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Question Number 185000 Answers: 0 Comments: 0

A man walks along straight path at a speed 4 ft/s. A spotlight is located on the ground 20 ft from the path and is kept focused on the man. At what rate is spotlight rotating when the man is 15 ft from the point on the path closest to the light?

$${A}\:{man}\:{walks}\:{along}\:{straight}\:{path}\: \\ $$$$\:{at}\:{a}\:{speed}\:\mathrm{4}\:{ft}/{s}.\:{A}\:{spotlight}\:{is} \\ $$$$\:{located}\:{on}\:{the}\:{ground}\:\mathrm{20}\:{ft}\:{from}\: \\ $$$$\:{the}\:{path}\:{and}\:{is}\:{kept}\:{focused}\:{on}\:{the}\:{man}. \\ $$$$\:{At}\:{what}\:{rate}\:{is}\:{spotlight}\:{rotating} \\ $$$$\:{when}\:{the}\:{man}\:{is}\:\mathrm{15}\:{ft}\:{from}\:{the}\: \\ $$$${point}\:{on}\:{the}\:{path}\:{closest}\:{to}\:{the}\:{light}?\: \\ $$$$\: \\ $$

Question Number 184989 Answers: 1 Comments: 0

2^x =4x x=? solution???

$$\mathrm{2}^{\mathrm{x}} =\mathrm{4x} \\ $$$$\mathrm{x}=? \\ $$$$\mathrm{solution}??? \\ $$

Question Number 184988 Answers: 1 Comments: 0

Question Number 185116 Answers: 1 Comments: 0

Question Number 184980 Answers: 2 Comments: 0

(√7) + (√6) = a (√7) − (√6) = ?

$$\sqrt{\mathrm{7}}\:\:+\:\:\sqrt{\mathrm{6}}\:\:=\:\:\mathrm{a} \\ $$$$\sqrt{\mathrm{7}}\:−\:\sqrt{\mathrm{6}}\:=\:? \\ $$

Question Number 184969 Answers: 1 Comments: 2

3 + (1/(6+(3^2 /(6+(5^2 /(6+(7^2 /(6+(9^2 /(6+......)) )) )) )) )) = 𝛑 provet that.

$$\:\: \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{3}\:+\:\frac{\mathrm{1}}{\mathrm{6}+\frac{\mathrm{3}^{\mathrm{2}} }{\mathrm{6}+\frac{\mathrm{5}^{\mathrm{2}} }{\mathrm{6}+\frac{\mathrm{7}^{\mathrm{2}} }{\mathrm{6}+\frac{\mathrm{9}^{\mathrm{2}} }{\mathrm{6}+......}\:\:\:}\:\:}\:\:}\:\:\:\:}\:\:=\:\boldsymbol{\pi} \\ $$$$\:\:\:\:\boldsymbol{\mathrm{provet}}\:\:\boldsymbol{\mathrm{that}}. \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 184960 Answers: 2 Comments: 0

Question Number 184959 Answers: 2 Comments: 0

Question Number 184958 Answers: 1 Comments: 0

Question Number 184955 Answers: 2 Comments: 0

Question Number 184944 Answers: 1 Comments: 0

please you help me Σ_(k=0) ^n sin(k)=??

$${please}\:{you}\:{help}\:{me} \\ $$$$\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}{sin}\left({k}\right)=?? \\ $$

Question Number 184942 Answers: 0 Comments: 2

f(x )= x + ⌊ x + (( ⌊ x_ ^ ⌋)/(⌊ (x^( 2) /(1 +x^( 2) )) ⌋+1)) ⌋ ⇒ f^( −1) (x )=?

$$ \\ $$$$\:\:\:\:{f}\left({x}\:\right)=\:{x}\:+\:\lfloor\:\:{x}\:+\:\frac{\:\lfloor\:\:\underset{} {\overset{} {{x}}}\:\:\rfloor}{\lfloor\:\:\:\frac{{x}^{\:\mathrm{2}} }{\mathrm{1}\:+{x}^{\:\mathrm{2}} }\:\:\:\rfloor+\mathrm{1}}\:\rfloor \\ $$$$\:\:\:\:\:\:\Rightarrow\:\:{f}^{\:−\mathrm{1}} \:\left({x}\:\right)=? \\ $$

