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Question Number 171260 Answers: 1 Comments: 0

Change to polar coordinates: ∫^( 4a) _0 ∫_(y^2 /4a) ^a (((x^2 −y^2 )/(x^2 +y^2 ))) dx dy

$$\underline{{Change}\:{to}\:{polar}\:{coordinates}:} \\ $$$$\underset{\mathrm{0}} {\int}^{\:\:\mathrm{4}{a}} \underset{{y}^{\mathrm{2}} /\mathrm{4}{a}} {\int}\overset{{a}} {\:}\:\:\left(\frac{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\right)\:{dx}\:{dy} \\ $$

Question Number 171255 Answers: 1 Comments: 2

Question Number 171253 Answers: 2 Comments: 0

Question Number 171247 Answers: 2 Comments: 0

lim_(x→2) ((x^2 −4)/(x−2))=...

$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{2}} −\mathrm{4}}{{x}−\mathrm{2}}=... \\ $$

Question Number 171244 Answers: 2 Comments: 3

(x/y)+(y/x)=((26)/5) ((x+y)/(x−y))=? (/)

$$\frac{{x}}{{y}}+\frac{{y}}{{x}}=\frac{\mathrm{26}}{\mathrm{5}} \\ $$$$\frac{{x}+{y}}{{x}−{y}}=? \\ $$$$\frac{}{} \\ $$

Question Number 171243 Answers: 1 Comments: 3

Question Number 171237 Answers: 0 Comments: 2

Question Number 171235 Answers: 1 Comments: 2

Question Number 171229 Answers: 0 Comments: 1

Question Number 171226 Answers: 0 Comments: 4

Possible number of order pairs satisfy 16^(x^2 +y) +16^(y^2 +x) =1 is

$${Possible}\:{number}\:{of}\:{order}\:{pairs} \\ $$$${satisfy}\:\mathrm{16}^{{x}^{\mathrm{2}} +{y}} +\mathrm{16}^{{y}^{\mathrm{2}} +{x}} =\mathrm{1}\:{is} \\ $$

Question Number 171223 Answers: 0 Comments: 0

In how many ways can you select 4 from 40 persons if every two persons may be selected together at most one time?

$${In}\:{how}\:{many}\:{ways}\:{can}\:{you}\:{select}\:\mathrm{4} \\ $$$${from}\:\mathrm{40}\:{persons}\:{if}\:{every}\:{two}\:{persons} \\ $$$${may}\:{be}\:{selected}\:{together}\:{at}\:{most}\:{one}\: \\ $$$${time}? \\ $$

Question Number 171221 Answers: 0 Comments: 0

Question Number 171216 Answers: 1 Comments: 1

Can you factor : x^2 −x−1=0

$${Can}\:{you}\:{factor}\:: \\ $$$${x}^{\mathrm{2}} −{x}−\mathrm{1}=\mathrm{0} \\ $$

Question Number 171204 Answers: 1 Comments: 0

if : bc^2 +ca^2 +ab^2 −a^2 b−b^2 c−c^2 a=0 prove that :a = b , b = c , c = a

$${if}\::\:{bc}^{\mathrm{2}} +{ca}^{\mathrm{2}} +{ab}^{\mathrm{2}} −{a}^{\mathrm{2}} {b}−{b}^{\mathrm{2}} {c}−{c}^{\mathrm{2}} {a}=\mathrm{0} \\ $$$${prove}\:{that}\::{a}\:=\:{b}\:,\:{b}\:=\:{c}\:,\:{c}\:=\:{a} \\ $$

