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Question Number 216010 Answers: 2 Comments: 0

Solve for x and y ax^2 + bxy + cy^2 = bx^2 + cxy + ay^2 = d.

$$\mathrm{Solve}\:\mathrm{for}\:{x}\:\mathrm{and}\:{y} \\ $$$${ax}^{\mathrm{2}} \:+\:{bxy}\:+\:{cy}^{\mathrm{2}} \:=\:{bx}^{\mathrm{2}} \:+\:{cxy}\:+\:{ay}^{\mathrm{2}} \:=\:{d}. \\ $$

Question Number 215999 Answers: 2 Comments: 0

if the fraction ((m^2 +25m)/(m+1)) is reductible. how many values does m take if is a 2 digit number? thanks

$${if}\:{the}\:{fraction}\:\frac{{m}^{\mathrm{2}} +\mathrm{25}{m}}{{m}+\mathrm{1}}\:\:{is}\:{reductible}.\:{how}\:{many}\:{values}\:{does}\:{m}\:\:{take}\:{if}\:{is}\:{a}\:\mathrm{2}\:{digit}\:\:{number}?\:{thanks} \\ $$

Question Number 215995 Answers: 1 Comments: 0

∫∫∫_D (√(x^2 +y^2 +z^2 )) dv = ? D = x^2 +y^2 +z^2 <z

$$\int\int\underset{{D}} {\int}\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} }\:\mathrm{dv}\:=\:? \\ $$$$\mathrm{D}\:=\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} <{z} \\ $$

Question Number 215994 Answers: 1 Comments: 0

Solve for z∈C: ∣z^z ∣=1

$$\mathrm{Solve}\:\mathrm{for}\:{z}\in\mathbb{C}:\:\:\:\:\:\mid{z}^{{z}} \mid=\mathrm{1} \\ $$

Question Number 215992 Answers: 1 Comments: 0

((√3) + (√2))^x + ((√3) − (√2))^x = 10. Solve for x.

$$\left(\sqrt{\mathrm{3}}\:+\:\sqrt{\mathrm{2}}\right)^{{x}} \:+\:\left(\sqrt{\mathrm{3}}\:−\:\sqrt{\mathrm{2}}\right)^{{x}} \:=\:\mathrm{10}.\:\mathrm{Solve} \\ $$$$\mathrm{for}\:{x}. \\ $$

Question Number 215991 Answers: 0 Comments: 1

Σ_(x=1) ^y x^n =0 n=?

$$\underset{{x}=\mathrm{1}} {\overset{{y}} {\sum}}{x}^{{n}} =\mathrm{0} \\ $$$${n}=? \\ $$

Question Number 215979 Answers: 0 Comments: 0

u_n = Σ_(k=n+1) ^(2n) (1/k) and v_n = Σ_(k=n) ^(2n−1) (1/k) • show that u_n and v_n are adjacent use ln(x+1) ≤ x and x≤−ln(1−x) and • show that u_n ≤ Σ_(k=n+1) ^(2n) (ln(k)−ln(k−1)) hence deduce that u_n ≤ ln2 • show that v_n ≥ Σ_(k=n) ^(2n−1) (ln(k+1)−ln(k)) hence deduce that v_n ≥ln2

$${u}_{{n}} \:=\:\underset{{k}={n}+\mathrm{1}} {\overset{\mathrm{2}{n}} {\sum}}\frac{\mathrm{1}}{{k}}\:{and}\:{v}_{{n}} \:=\:\underset{{k}={n}} {\overset{\mathrm{2}{n}−\mathrm{1}} {\sum}}\frac{\mathrm{1}}{{k}} \\ $$$$\bullet\:{show}\:{that}\:{u}_{{n}} \:{and}\:{v}_{{n}} \:{are}\:{adjacent} \\ $$$${use}\:{ln}\left({x}+\mathrm{1}\right)\:\leqslant\:{x}\:{and}\:{x}\leqslant−{ln}\left(\mathrm{1}−{x}\right)\:{and} \\ $$$$\bullet\:{show}\:{that}\:{u}_{{n}} \:\leqslant\:\underset{{k}={n}+\mathrm{1}} {\overset{\mathrm{2}{n}} {\sum}}\left({ln}\left({k}\right)−{ln}\left({k}−\mathrm{1}\right)\right) \\ $$$${hence}\:{deduce}\:{that}\:{u}_{{n}} \:\leqslant\:{ln}\mathrm{2} \\ $$$$\bullet\:{show}\:{that}\:{v}_{{n}} \:\geqslant\:\underset{{k}={n}} {\overset{\mathrm{2}{n}−\mathrm{1}} {\sum}}\left({ln}\left({k}+\mathrm{1}\right)−{ln}\left({k}\right)\right) \\ $$$${hence}\:{deduce}\:{that}\:{v}_{{n}} \geqslant{ln}\mathrm{2} \\ $$

Question Number 215975 Answers: 2 Comments: 0

Question Number 215974 Answers: 1 Comments: 0

∫(√((2sin^(−1) x−x(√(1−x^2 )))^2 +x^4 ))dx

$$\int\sqrt{\left(\mathrm{2sin}^{−\mathrm{1}} {x}−{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right)^{\mathrm{2}} +{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 215973 Answers: 2 Comments: 0

(a + b) ∝ c and (b + c) ∝ a. Prove that (c + a) ∝ b.

