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Question Number 9453 Answers: 1 Comments: 0

find dc′s dr′s of a mormal to the plane 2x+(5/2)y+(7/8)z=23

$$\mathrm{find}\:\mathrm{dc}'\mathrm{s}\:\mathrm{dr}'\mathrm{s}\:\mathrm{of}\:\mathrm{a}\:\mathrm{mormal}\:\mathrm{to}\:\mathrm{the}\: \\ $$$$\mathrm{plane}\:\mathrm{2x}+\frac{\mathrm{5}}{\mathrm{2}}\mathrm{y}+\frac{\mathrm{7}}{\mathrm{8}}\mathrm{z}=\mathrm{23} \\ $$

Question Number 9449 Answers: 1 Comments: 0

2xy = x + y ...... (i) 6xz = 6z − 2x ..... (ii) 3yz = 3y + 4z ....... (iii) Solve for x, y and z

$$\mathrm{2xy}\:=\:\mathrm{x}\:+\:\mathrm{y}\:\:\:\:\:......\:\left(\mathrm{i}\right) \\ $$$$\mathrm{6xz}\:=\:\mathrm{6z}\:−\:\mathrm{2x}\:\:\:\:.....\:\left(\mathrm{ii}\right) \\ $$$$\mathrm{3yz}\:=\:\mathrm{3y}\:+\:\mathrm{4z}\:\:\:.......\:\left(\mathrm{iii}\right) \\ $$$$ \\ $$$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x},\:\mathrm{y}\:\mathrm{and}\:\mathrm{z} \\ $$

Question Number 9439 Answers: 3 Comments: 1

Solve for x , y and z (x + 1)(y + 3) = 8 ....... (i) (y + 3)(z − 1) = 3 ......... (ii) (z − 1)(x + 1) = 2 ......... (iii)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:,\:\mathrm{y}\:\mathrm{and}\:\mathrm{z} \\ $$$$\left(\mathrm{x}\:+\:\mathrm{1}\right)\left(\mathrm{y}\:+\:\mathrm{3}\right)\:=\:\mathrm{8}\:\:\:.......\:\left(\mathrm{i}\right) \\ $$$$\left(\mathrm{y}\:+\:\mathrm{3}\right)\left(\mathrm{z}\:−\:\mathrm{1}\right)\:=\:\mathrm{3}\:\:.........\:\left(\mathrm{ii}\right) \\ $$$$\left(\mathrm{z}\:−\:\mathrm{1}\right)\left(\mathrm{x}\:+\:\mathrm{1}\right)\:=\:\mathrm{2}\:\:\:.........\:\left(\mathrm{iii}\right) \\ $$

Question Number 9438 Answers: 1 Comments: 0

Solve for x, y and z 2xy = x + y ...... (i) 6xz = 6z − 2x ....... (ii) 3yz = 3y + 4z ......... (iii) That is the correct question sir.

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x},\:\mathrm{y}\:\mathrm{and}\:\mathrm{z} \\ $$$$\mathrm{2xy}\:=\:\mathrm{x}\:+\:\mathrm{y}\:\:\:\:\:\:......\:\left(\mathrm{i}\right) \\ $$$$\mathrm{6xz}\:=\:\mathrm{6z}\:−\:\mathrm{2x}\:\:\:\:.......\:\left(\mathrm{ii}\right) \\ $$$$\mathrm{3yz}\:=\:\mathrm{3y}\:+\:\mathrm{4z}\:\:\:\:.........\:\left(\mathrm{iii}\right) \\ $$$$ \\ $$$$\mathrm{That}\:\mathrm{is}\:\mathrm{the}\:\mathrm{correct}\:\mathrm{question}\:\mathrm{sir}. \\ $$

Question Number 9436 Answers: 2 Comments: 0

If they said that Σ_(k=1) ^∞ k diverges, why 1 + 2 + 3 + 4 + ... = − (1/(12)) ?

$$\mathrm{If}\:\mathrm{they}\:\mathrm{said}\:\mathrm{that}\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:{k}\:\mathrm{diverges},\:\mathrm{why} \\ $$$$\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}\:+\:\mathrm{4}\:+\:...\:=\:−\:\frac{\mathrm{1}}{\mathrm{12}}\:? \\ $$

Question Number 9460 Answers: 1 Comments: 0

Question Number 9461 Answers: 1 Comments: 0

(dy/dx) = ((1 + y)/(2 + x)) solve the differential equation.

