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Question Number 170212 Answers: 3 Comments: 0

which rectangle with integer length side have numerically the same area and perimeter? Find them all. Find a proof that convinces that you have found them all. what about right− angled triangle? how many solutions?

$$\:\mathrm{which}\:\mathrm{rectangle}\:\mathrm{with}\:\mathrm{integer}\:\mathrm{length}\: \\ $$$$\:\:\mathrm{side}\:\mathrm{have}\:\mathrm{numerically}\:\mathrm{the}\:\mathrm{same}\:\mathrm{area} \\ $$$$\:\:\mathrm{and}\:\mathrm{perimeter}?\:\mathrm{Find}\:\mathrm{them}\:\mathrm{all}.\:\mathrm{Find} \\ $$$$\:\mathrm{a}\:\mathrm{proof}\:\mathrm{that}\:\mathrm{convinces}\:\mathrm{that}\:\mathrm{you}\:\mathrm{have} \\ $$$$\:\mathrm{found}\:\mathrm{them}\:\mathrm{all}.\:\mathrm{what}\:\mathrm{about}\:\mathrm{right}− \\ $$$$\:\mathrm{angled}\:\mathrm{triangle}?\:\mathrm{how}\:\mathrm{many}\:\mathrm{solutions}? \\ $$

Question Number 170211 Answers: 1 Comments: 0

lim_(x→0) (((tan^(−1) (((x−x(√(1−x^2 )))/( (√(1−x^2 ))+x^2 ))))/x^3 ))=? pleas solve this

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{tan}^{−\mathrm{1}} \left(\frac{{x}−{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }+{x}^{\mathrm{2}} }\right)}{{x}^{\mathrm{3}} }\right)=? \\ $$$${pleas}\:{solve}\:{this} \\ $$

Question Number 170206 Answers: 2 Comments: 0

1. { ((y^(log_x y) =x^4 )),((log_2 (y−x)=1)) :} 2. 25^(−x) −5^(−x+1) ≥50

$$\mathrm{1}.\:\:\:\:\begin{cases}{{y}^{{log}_{{x}} {y}} ={x}^{\mathrm{4}} }\\{{log}_{\mathrm{2}} \left({y}−{x}\right)=\mathrm{1}}\end{cases} \\ $$$$\mathrm{2}.\:\:\:\:\:\mathrm{25}^{−{x}} −\mathrm{5}^{−{x}+\mathrm{1}} \geqslant\mathrm{50} \\ $$

Question Number 170205 Answers: 1 Comments: 0

If x is nearer a than b in [a,b], is (√x) necessarily nearer (√a) than (√b) Give a proof of counterexample

$$\:\mathrm{If}\:\mathrm{x}\:\mathrm{is}\:\mathrm{nearer}\:\:\:\mathrm{a}\:\:\mathrm{than}\:\:\mathrm{b}\:\:\mathrm{in}\:\left[\mathrm{a},\mathrm{b}\right],\: \\ $$$$\mathrm{is}\:\sqrt{\mathrm{x}}\:\mathrm{necessarily}\:\mathrm{nearer}\:\sqrt{\mathrm{a}}\:\:\mathrm{than}\:\sqrt{\mathrm{b}} \\ $$$$ \\ $$$$\mathrm{Give}\:\mathrm{a}\:\mathrm{proof}\:\mathrm{of}\:\mathrm{counterexample} \\ $$