$$\left({a}\:+\:{b}\right)\:\propto\:{c}\:\mathrm{and}\:\left({b}\:+\:{c}\right)\:\propto\:{a}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\left({c}\:+\:{a}\right)\:\propto\:{b}. \\ $$

Question Number 215963 Answers: 1 Comments: 0

Question Number 215957 Answers: 0 Comments: 2

b^2 −4ac

$${b}^{\mathrm{2}} −\mathrm{4}{ac} \\ $$

Question Number 215958 Answers: 2 Comments: 0

Find the only function that satisfy the expression below: ((dy/dx))^2 = (d^2 y/dx^2 )

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{only}\:\mathrm{function}\:\mathrm{that}\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\mathrm{expression}\:\mathrm{below}: \\ $$$$\:\:\:\:\:\:\:\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{\mathrm{2}} \:\:=\:\:\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} } \\ $$

Question Number 215952 Answers: 0 Comments: 1

Question Number 215951 Answers: 1 Comments: 0

E_n = 3^E_(n−1) , n≥2 find the unit digit of E_(1000)

$${E}_{{n}} \:=\:\mathrm{3}^{{E}_{{n}−\mathrm{1}} } ,\:{n}\geqslant\mathrm{2} \\ $$$${find}\:{the}\:{unit}\:{digit}\:{of}\:{E}_{\mathrm{1000}} \\ $$

Question Number 215944 Answers: 2 Comments: 0

if m,n,z ∈N so , m<n and z<m then z<n ?

$${if}\:{m},{n},{z}\:\in{N}\:{so}\:,\:{m}<{n}\:{and}\:{z}<{m}\:{then}\:{z}<{n}\:?\: \\ $$

Question Number 215943 Answers: 1 Comments: 0

Question Number 215939 Answers: 1 Comments: 0

for any natural numbers m,n then m=n or m<n or m>n ? prove

$${for}\:{any}\:{natural}\:{numbers}\:{m},{n}\:{then}\:{m}={n}\:{or}\:{m}<{n}\:{or}\:{m}>{n}\:?\:{prove} \\ $$

Question Number 215919 Answers: 0 Comments: 1

Is absolute value of x linear equation ?

$$\:\:\:{Is}\:{absolute}\:{value}\:{of}\:{x}\:{linear}\:{equation}\:?\: \\ $$$$ \\ $$

Question Number 215918 Answers: 3 Comments: 0

why ((d )/dz)e^z =e^z ?? why dose not (de^z /dz)=(de^z /dz)=(e^z /z) ???

$$\mathrm{why}\:\:\frac{\mathrm{d}\:\:}{\mathrm{d}{z}}{e}^{{z}} ={e}^{{z}} \:?? \\ $$$$\mathrm{why}\:\mathrm{dose}\:\mathrm{not}\:\frac{\mathrm{d}{e}^{{z}} }{\mathrm{d}{z}}=\frac{\cancel{\mathrm{d}}{e}^{{z}} }{\cancel{\mathrm{d}}{z}}=\frac{{e}^{{z}} }{{z}}\:??? \\ $$

Question Number 215908 Answers: 1 Comments: 0

K.1 y=(3/2)x+1 determinant ((x,y),((−2),),((−1),),(0,),(1,),(2,))and then plot

$$\mathrm{K}.\mathrm{1} \\ $$$${y}=\frac{\mathrm{3}}{\mathrm{2}}{x}+\mathrm{1} \\ $$$$\begin{array}{|c|c|c|c|c|c|}{{x}}&\hline{{y}}\\{−\mathrm{2}}&\hline{}\\{−\mathrm{1}}&\hline{}\\{\mathrm{0}}&\hline{}\\{\mathrm{1}}&\hline{}\\{\mathrm{2}}&\hline{}\\\hline\end{array}\mathrm{and}\:\mathrm{then}\:\mathrm{plot} \\ $$

Question Number 215898 Answers: 1 Comments: 1

x^n +y^n +z^n = 0 n = ?

$${x}^{{n}} +{y}^{{n}} +{z}^{{n}} \:=\:\mathrm{0} \\ $$$${n}\:=\:? \\ $$

Question Number 215893 Answers: 4 Comments: 0

Find: 1) lim_(x→0) ((1 − cos2x)/x^2 ) = ? 2) Σ_(n=1) ^(n=∞) (n^2 /3^n ) = ?

$$\mathrm{Find}: \\ $$$$\left.\mathrm{1}\right)\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}\:−\:\mathrm{cos2x}}{\mathrm{x}^{\mathrm{2}} }\:=\:? \\ $$$$\left.\mathrm{2}\right)\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}=\infty} {\sum}}\:\frac{\mathrm{n}^{\mathrm{2}} }{\mathrm{3}^{\boldsymbol{\mathrm{n}}} }\:=\:? \\ $$

Question Number 215889 Answers: 1 Comments: 5

Find: lim_(h→0) (((x + h)^3 + x^3 )/h) = ?

$$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{h}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{x}\:+\:\mathrm{h}\right)^{\mathrm{3}} \:+\:\mathrm{x}^{\mathrm{3}} }{\mathrm{h}}\:=\:? \\ $$

Question Number 215887 Answers: 0 Comments: 2

Question Number 215885 Answers: 1 Comments: 1

Area of ABC ?

$$\:\mathrm{Area}\:\:\mathrm{of}\:\mathrm{ABC}\:? \\ $$

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