$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{1}\:+\:\mathrm{y}}{\mathrm{2}\:+\:\mathrm{x}} \\ $$$$\mathrm{solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}. \\ $$

Question Number 9424 Answers: 1 Comments: 0

Solve for x, y : x, y ∈ R x^3 − 3xy^2 = − 46 ........ (i) 3x^2 y − y^3 = 9 ..........(ii)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x},\:\mathrm{y}\::\:\:\mathrm{x},\:\mathrm{y}\:\in\:\mathrm{R} \\ $$$$\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{3xy}^{\mathrm{2}} \:=\:−\:\mathrm{46}\:\:\:........\:\left(\mathrm{i}\right) \\ $$$$\mathrm{3x}^{\mathrm{2}} \mathrm{y}\:−\:\mathrm{y}^{\mathrm{3}} \:=\:\mathrm{9}\:\:\:..........\left(\mathrm{ii}\right) \\ $$

Question Number 9423 Answers: 1 Comments: 3

if x and y are two sets such that n(x) =17 , n(y)=23 and n(X∪Y) =38, find n(X∪Y).

$${if}\:{x}\:{and}\:{y}\:{are}\:{two}\:{sets}\:{such}\:{that}\:{n}\left({x}\right) \\ $$$$=\mathrm{17}\:,\:{n}\left({y}\right)=\mathrm{23}\:{and}\:{n}\left({X}\cup{Y}\right)\:=\mathrm{38}, \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{n}}\left({X}\cup{Y}\right). \\ $$

Question Number 9422 Answers: 0 Comments: 0

The value of ^(95) C_4 +Σ_(j=1) ^5 ^(100−j) C_3 is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\:^{\mathrm{95}} {C}_{\mathrm{4}} +\underset{{j}=\mathrm{1}} {\overset{\mathrm{5}} {\sum}}\:^{\mathrm{100}−{j}} {C}_{\mathrm{3}} \:\:\mathrm{is} \\ $$

Question Number 9421 Answers: 1 Comments: 0

If the sum of the coefficients in the expansion of (a+b)^n is 4096, then the greatest coefficient in the expansion is

$$\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{coefficients}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left({a}+{b}\right)^{{n}} \:\mathrm{is}\:\mathrm{4096},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{is} \\ $$

Question Number 9414 Answers: 1 Comments: 0

tanA+cot=A= 2cosec2A

$${tanA}+{cot}={A}=\:\mathrm{2}{cosec}\mathrm{2}{A} \\ $$

Question Number 9420 Answers: 0 Comments: 0

x and y are two binary numbers which are in 4 − bit 2′s complement formate, where x = 00102 and y = 11012 : clearly, y is a negative number. what is the result of x + y in decimal formate.

$$\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{are}\:\mathrm{two}\:\mathrm{binary}\:\mathrm{numbers}\:\mathrm{which}\:\mathrm{are}\: \\ $$$$\mathrm{in}\:\mathrm{4}\:−\:\mathrm{bit}\:\mathrm{2}'\mathrm{s}\:\mathrm{complement}\:\mathrm{formate},\: \\ $$$$\mathrm{where}\:\mathrm{x}\:=\:\mathrm{00102}\:\mathrm{and}\:\mathrm{y}\:=\:\mathrm{11012}\::\:\mathrm{clearly}, \\ $$$$\mathrm{y}\:\mathrm{is}\:\mathrm{a}\:\mathrm{negative}\:\mathrm{number}.\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{result} \\ $$$$\mathrm{of}\:\mathrm{x}\:+\:\mathrm{y}\:\mathrm{in}\:\mathrm{decimal}\:\mathrm{formate}. \\ $$

Question Number 9404 Answers: 1 Comments: 0

Question Number 9403 Answers: 2 Comments: 0

Question Number 9400 Answers: 1 Comments: 0

expand : y = e^x , about the point x = 1 using taylor′s series.

