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Question Number 99433 Answers: 2 Comments: 1

sin7φ+cos2φ=−2 Find,φ

$${sin}\mathrm{7}\phi+{cos}\mathrm{2}\phi=−\mathrm{2} \\ $$$${Find},\phi \\ $$

Question Number 99430 Answers: 1 Comments: 0

Question Number 99429 Answers: 0 Comments: 0

Solve for n in the equation A_n ^(n−2) =56 {where A_n ^r =n−permution r}

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{n}\:\mathrm{in}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{A}_{\mathrm{n}} ^{\mathrm{n}−\mathrm{2}} =\mathrm{56}\:\left\{\mathrm{where}\:\mathrm{A}_{\mathrm{n}} ^{\mathrm{r}} =\mathrm{n}−\mathrm{permution}\:\mathrm{r}\right\} \\ $$

Question Number 99421 Answers: 0 Comments: 0

Question Number 99413 Answers: 1 Comments: 0

∫_0 ^(+∞) ((sin(ax))/(e^(2πx) −1))dx

$$\int_{\mathrm{0}} ^{+\infty} \frac{{sin}\left({ax}\right)}{{e}^{\mathrm{2}\pi{x}} −\mathrm{1}}{dx} \\ $$

Question Number 99411 Answers: 0 Comments: 2

Solve the equation xa^(1/x) +(1/x)a^x =2a where,a{−1,0,1}

$${Solve}\:{the}\:{equation} \\ $$$${xa}^{\frac{\mathrm{1}}{{x}}} +\frac{\mathrm{1}}{{x}}{a}^{{x}} =\mathrm{2}{a} \\ $$$${where},{a}\left\{−\mathrm{1},\mathrm{0},\mathrm{1}\right\} \\ $$

Question Number 99410 Answers: 1 Comments: 2

Question Number 99403 Answers: 1 Comments: 1

∫ x^x dx

$$\int\:\mathrm{x}^{\mathrm{x}} \:\:\mathrm{dx} \\ $$

Question Number 99392 Answers: 1 Comments: 1

Question Number 99385 Answers: 2 Comments: 0

Prove sin^4 A=(3/8)−(1/2)cos2A+(1/8)cos4A

$$\mathrm{Prove}\:\mathrm{sin}^{\mathrm{4}} \mathrm{A}=\frac{\mathrm{3}}{\mathrm{8}}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos2A}+\frac{\mathrm{1}}{\mathrm{8}}\mathrm{cos4A} \\ $$

Question Number 99625 Answers: 1 Comments: 0

If f(x)=cos^2 x + sec^2 x, its value always is

$$\mathrm{If}\:\:{f}\left({x}\right)=\mathrm{cos}^{\mathrm{2}} {x}\:+\:\mathrm{sec}^{\mathrm{2}} {x},\:\mathrm{its}\:\mathrm{value} \\ $$$$\mathrm{always}\:\mathrm{is} \\ $$

Question Number 99366 Answers: 2 Comments: 0

Two buses start from a point such that one bus travelling at 80 km/h reaches its destination 2 hours before the other bus which travels at 60 km/h. However the distance travelled by the bus travelling at 60 km/h is 40 km more than that of the other bus. Find the distance travelled by the bus which is travelling at 80 km/h.