Question Number 184941 Answers: 0 Comments: 0

Determiner une relation entre les coeficients de x,y,z pour que z=x+y a_1 x+b_1 y+c_1 z=u a_2 x+b_2 y+c_2 z=v a_3 x+b_3 y+c_3 z=w

$${Determiner}\:{une}\:{relation}\:{entre} \\ $$$${les}\:{coeficients}\:{de}\:{x},{y},{z}\: \\ $$$${pour}\:{que}\:\:{z}={x}+{y} \\ $$$$ \\ $$$${a}_{\mathrm{1}} {x}+{b}_{\mathrm{1}} {y}+{c}_{\mathrm{1}} {z}={u} \\ $$$${a}_{\mathrm{2}} {x}+{b}_{\mathrm{2}} {y}+{c}_{\mathrm{2}} {z}={v} \\ $$$${a}_{\mathrm{3}} {x}+{b}_{\mathrm{3}} {y}+{c}_{\mathrm{3}} {z}={w} \\ $$$$ \\ $$

Question Number 184939 Answers: 1 Comments: 0

What′s the convergent equation of this series? x_1 ^2 +x_2 ^2 +x_3 ^2 +...+x_n ^2 Help!

$$\mathrm{What}'\mathrm{s}\:\mathrm{the}\:\mathrm{convergent}\:\mathrm{equation} \\ $$$$\mathrm{of}\:\mathrm{this}\:\mathrm{series}? \\ $$$$\mathrm{x}_{\mathrm{1}} ^{\mathrm{2}} +\mathrm{x}_{\mathrm{2}} ^{\mathrm{2}} +\mathrm{x}_{\mathrm{3}} ^{\mathrm{2}} +...+\mathrm{x}_{\mathrm{n}} ^{\mathrm{2}} \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 184938 Answers: 2 Comments: 0

If , { (( f : [ (√2) , +∞ ) → R )),(( f (x ) = x^( 2) + ⌊ (( 1)/(1 − ⌊ x^( 2) ⌋)) ⌋ )) :} ⇒ ⌊ f^( −1) ( π ) ⌋ = ?

$$ \\ $$$$\:\:\:\:\:\mathrm{If}\:\:,\:\:\begin{cases}{\:\:{f}\:\::\:\:\left[\:\sqrt{\mathrm{2}}\:,\:+\infty\:\right)\:\rightarrow\:\mathbb{R}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\\{\:\:\:{f}\:\left({x}\:\right)\:=\:{x}^{\:\mathrm{2}} \:\:+\:\lfloor\:\frac{\:\mathrm{1}}{\mathrm{1}\:−\:\lfloor\:{x}^{\:\mathrm{2}} \:\rfloor}\:\rfloor\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{cases} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\:\:\:\lfloor\:\:{f}^{\:−\mathrm{1}} \:\left(\:\pi\:\right)\:\rfloor\:=\:? \\ $$$$ \\ $$$$ \\ $$

Question Number 184937 Answers: 0 Comments: 0

find the laplace transform of the differential equation below (dy/dt) + 5y(t) + 6∫_0 ^t y(τ)dτ = u(t) where y(0) = 2

$$\mathrm{find}\:\mathrm{the}\:\mathrm{laplace}\:\mathrm{transform}\:\mathrm{of}\:\mathrm{the}\:\mathrm{differential} \\ $$$$\mathrm{equation}\:\mathrm{below} \\ $$$$\frac{{dy}}{{dt}}\:+\:\mathrm{5}{y}\left({t}\right)\:+\:\mathrm{6}\int_{\mathrm{0}} ^{{t}} {y}\left(\tau\right){d}\tau\:=\:{u}\left({t}\right)\:\mathrm{where}\:{y}\left(\mathrm{0}\right)\:=\:\mathrm{2} \\ $$

Question Number 184936 Answers: 1 Comments: 0

Use Laplace transform to solve the differential equation ((d^2 v(t))/dt^2 ) +6((dv(t))/dt) + 8v(t) = 2u(t) when v(0) = 1 and v^• (0) = −2

$$\mathrm{Use}\:\mathrm{Laplace}\:\mathrm{transform}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{differential} \\ $$$$\mathrm{equation} \\ $$$$\:\frac{{d}^{\mathrm{2}} {v}\left({t}\right)}{{dt}^{\mathrm{2}} }\:+\mathrm{6}\frac{{dv}\left({t}\right)}{{dt}}\:+\:\mathrm{8}{v}\left({t}\right)\:=\:\mathrm{2}{u}\left({t}\right)\:\: \\ $$$$\mathrm{when}\:{v}\left(\mathrm{0}\right)\:=\:\mathrm{1}\:\mathrm{and}\:\overset{\bullet} {{v}}\left(\mathrm{0}\right)\:=\:−\mathrm{2} \\ $$

Question Number 184932 Answers: 1 Comments: 0

Question Number 184927 Answers: 2 Comments: 0

s=(2/(11^0 ))+(6/(11))+((10)/(11^2 ))+((14)/(11^3 ))+((18)/(11^4 ))+∙∙∙∙ s=?

