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(2/((x − 1)^(2 ) )) + (4/((y + 2)^2 )) + (5/z^2 ) = (9/4) (4/((x − 1)^2 )) − (2/((x + 2)^2 )) − (1/z^2 ) = (1/2) (3/((z − 1)^2 )) + (6/((y + 2)^2 )) − (2/z^2 ) = 1 (z − 1)^2 + (y + 2)^2 + z^2 = ???

$$\frac{\mathrm{2}}{\left({x}\:−\:\mathrm{1}\right)^{\mathrm{2}\:} }\:+\:\frac{\mathrm{4}}{\left({y}\:+\:\mathrm{2}\right)^{\mathrm{2}} }\:+\:\frac{\mathrm{5}}{{z}^{\mathrm{2}} }\:=\:\frac{\mathrm{9}}{\mathrm{4}} \\ $$$$\frac{\mathrm{4}}{\left({x}\:−\:\mathrm{1}\right)^{\mathrm{2}} }\:−\:\frac{\mathrm{2}}{\left({x}\:+\:\mathrm{2}\right)^{\mathrm{2}} }\:−\:\frac{\mathrm{1}}{{z}^{\mathrm{2}} }\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\frac{\mathrm{3}}{\left({z}\:−\:\mathrm{1}\right)^{\mathrm{2}} }\:+\:\frac{\mathrm{6}}{\left({y}\:+\:\mathrm{2}\right)^{\mathrm{2}} }\:−\:\frac{\mathrm{2}}{{z}^{\mathrm{2}} }\:=\:\mathrm{1} \\ $$$$ \\ $$$$\left({z}\:−\:\mathrm{1}\right)^{\mathrm{2}} \:+\:\left({y}\:+\:\mathrm{2}\right)^{\mathrm{2}} \:\:+\:{z}^{\mathrm{2}} \:=\:??? \\ $$

Question Number 11072 Answers: 0 Comments: 0

Question Number 11071 Answers: 0 Comments: 0

Question Number 11070 Answers: 1 Comments: 0

m∈Z , x^2 −(m+1)x+m^2 −16=0 f(x_1 )=f(x_2 )=0 ,x_1 <0, 0<x_2 ⇒Σm=?

$${m}\in{Z}\:,\:{x}^{\mathrm{2}} −\left({m}+\mathrm{1}\right){x}+{m}^{\mathrm{2}} −\mathrm{16}=\mathrm{0} \\ $$$${f}\left({x}_{\mathrm{1}} \right)={f}\left({x}_{\mathrm{2}} \right)=\mathrm{0}\:\:,{x}_{\mathrm{1}} <\mathrm{0},\:\mathrm{0}<{x}_{\mathrm{2}} \:\Rightarrow\Sigma{m}=? \\ $$

Question Number 11069 Answers: 0 Comments: 1

Question Number 11067 Answers: 0 Comments: 4

if E={f∣f:R→R continuous function with f(x)∈Q, ∀x∈R}, then E=....???

$${if}\:{E}=\left\{{f}\mid{f}:\mathbb{R}\rightarrow\mathbb{R}\:{continuous}\:{function}\:{with}\:{f}\left({x}\right)\in\mathbb{Q},\:\forall{x}\in\mathbb{R}\right\}, \\ $$$${then}\:{E}=....??? \\ $$

Question Number 11061 Answers: 0 Comments: 2

A 3 dimentional parabola f(x, y, z) has a focus P(x, y, z)=(p, q, r). A rectangular box with side lengths a, b, and c (see diagram), has a point P on the front center point of its face. If the origin lies on the opposite face, in the middle, what is the function of the curve? Note Origin O(x, y, z)=(0, 0, 0) O(x, y, z) = (p−c, q, r)

$$\mathrm{A}\:\mathrm{3}\:\mathrm{dimentional}\:\mathrm{parabola}\:{f}\left({x},\:{y},\:{z}\right) \\ $$$$\mathrm{has}\:\mathrm{a}\:\mathrm{focus}\:{P}\left({x},\:{y},\:{z}\right)=\left({p},\:{q},\:{r}\right). \\ $$$$\: \\ $$$$\mathrm{A}\:\mathrm{rectangular}\:\mathrm{box}\:\mathrm{with}\:\mathrm{side}\:\mathrm{lengths} \\ $$$${a},\:{b},\:\mathrm{and}\:{c}\:\left(\mathrm{see}\:\mathrm{diagram}\right),\:\mathrm{has}\:\mathrm{a}\:\mathrm{point}\:{P} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{front}\:\mathrm{center}\:\mathrm{point}\:\mathrm{of}\:\mathrm{its}\:\mathrm{face}. \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{origin}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{opposite}\:\mathrm{face}, \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{middle},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{function}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{curve}? \\ $$$$\: \\ $$$$\boldsymbol{\mathrm{Note}} \\ $$$$\mathrm{Origin}\:{O}\left({x},\:{y},\:{z}\right)=\left(\mathrm{0},\:\mathrm{0},\:\mathrm{0}\right) \\ $$$${O}\left({x},\:{y},\:{z}\right)\:=\:\left({p}−{c},\:{q},\:{r}\right) \\ $$

Question Number 11050 Answers: 1 Comments: 0

The function f(x)=acosx+b where a<0 has a maximum value of 8 and a minimum value of −2.Find a+b.

$${The}\:{function}\:{f}\left({x}\right)={acosx}+{b}\:{where} \\ $$$${a}<\mathrm{0}\:{has}\:{a}\:{maximum}\:{value}\:{of}\:\mathrm{8}\:{and} \\ $$$${a}\:{minimum}\:{value}\:{of}\:−\mathrm{2}.\boldsymbol{{F}}{ind}\:{a}+{b}. \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 11049 Answers: 1 Comments: 1

If n^2 + 3n + 1 is divisible by 3n + 10 Find out all possible solution for n

$$\mathrm{If}\:\:{n}^{\mathrm{2}} \:+\:\mathrm{3}{n}\:+\:\mathrm{1}\:\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3}{n}\:+\:\mathrm{10} \\ $$$$\mathrm{Find}\:\mathrm{out}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solution}\:\mathrm{for}\:{n}\: \\ $$

Question Number 11048 Answers: 4 Comments: 0

Which one is largest? (without using calculator) 31^(11) or 17^(14) ??

$$\mathrm{Which}\:\mathrm{one}\:\mathrm{is}\:\mathrm{largest}?\:\left(\mathrm{without}\:\mathrm{using}\:\mathrm{calculator}\right) \\ $$$$\mathrm{31}^{\mathrm{11}} \:\mathrm{or}\:\mathrm{17}^{\mathrm{14}} \:\:?? \\ $$

Question Number 11042 Answers: 1 Comments: 0

∫cos(x)(√(((sin(x)+1)/(sin(x)−1)) )) dx