$$\mathrm{Two}\:\mathrm{buses}\:\mathrm{start}\:\mathrm{from}\:\mathrm{a}\:\mathrm{point}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{one}\:\mathrm{bus}\:\mathrm{travelling}\:\mathrm{at}\:\mathrm{80}\:\mathrm{km}/\mathrm{h}\:\mathrm{reaches} \\ $$$$\mathrm{its}\:\mathrm{destination}\:\mathrm{2}\:\mathrm{hours}\:\mathrm{before}\:\mathrm{the}\:\mathrm{other} \\ $$$$\mathrm{bus}\:\mathrm{which}\:\mathrm{travels}\:\mathrm{at}\:\mathrm{60}\:\mathrm{km}/\mathrm{h}.\:\mathrm{However} \\ $$$$\mathrm{the}\:\mathrm{distance}\:\mathrm{travelled}\:\mathrm{by}\:\mathrm{the}\:\mathrm{bus} \\ $$$$\mathrm{travelling}\:\mathrm{at}\:\mathrm{60}\:\mathrm{km}/\mathrm{h}\:\mathrm{is}\:\mathrm{40}\:\mathrm{km}\:\mathrm{more}\:\mathrm{than} \\ $$$$\mathrm{that}\:\mathrm{of}\:\mathrm{the}\:\mathrm{other}\:\mathrm{bus}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{distance} \\ $$$$\mathrm{travelled}\:\mathrm{by}\:\mathrm{the}\:\mathrm{bus}\:\mathrm{which}\:\mathrm{is}\:\mathrm{travelling} \\ $$$$\mathrm{at}\:\mathrm{80}\:\mathrm{km}/\mathrm{h}. \\ $$

Question Number 99368 Answers: 0 Comments: 1

please sir my problem in my solution is where?

$${please}\:{sir}\:{my}\:{problem}\:{in}\:{my}\:{solution} \\ $$$${is}\:{where}? \\ $$

Question Number 99358 Answers: 1 Comments: 1

15 men can complete a work in 10 days, working 8 hrs. per day. How many persons are required to complete double the work in 25 days, working 6 hrs. per day?

$$\mathrm{15}\:\mathrm{men}\:\mathrm{can}\:\mathrm{complete}\:\mathrm{a}\:\mathrm{work}\:\mathrm{in}\:\mathrm{10}\:\mathrm{days}, \\ $$$$\mathrm{working}\:\mathrm{8}\:\mathrm{hrs}.\:\mathrm{per}\:\mathrm{day}.\:\mathrm{How}\:\mathrm{many} \\ $$$$\mathrm{persons}\:\mathrm{are}\:\mathrm{required}\:\mathrm{to}\:\mathrm{complete} \\ $$$$\mathrm{double}\:\mathrm{the}\:\mathrm{work}\:\mathrm{in}\:\mathrm{25}\:\mathrm{days},\:\mathrm{working} \\ $$$$\mathrm{6}\:\mathrm{hrs}.\:\mathrm{per}\:\mathrm{day}? \\ $$

Question Number 99357 Answers: 1 Comments: 1

x^2 +xy +y^2 −3y = 10 , find the value of (dy/dx) at x= 2

$$\mathrm{x}^{\mathrm{2}} +\mathrm{xy}\:+\mathrm{y}^{\mathrm{2}} −\mathrm{3y}\:=\:\mathrm{10}\:,\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}\:\mathrm{at}\:\mathrm{x}=\:\mathrm{2}\: \\ $$

Question Number 99355 Answers: 0 Comments: 2

lim_(x→∞) ((1/x^2 ) −cot^2 x ) =?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\:−\mathrm{cot}\:^{\mathrm{2}} \mathrm{x}\:\right)\:=? \\ $$

Question Number 99352 Answers: 2 Comments: 0

log_3 2, log_6 2, log_(12) 2 are in

$$\mathrm{log}_{\mathrm{3}} \mathrm{2},\:\:\mathrm{log}_{\mathrm{6}} \mathrm{2},\:\:\mathrm{log}_{\mathrm{12}} \mathrm{2}\:\:\:\mathrm{are}\:\mathrm{in} \\ $$

Question Number 99351 Answers: 0 Comments: 5

The sum of n terms of the series 1^2 − 2^2 + 3^2 − 4^2 + 5^2 − 6^2 +.... is

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:{n}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series}\: \\ $$$$\mathrm{1}^{\mathrm{2}} \:−\:\mathrm{2}^{\mathrm{2}} \:+\:\mathrm{3}^{\mathrm{2}} \:−\:\mathrm{4}^{\mathrm{2}} \:+\:\mathrm{5}^{\mathrm{2}} \:−\:\mathrm{6}^{\mathrm{2}} \:+....\:\mathrm{is} \\ $$

Question Number 99350 Answers: 0 Comments: 1

lim_(x→−∞) ((3−x)/((√(9x^2 −8)) )) ?