$${s}=\frac{\mathrm{2}}{\mathrm{11}^{\mathrm{0}} }+\frac{\mathrm{6}}{\mathrm{11}}+\frac{\mathrm{10}}{\mathrm{11}^{\mathrm{2}} }+\frac{\mathrm{14}}{\mathrm{11}^{\mathrm{3}} }+\frac{\mathrm{18}}{\mathrm{11}^{\mathrm{4}} }+\centerdot\centerdot\centerdot\centerdot \\ $$$${s}=? \\ $$

Question Number 184925 Answers: 1 Comments: 1

Question Number 184920 Answers: 1 Comments: 0

Investigate the series (1/(1×2))+(1/(2×3))+(1/(3×4))+(1/(4×5))+... Does it Converges or Diverges?

$$\mathrm{Investigate}\:\mathrm{the}\:\mathrm{series} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}×\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{3}×\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{4}×\mathrm{5}}+... \\ $$$$\mathrm{Does}\:\mathrm{it}\:\mathrm{Converges}\:\mathrm{or}\:\mathrm{Diverges}? \\ $$

Question Number 184918 Answers: 2 Comments: 2

Show that 1+(1/2)+(1/3)+(1/4)+(1/5)+(1/6)+... is not convergent Hi

$$\mathrm{Show}\:\mathrm{that}\: \\ $$$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{5}}+\frac{\mathrm{1}}{\mathrm{6}}+...\:\mathrm{is}\: \\ $$$$\mathrm{not}\:\mathrm{convergent} \\ $$$$ \\ $$$$\mathrm{Hi} \\ $$

Question Number 184915 Answers: 0 Comments: 2

Consider the series below 1+5+25+125+... Investigate whether it is convergent or divergent. Thanks

$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{series}\:\mathrm{below} \\ $$$$\mathrm{1}+\mathrm{5}+\mathrm{25}+\mathrm{125}+...\:\mathrm{Investigate} \\ $$$$\mathrm{whether}\:\mathrm{it}\:\mathrm{is}\:\mathrm{convergent}\:\mathrm{or}\: \\ $$$$\mathrm{divergent}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Thanks} \\ $$

Question Number 184914 Answers: 0 Comments: 1

Lindsey randomly selects 2 distinct days each lveek to go to the gym. Jess randomly selects 3 distinct days each tveek to go to the same gym. What is the probability that Lindsey and Jess will both be at the gym on the same day at least once in any given week? Express your anslver as a common fraction.

$$ \\ $$ Lindsey randomly selects 2 distinct days each lveek to go to the gym. Jess randomly selects 3 distinct days each tveek to go to the same gym. What is the probability that Lindsey and Jess will both be at the gym on the same day at least once in any given week? Express your anslver as a common fraction.

Question Number 184913 Answers: 0 Comments: 0

Question Number 184903 Answers: 1 Comments: 0

lim_(x→0) ((e^x +e^(−x) −2)/x^2 )=?? let x=2t { ((x→0)),((t→0)) :} lim_(x→0) ((e^x +e^(−x) −2)/x^2 )=lim_(t→0) ((e^(2t) +e^(−2t) −2)/(4t^2 ))=(1/4)lim_(t→0) (((e^t −e^(−t) )/t))^2 =(1/4)lim_(t→0) (((e^t −1)/t)+((e^(−t) −1)/(−t)))^2 =(1/4)(1+1)^2 =1

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{e}^{\mathrm{x}} +\mathrm{e}^{−\mathrm{x}} −\mathrm{2}}{\mathrm{x}^{\mathrm{2}} }=?? \\ $$$$\mathrm{let}\:\mathrm{x}=\mathrm{2t}\:\begin{cases}{\mathrm{x}\rightarrow\mathrm{0}}\\{\mathrm{t}\rightarrow\mathrm{0}}\end{cases} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{e}^{\mathrm{x}} +\mathrm{e}^{−\mathrm{x}} −\mathrm{2}}{\mathrm{x}^{\mathrm{2}} }=\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{e}^{\mathrm{2t}} +\mathrm{e}^{−\mathrm{2t}} −\mathrm{2}}{\mathrm{4t}^{\mathrm{2}} }=\frac{\mathrm{1}}{\mathrm{4}}\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{e}^{\mathrm{t}} −\mathrm{e}^{−\mathrm{t}} }{\mathrm{t}}\right)^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{4}}\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{e}^{\mathrm{t}} −\mathrm{1}}{\mathrm{t}}+\frac{\mathrm{e}^{−\mathrm{t}} −\mathrm{1}}{−\mathrm{t}}\right)^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{1}+\mathrm{1}\right)^{\mathrm{2}} =\mathrm{1} \\ $$

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