Question Number 171213 Answers: 0 Comments: 0

In electricity, the electrostatic field is defined as: E = ∫_0 ^π [((a^2 σ sin θ)/(2ε(√(a^2 −x^2 −2ax cosθ))))]dθ where a,σ and ε are constants. Consider that x>a and show that E= ((a^2 σ)/(εx))

$$\mathrm{In}\:\mathrm{electricity},\:\mathrm{the}\:\mathrm{electrostatic}\:\mathrm{field} \\ $$$$\mathrm{is}\:\mathrm{defined}\:\mathrm{as}: \\ $$$${E}\:=\:\int_{\mathrm{0}} ^{\pi} \left[\frac{{a}^{\mathrm{2}} \sigma\:\mathrm{sin}\:\theta}{\mathrm{2}\epsilon\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} −\mathrm{2}{ax}\:\mathrm{cos}\theta}}\right]{d}\theta \\ $$$$\mathrm{where}\:{a},\sigma\:\mathrm{and}\:\epsilon\:\mathrm{are}\:\mathrm{constants}.\:\mathrm{Consider} \\ $$$$\mathrm{that}\:{x}>{a}\:\mathrm{and}\:\mathrm{show}\:\mathrm{that}\:{E}=\:\frac{{a}^{\mathrm{2}} \sigma}{\epsilon{x}} \\ $$

Question Number 171199 Answers: 2 Comments: 1

solve x^2 +y^2 −xy=9 y^2 +z^2 −yz=30 z^2 +x^2 −zx=50

$${solve} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −{xy}=\mathrm{9} \\ $$$${y}^{\mathrm{2}} +{z}^{\mathrm{2}} −{yz}=\mathrm{30} \\ $$$${z}^{\mathrm{2}} +{x}^{\mathrm{2}} −{zx}=\mathrm{50} \\ $$

Question Number 171198 Answers: 1 Comments: 0

evaluate ∫_0 ^( π) log (a+cos x)dx

$$ \\ $$$$\:\:{evaluate} \\ $$$$\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\pi} \mathrm{log}\:\left({a}+\mathrm{cos}\:{x}\right){dx} \\ $$

Question Number 171194 Answers: 0 Comments: 0

Question Number 171179 Answers: 1 Comments: 0

Question Number 171171 Answers: 1 Comments: 2

Question Number 171170 Answers: 0 Comments: 0

Question Number 171165 Answers: 1 Comments: 0

A triangle QRS is to be constructed from a line segment of lenght 15cm. Construct the triangle using the division of the line segment into the ratio 5:4:3 such that QS and RS are laegest and smallest ratio respectively. circumscribe the triangle by locating the circumcenter.

$${A}\:{triangle}\:{QRS}\:{is}\:{to}\:{be}\:{constructed}\:{from} \\ $$$${a}\:{line}\:{segment}\:{of}\:{lenght}\:\mathrm{15}{cm}.\: \\ $$$${Construct}\:{the}\:{triangle}\:{using}\:{the} \\ $$$${division}\:{of}\:{the}\:{line}\:{segment}\:{into}\:{the} \\ $$$${ratio}\:\mathrm{5}:\mathrm{4}:\mathrm{3}\:{such}\:{that}\:{QS}\:{and}\:{RS}\:{are} \\ $$$${laegest}\:{and}\:{smallest}\:{ratio}\:{respectively}. \\ $$$${circumscribe}\:{the}\:{triangle}\:{by}\:{locating} \\ $$$${the}\:{circumcenter}. \\ $$

Question Number 171164 Answers: 2 Comments: 0

show that the common chord of the circle x^2 +y^2 =4 and x^2 +y^2 −4x−2y−4=0 passes through the origin.

Question Number 171161 Answers: 1 Comments: 0

Question Number 171160 Answers: 1 Comments: 0

Question Number 171156 Answers: 0 Comments: 0

show that the equation 3x^2 +3y^2 −24x+12y+12=0 is a circle

$$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{equation}}\: \\ $$$$\:\mathrm{3}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{3}\boldsymbol{\mathrm{y}}^{\mathrm{2}} −\mathrm{24}\boldsymbol{\mathrm{x}}+\mathrm{12}\boldsymbol{\mathrm{y}}+\mathrm{12}=\mathrm{0} \\ $$$$\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{circle}} \\ $$

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