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Question Number 153401 Answers: 2 Comments: 1

Question Number 153399 Answers: 0 Comments: 2

Question Number 153398 Answers: 0 Comments: 0

find the slop of the tangent to the curve y=7cosx at x=(π/4)

$${find}\:{the}\:{slop}\:{of}\:{the}\:{tangent}\:{to}\:{the}\:{curve} \\ $$$${y}=\mathrm{7}{cosx}\:\:{at}\:\:{x}=\frac{\pi}{\mathrm{4}} \\ $$

Question Number 153395 Answers: 1 Comments: 0

given that f(x)=4x^3 −48x. find the stationary point of f(x)

$${given}\:{that}\:\:{f}\left({x}\right)=\mathrm{4}{x}^{\mathrm{3}} −\mathrm{48}{x}.\:{find}\: \\ $$$${the}\:{stationary}\:{point}\:{of}\:{f}\left({x}\right) \\ $$

Question Number 153464 Answers: 3 Comments: 1

Question Number 153384 Answers: 2 Comments: 0

Question Number 153381 Answers: 0 Comments: 2

let x;y;z≥0 and x^2 +y^2 +z^2 =12 find the min value of S = x + y + z + xyz + (1/(xy + yz + zx))

$$\mathrm{let}\:\:\mathrm{x};\mathrm{y};\mathrm{z}\geqslant\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{12} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{min}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{S}\:=\:\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:+\:\mathrm{xyz}\:+\:\frac{\mathrm{1}}{\mathrm{xy}\:+\:\mathrm{yz}\:+\:\mathrm{zx}} \\ $$

Question Number 153374 Answers: 0 Comments: 4

Question Number 153352 Answers: 4 Comments: 0

lim_(x→∞) ((27^x +9^x ))^(1/3) −(√(9^x +3^x )) =?

$$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\sqrt[{\mathrm{3}}]{\mathrm{27}^{{x}} +\mathrm{9}^{{x}} }\:−\sqrt{\mathrm{9}^{{x}} +\mathrm{3}^{{x}} }\:=? \\ $$

Question Number 153346 Answers: 2 Comments: 0

Question Number 153345 Answers: 1 Comments: 0

Question Number 153342 Answers: 2 Comments: 1

Question Number 153340 Answers: 1 Comments: 0

Solve .. x , y , z ∈ R^( +) & x+ y= z K := Min_ ((( x^( 4) + y^( 4) + z^( 4) )/(x^( 2) y^( 2) )) ) = ? ■ Source : Elementary Olympid Book m.n

$$ \\ $$$$\:\:\:\:\:\mathrm{Solve}\:.. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}\:,\:\mathrm{y}\:,\:\mathrm{z}\:\in\:\mathbb{R}^{\:+} \:\&\:\:\mathrm{x}+\:\mathrm{y}=\:\mathrm{z} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{K}\::=\:\mathrm{Min}_{\:} \:\left(\frac{\:\mathrm{x}^{\:\mathrm{4}} \:+\:\mathrm{y}^{\:\mathrm{4}} +\:\mathrm{z}^{\:\mathrm{4}} }{\mathrm{x}^{\:\mathrm{2}} \mathrm{y}^{\:\mathrm{2}} }\:\right)\:=\:?\:\:\:\:\:\:\:\:\:\:\blacksquare\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\mathrm{Source}\::\:\:\mathrm{Elementary}\:\mathrm{Olympid}\:\mathrm{Book}\:\:{m}.{n} \\ $$$$ \\ $$

Question Number 153339 Answers: 2 Comments: 0

((x−1)/x)+((x−2)/x)+((x−3)/x)+…+(1/x)=3 x=? ∵∴∵∴∵ Easy question∴∵∴∵∴∵

$$\:\:\frac{{x}−\mathrm{1}}{{x}}+\frac{{x}−\mathrm{2}}{{x}}+\frac{{x}−\mathrm{3}}{{x}}+\ldots+\frac{\mathrm{1}}{{x}}=\mathrm{3}\:\:\:\:{x}=? \\ $$$$\because\therefore\because\therefore\because\:\:{Easy}\:{question}\therefore\because\therefore\because\therefore\because \\ $$

Question Number 153335 Answers: 0 Comments: 0

Question Number 153312 Answers: 0 Comments: 3

Question Number 153263 Answers: 0 Comments: 0

Question Number 153257 Answers: 2 Comments: 0

Find set of k value so that ∣x∣ + ∣x−1∣ + ∣x−4∣ = k a. has one solution b. has two solutions c. has many solutions d. has no solution

$${Find}\:\:{set}\:\:{of}\:\:{k}\:\:{value}\:\:{so}\:\:{that} \\ $$$$\:\:\:\:\:\:\:\mid{x}\mid\:+\:\mid{x}−\mathrm{1}\mid\:+\:\mid{x}−\mathrm{4}\mid\:=\:{k} \\ $$$${a}.\:{has}\:\:{one}\:\:{solution} \\ $$$${b}.\:{has}\:\:{two}\:\:{solutions} \\ $$$${c}.\:{has}\:\:{many}\:\:{solutions} \\ $$$${d}.\:{has}\:\:{no}\:\:{solution} \\ $$

Question Number 153256 Answers: 0 Comments: 1

Question Number 153252 Answers: 1 Comments: 0

Question Number 153249 Answers: 1 Comments: 0

Question Number 153245 Answers: 2 Comments: 0

{ ((x^3 −3x^2 y=30)),((y^3 −3xy^2 =10)) :} (x,y)=?

$$\:\:\begin{cases}{{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} {y}=\mathrm{30}}\\{{y}^{\mathrm{3}} −\mathrm{3}{xy}^{\mathrm{2}} =\mathrm{10}}\end{cases} \\ $$$$\:\left({x},{y}\right)=? \\ $$

Question Number 153239 Answers: 1 Comments: 0

Question Number 153227 Answers: 2 Comments: 0

let D= [((v 5)),(((1/3) m)) ] find number (v) and (m) such that D^2 =5I (I=identity matrix)

$${let}\:{D}=\begin{bmatrix}{{v}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{5}}\\{\frac{\mathrm{1}}{\mathrm{3}}\:\:\:\:\:\:\:\:\:\:\:\:\:{m}}\end{bmatrix}\:{find}\:{number}\:\left({v}\right)\:{and} \\ $$$$\left({m}\right)\:{such}\:{that}\:{D}^{\mathrm{2}} =\mathrm{5}{I}\:\:\:\:\:\left({I}={identity}\:{matrix}\right) \\ $$

Question Number 153226 Answers: 1 Comments: 4

Question Number 153220 Answers: 1 Comments: 0

in how many ways can the number n be written as a sum of three positive integers if representations differing in the order of the terms are considered to be different?

$$\: \\ $$$$\:\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{the}\:\mathrm{number}\:\: \\ $$$$\:{n}\:\mathrm{be}\:\mathrm{written}\:\mathrm{as}\:\mathrm{a}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{three}\:\mathrm{positive}\:\: \\ $$$$\:\mathrm{integers}\:\mathrm{if}\:\mathrm{representations}\:\mathrm{differing}\:\: \\ $$$$\:\mathrm{in}\:\mathrm{the}\:\mathrm{order}\:\mathrm{of}\:\mathrm{the}\:\mathrm{terms}\:\mathrm{are}\:\mathrm{considered}\:\: \\ $$$$\:\mathrm{to}\:\mathrm{be}\:\mathrm{different}?\:\: \\ $$$$\: \\ $$

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