Question Number 170203 Answers: 1 Comments: 0

solve: 5^(lgx) =50−x^(lg5)

$${solve}:\:\mathrm{5}^{{lgx}} =\mathrm{50}−{x}^{{lg}\mathrm{5}} \\ $$

Question Number 170202 Answers: 0 Comments: 10

A point is 3cm, 4cm and 5cm away from three vertices of a rectangle. How far can it be from the 4th vertex. Find all solutions

$$\:\mathrm{A}\:\mathrm{point}\:\mathrm{is}\:\mathrm{3cm},\:\mathrm{4cm}\:\mathrm{and}\:\mathrm{5cm}\:\mathrm{away}\: \\ $$$$\:\:\mathrm{from}\:\mathrm{three}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{a}\:\mathrm{rectangle}.\: \\ $$$$\:\mathrm{How}\:\mathrm{far}\:\mathrm{can}\:\mathrm{it}\:\mathrm{be}\:\mathrm{from}\:\mathrm{the}\:\mathrm{4th}\:\mathrm{vertex}. \\ $$$$ \\ $$$$\mathrm{Find}\:\mathrm{all}\:\mathrm{solutions} \\ $$

Question Number 170199 Answers: 1 Comments: 0

Find the first four terms of the series for e^x sinhx Mastermind

$${Find}\:{the}\:{first}\:{four}\:{terms}\:{of}\:{the}\:{series} \\ $$$${for}\:{e}^{{x}} {sinhx} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 170198 Answers: 1 Comments: 0

Find the first three term of the series for e^x ln(1+x) Mastermind

$${Find}\:{the}\:{first}\:{three}\:{term}\:{of}\:{the}\:{series} \\ $$$${for}\:{e}^{{x}} {ln}\left(\mathrm{1}+{x}\right) \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 170197 Answers: 1 Comments: 0

Question Number 170196 Answers: 0 Comments: 0

Question Number 170311 Answers: 1 Comments: 0

5(dy/dx)=tan(2x+2y+6) Mastermind

$$\mathrm{5}\frac{{dy}}{{dx}}={tan}\left(\mathrm{2}{x}+\mathrm{2}{y}+\mathrm{6}\right) \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 170189 Answers: 0 Comments: 2

Question Number 170185 Answers: 0 Comments: 1

Question Number 170184 Answers: 0 Comments: 0

Question Number 170183 Answers: 0 Comments: 0

Question Number 170182 Answers: 1 Comments: 1

lim_(x→0) [x∙sin(1/x)]=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[{x}\centerdot{sin}\frac{\mathrm{1}}{{x}}\right]=? \\ $$

Question Number 170181 Answers: 1 Comments: 0

Question Number 170166 Answers: 1 Comments: 1

lim_(x→0) ((1/(sin^2 x))−(1/x^2 ))=? please solve it describely.

$${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\left(\frac{\mathrm{1}}{{sin}^{\mathrm{2}} {x}}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)=? \\ $$$${please}\:{solve}\:{it}\:{describely}. \\ $$

Question Number 170187 Answers: 1 Comments: 3

Question Number 170159 Answers: 1 Comments: 0

lim_(x→4) ((e !x−24)/( (√x)−2))=?

$$\underset{{x}\rightarrow\mathrm{4}} {\mathrm{lim}}\:\frac{{e}\:!{x}−\mathrm{24}}{\:\sqrt{{x}}−\mathrm{2}}=? \\ $$

Question Number 170155 Answers: 1 Comments: 0

Given f(x)=x(√(1−x+(√(1−x)))) where 0≤x≤1 find max f(x)

$$\:\:{Given}\:{f}\left({x}\right)={x}\sqrt{\mathrm{1}−{x}+\sqrt{\mathrm{1}−{x}}} \\ $$$$\:{where}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1} \\ $$$$\:{find}\:{max}\:{f}\left({x}\right) \\ $$

Question Number 170154 Answers: 0 Comments: 0

Question Number 170150 Answers: 1 Comments: 0

Question Number 170148 Answers: 1 Comments: 0

Question Number 170255 Answers: 1 Comments: 0

(d/dx)[∫_2 ^x e^t^2 dt=?

$$\frac{{d}}{{dx}}\left[\int_{\mathrm{2}} ^{{x}} {e}^{{t}^{\mathrm{2}} } {dt}=?\right. \\ $$

Question Number 170143 Answers: 0 Comments: 3

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