Question and Answers Forum

Let the points ABC form a triangle on the cartesian plane, whose area is 20. Let the coordinates of said points be A(8, 6) B(2, 4) and C(x, y) If ∣AC∣=∣BC∣, find the coordinates of point C.

$${Let}\:{the}\:{points}\:{ABC}\:{form}\:{a}\:{triangle}\:{on}\:{the} \\ $$$${cartesian}\:{plane},\:{whose}\:{area}\:{is}\:\mathrm{20}.\:{Let}\:{the}\:{coordinates} \\ $$$${of}\:{said}\:{points}\:{be}\:{A}\left(\mathrm{8},\:\mathrm{6}\right)\:{B}\left(\mathrm{2},\:\mathrm{4}\right)\:{and}\:{C}\left({x},\:{y}\right) \\ $$$${If}\:\mid{AC}\mid=\mid{BC}\mid,\:{find}\:{the}\:{coordinates}\:{of}\:{point}\:{C}. \\ $$

Question Number 180641 Answers: 4 Comments: 0

if a+b+c+d+e=8 and a^2 +b^2 +c^2 +d^2 +e^2 =16, what is the maximal value of a ?

$${if}\:{a}+{b}+{c}+{d}+{e}=\mathrm{8}\:{and} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +{d}^{\mathrm{2}} +{e}^{\mathrm{2}} =\mathrm{16},\:{what}\:{is}\:{the} \\ $$$${maximal}\:{value}\:{of}\:{a}\:? \\ $$

Question Number 178358 Answers: 0 Comments: 0

Show that when x is small ln (cosh x)≈(x^2 /2)−(x^4 /(12))+... and that when x is large ln (cosh x)≈x−ln 2

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{when}\:\mathrm{x}\:\mathrm{is}\:\mathrm{small}\: \\ $$$$\mathrm{ln}\:\left(\mathrm{cosh}\:\mathrm{x}\right)\approx\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}−\frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{12}}+...\:\mathrm{and} \\ $$$$\mathrm{that}\:\mathrm{when}\:\mathrm{x}\:\mathrm{is}\:\mathrm{large}\:\mathrm{ln}\:\left(\mathrm{cosh}\:\mathrm{x}\right)\approx\mathrm{x}−\mathrm{ln}\:\mathrm{2} \\ $$

Question Number 178357 Answers: 1 Comments: 0

Given that sinh^(−1) x=sech^(−1) x show x=(√((((√5)−1)/2) ))

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{sinh}\:^{−\mathrm{1}} \mathrm{x}=\mathrm{sech}\:^{−\mathrm{1}} \mathrm{x}\:\:\: \\ $$$$\mathrm{show} \\ $$$$\mathrm{x}=\sqrt{\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{2}}\:} \\ $$

Question Number 178356 Answers: 1 Comments: 0

Solve simultaneous sinh x+cosh y=5 sinh^2 x+cosh^2 y=13

$$\mathrm{Solve}\:\mathrm{simultaneous} \\ $$$$\mathrm{sinh}\:\mathrm{x}+\mathrm{cosh}\:\mathrm{y}=\mathrm{5} \\ $$$$\mathrm{sinh}\:^{\mathrm{2}} \mathrm{x}+\mathrm{cosh}\:^{\mathrm{2}} \mathrm{y}=\mathrm{13} \\ $$

Question Number 178355 Answers: 1 Comments: 0

Show that cosh x>sinh x

$$\mathrm{Show}\:\mathrm{that}\: \\ $$$$\mathrm{cosh}\:\mathrm{x}>\mathrm{sinh}\:\mathrm{x} \\ $$

Question Number 178354 Answers: 1 Comments: 0

Show that the minimum value of sinh x+ncosh x is (√(n^2 −1)) and this occurs x=0.5ln (((n−1)/(n+1)))

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{sinh}\:\mathrm{x}+\mathrm{ncosh}\:\mathrm{x}\:\mathrm{is}\:\sqrt{\mathrm{n}^{\mathrm{2}} −\mathrm{1}} \\ $$$$\mathrm{and}\:\mathrm{this}\:\mathrm{occurs}\:\mathrm{x}=\mathrm{0}.\mathrm{5ln}\:\left(\frac{\mathrm{n}−\mathrm{1}}{\mathrm{n}+\mathrm{1}}\right) \\ $$

Question Number 179992 Answers: 0 Comments: 0

What is the absolute error for the measurements: (a) 250m to the nearest 10m. (b) 143m to three sig. figures. (c) 41500cm to the nearest 100.

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{absolute}\:\mathrm{error}\:\mathrm{for}\:\mathrm{the} \\ $$$$\mathrm{measurements}: \\ $$$$\:\:\:\:\left({a}\right)\:\mathrm{250}{m}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{10}{m}. \\ $$$$\:\:\:\:\left({b}\right)\:\mathrm{143}{m}\:\mathrm{to}\:\mathrm{three}\:\mathrm{sig}.\:\mathrm{figures}. \\ $$$$\:\:\:\:\left({c}\right)\:\:\mathrm{41500}{cm}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{100}. \\ $$

Question Number 178347 Answers: 2 Comments: 0

Let f(x)= (ax+1)^5 .(1+bx)^4 ; a,b ∈ N if times of x equal 62 so what are possible values of the sum a, b?

$${Let}\:{f}\left({x}\right)=\:\left({ax}+\mathrm{1}\right)^{\mathrm{5}} .\left(\mathrm{1}+{bx}\right)^{\mathrm{4}} \:;\:{a},{b}\:\in\:\mathbb{N} \\ $$$$\:{if}\:{times}\:{of}\:{x}\:{equal}\:\mathrm{62}\:{so}\:{what}\:{are}\:{possible}\:{values} \\ $$$$\:{of}\:{the}\:{sum}\:{a},\:{b}? \\ $$$$ \\ $$

Question Number 178338 Answers: 3 Comments: 1

Let S= {1, 2, ..., 9, 0} A: How many multiples of eight of four digits can be formed from S B: The same question for different digits

$${Let}\:{S}=\:\left\{\mathrm{1},\:\mathrm{2},\:...,\:\mathrm{9},\:\mathrm{0}\right\}\:\boldsymbol{{A}}:\:{How}\:{many}\:{multiples} \\ $$$$\:{of}\:{eight}\:{of}\:{four}\:{digits}\:{can}\:{be}\:{formed}\:{from}\:{S} \\ $$$$\:\boldsymbol{{B}}:\:{The}\:{same}\:{question}\:{for}\:{different}\:{digits} \\ $$

Question Number 178320 Answers: 1 Comments: 2

Question Number 178305 Answers: 0 Comments: 0

Question Number 178251 Answers: 3 Comments: 0

solve (x^2 −5)^2 −x=5

$${solve} \\ $$$$\left({x}^{\mathrm{2}} −\mathrm{5}\right)^{\mathrm{2}} −{x}=\mathrm{5} \\ $$

Question Number 178240 Answers: 1 Comments: 0

((a^(n+1) + b^(n+1) )/(a^n + b^n )) = (√(ab)) find n=?

$$\frac{\mathrm{a}^{\boldsymbol{\mathrm{n}}+\mathrm{1}} \:+\:\mathrm{b}^{\boldsymbol{\mathrm{n}}+\mathrm{1}} }{\mathrm{a}^{\boldsymbol{\mathrm{n}}} \:+\:\mathrm{b}^{\boldsymbol{\mathrm{n}}} }\:=\:\sqrt{\mathrm{ab}}\:\:\:\mathrm{find}\:\:\:\mathrm{n}=? \\ $$

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