{v}}+\frac{\mathrm{v}}{\mathrm{45}}\:\mathrm{where}\:\mathrm{v}\:\mathrm{is}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{car}. \\ $$$$\mathrm{How}\:\mathrm{should}\:\mathrm{be}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{car}\:\mathrm{to}\:\mathrm{reduce} \\ $$$$\mathrm{minimally}\:\mathrm{the}\:\mathrm{consumption}\:\mathrm{of}\:\mathrm{gazoil}? \\ $$

Question Number 104038 Answers: 1 Comments: 0

what is the largest positive integer n such that n^3 +100 is divisible by n+10 ?

$${what}\:{is}\:{the}\:{largest}\:{positive} \\ $$$${integer}\:{n}\:{such}\:{that}\:{n}^{\mathrm{3}} +\mathrm{100}\:{is} \\ $$$${divisible}\:{by}\:{n}+\mathrm{10}\:?\: \\ $$

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 104035 Answers: 1 Comments: 0

Find the image of point OP^(→) = p^ in the line r^ =a^ +λb^ .

$${Find}\:{the}\:{image}\:{of}\:{point}\:\overset{\rightarrow} {{OP}}\:=\:\bar {{p}}\:\:{in} \\ $$$${the}\:{line}\:\:\bar {{r}}=\bar {{a}}+\lambda\bar {{b}}\:. \\ $$

Question Number 104034 Answers: 2 Comments: 0

Solve: y^(′′) +2y^′ +2y=secax

$${Solve}:\:{y}^{''} +\mathrm{2}{y}^{'} +\mathrm{2}{y}={secax} \\ $$

Question Number 104028 Answers: 2 Comments: 0

calculate ∫_(20) ^(+∞) (dx/((x−18)^(19) (x−19)^(18) ))

$$\mathrm{calculate}\:\:\int_{\mathrm{20}} ^{+\infty} \:\:\frac{\mathrm{dx}}{\left(\mathrm{x}−\mathrm{18}\right)^{\mathrm{19}} \left(\mathrm{x}−\mathrm{19}\right)^{\mathrm{18}} } \\ $$

Question Number 104016 Answers: 1 Comments: 0

Question Number 104023 Answers: 0 Comments: 1

Question Number 103998 Answers: 3 Comments: 5

if f(x)=x^(3/2) f′(0)=0 or not exist

$${if}\:\:\:\:{f}\left({x}\right)={x}^{\frac{\mathrm{3}}{\mathrm{2}}} \\ $$$${f}'\left(\mathrm{0}\right)=\mathrm{0}\:\:{or}\:{not}\:{exist} \\ $$

Question Number 103986 Answers: 1 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 103984 Answers: 0 Comments: 1

tan^2 (x)+tan^2 (2x)+tan^2 (4x)=33 x=?

$$\:\:\:\:\boldsymbol{{tan}}^{\mathrm{2}} \left(\boldsymbol{{x}}\right)+\boldsymbol{{tan}}^{\mathrm{2}} \left(\mathrm{2}\boldsymbol{{x}}\right)+\boldsymbol{{tan}}^{\mathrm{2}} \left(\mathrm{4}\boldsymbol{{x}}\right)=\mathrm{33} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{x}}=? \\ $$

Question Number 103979 Answers: 0 Comments: 1

show right and left sid limitation of lim_(x→0) ((ln(b−x))/(ax))

$$\:\:{show}\:{right}\:{and}\:{left}\:{sid}\:\:\:\:{limitation}\:\:\:\: \\ $$$${of}\:\:\:{li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{{ln}\left({b}−{x}\right)}{{ax}} \\ $$$$ \\ $$

Question Number 103974 Answers: 2 Comments: 0

calculate ∫_(−∞) ^(+∞) (dx/((x^2 −x+1)(x^2 +3)^2 ))

$${calculate}\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} } \\ $$

Question Number 103969 Answers: 1 Comments: 0

how do you solve (D^3 +12D^2 +36D)y=0 by constant coefficients