$$\mathrm{expand}\::\:\:\mathrm{y}\:=\:\mathrm{e}^{\mathrm{x}} \:,\:\mathrm{about}\:\mathrm{the}\:\mathrm{point}\:\mathrm{x}\:=\:\mathrm{1} \\ $$$$\mathrm{using}\:\mathrm{taylor}'\mathrm{s}\:\mathrm{series}. \\ $$

Question Number 9399 Answers: 0 Comments: 0

Find the root of bx^3 − (3b − 2)x^2 − 2(5b − 3)x + 20 = 0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{root}\:\mathrm{of} \\ $$$$\mathrm{bx}^{\mathrm{3}} \:−\:\left(\mathrm{3b}\:−\:\mathrm{2}\right)\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{2}\left(\mathrm{5b}\:−\:\mathrm{3}\right)\mathrm{x}\:+\:\mathrm{20}\:=\:\mathrm{0} \\ $$

Question Number 9419 Answers: 0 Comments: 0

Develop an algorithm and draw a flowchat to find the sum of numbers from 1 − 100

$$\mathrm{Develop}\:\mathrm{an}\:\mathrm{algorithm}\:\mathrm{and}\:\mathrm{draw}\:\mathrm{a}\:\mathrm{flowchat} \\ $$$$\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{numbers}\:\mathrm{from}\:\mathrm{1}\:−\:\mathrm{100} \\ $$

Question Number 9396 Answers: 1 Comments: 1

(d^2 y/dx^2 )+4y=tan 2x

$$\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }+\mathrm{4y}=\mathrm{tan}\:\mathrm{2x} \\ $$

Question Number 9407 Answers: 0 Comments: 0

π = 180° = Π π = 3,141... = π Solve (find n ∈ N): Σ_(k=1) ^∞ ((sin(2Πk∙10^n π))/k) + Σ_(k=1) ^∞ ((sin(2Πk∙10^n e))/k) = 0

$$\pi\:=\:\mathrm{180}°\:=\:\Pi \\ $$$$\pi\:=\:\mathrm{3},\mathrm{141}...\:=\:\pi \\ $$$$\mathrm{Solve}\:\left(\mathrm{find}\:{n}\:\in\:\mathbb{N}\right): \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{2}\Pi{k}\centerdot\mathrm{10}^{{n}} \pi\right)}{{k}}\:+\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{2}\Pi{k}\centerdot\mathrm{10}^{{n}} {e}\right)}{{k}}\:=\:\mathrm{0} \\ $$$$ \\ $$

Question Number 9392 Answers: 1 Comments: 0

x^x = 16 find the value of x. please show workings.

$$\mathrm{x}^{\mathrm{x}} \:=\:\mathrm{16} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}. \\ $$$$\mathrm{please}\:\mathrm{show}\:\mathrm{workings}. \\ $$

Question Number 9391 Answers: 0 Comments: 0

Σ_(n=2) ^(100) (1 − (1/n^(2 ) ))

$$\underset{{n}=\mathrm{2}} {\overset{\mathrm{100}} {\sum}}\:\left(\mathrm{1}\:−\:\frac{\mathrm{1}}{{n}^{\mathrm{2}\:} }\right) \\ $$

Question Number 9382 Answers: 1 Comments: 1

Question Number 9381 Answers: 0 Comments: 0

∫_0 ^(π/2) ln (((4 + 3sinx)/(4 + 3cosx))) dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\mathrm{ln}\:\left(\frac{\mathrm{4}\:+\:\mathrm{3sinx}}{\mathrm{4}\:+\:\mathrm{3cosx}}\right)\:\mathrm{dx} \\ $$

Question Number 9380 Answers: 0 Comments: 0

S=Σ_(n=1) ^∞ n^(−n) S=??

$${S}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{n}^{−{n}} \\ $$$${S}=?? \\ $$

Question Number 9379 Answers: 0 Comments: 0

S=Σ_(n=1) ^∞ (−n)^(1−n) S=??

$${S}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−{n}\right)^{\mathrm{1}−{n}} \\ $$$${S}=?? \\ $$

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