$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\frac{\mathrm{3}−\mathrm{x}}{\sqrt{\mathrm{9x}^{\mathrm{2}} −\mathrm{8}}\:}\:? \\ $$

Question Number 99348 Answers: 1 Comments: 1

Question Number 99344 Answers: 3 Comments: 0

lim_(x→∞) (2^x + 3^x )^(1/x) ?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{2}^{\mathrm{x}} \:+\:\mathrm{3}^{\mathrm{x}} \:\right)^{\frac{\mathrm{1}}{\mathrm{x}}} \:? \\ $$

Question Number 99341 Answers: 0 Comments: 1

if lim_(x→3) ((x−(√(ax+b)))/(2x−6)) = −(1/6) then a−2b =

$$\mathrm{if}\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\frac{\mathrm{x}−\sqrt{\mathrm{ax}+\mathrm{b}}}{\mathrm{2x}−\mathrm{6}}\:=\:−\frac{\mathrm{1}}{\mathrm{6}} \\ $$$$\mathrm{then}\:\mathrm{a}−\mathrm{2b}\:=\: \\ $$

Question Number 99340 Answers: 0 Comments: 3

Given a function f(x)= { ((2x−a , x<−3)),((ax+b , −3≤x≤3)),((b−5x , x>3)) :} find the value of a and b such that lim_(x→−3) f(x) and lim_(x→3) f(x) exist

$$\mathrm{Given}\:\mathrm{a}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\mathrm{2x}−\mathrm{a}\:,\:\mathrm{x}<−\mathrm{3}}\\{\mathrm{ax}+\mathrm{b}\:,\:−\mathrm{3}\leqslant\mathrm{x}\leqslant\mathrm{3}}\\{\mathrm{b}−\mathrm{5x}\:,\:\mathrm{x}>\mathrm{3}}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\underset{{x}\rightarrow−\mathrm{3}} {\mathrm{lim}f}\left(\mathrm{x}\right)\:\mathrm{and}\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{exist}\: \\ $$

Question Number 99326 Answers: 1 Comments: 0

Question Number 99322 Answers: 1 Comments: 0

what is remainder of 2^7^(2002) divided by 352

$${what}\:{is}\:{remainder}\:{of}\:\mathrm{2}^{\mathrm{7}^{\mathrm{2002}} } \:{divided} \\ $$$${by}\:\mathrm{352}\: \\ $$

Question Number 99321 Answers: 1 Comments: 2

[((Angle(𝛉)),(sin(𝛉)),(cos(𝛉)[)),(0^° ,0,1),((15°),(((√6)−(√2))/4),(((√6)+(√2))/4)),((18°),(((√5)−1)/4),((√(5+(√5)))/(2(√2)))),((30°),(1/2),((√3)/2)),((36°),((√(5−(√5)))/(2(√2))),(((√5)+1)/4)),((45°),(1/(√2)),(1/(√2))),((54°),(((√5)+1)/4),((√(5−(√5)))/(2(√2)))),((60°),((√3)/2),(1/2)),((72°),((√(5+(√5)))/(2(√2))),(((√5)−1)/4)),((75°),(((√6)+(√2))/4),(((√6)−(√2))/4)),((90°),1,0) ] sin(𝛉)=cos(90°−𝛉)

$$\begin{bmatrix}{\boldsymbol{\mathrm{Angle}}\left(\boldsymbol{\theta}\right)}&{\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\theta}\right)}&{\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\theta}\right)\left[\right.}\\{\mathrm{0}^{°} }&{\mathrm{0}}&{\mathrm{1}}\\{\mathrm{15}°}&{\frac{\sqrt{\mathrm{6}}−\sqrt{\mathrm{2}}}{\mathrm{4}}}&{\frac{\sqrt{\mathrm{6}}+\sqrt{\mathrm{2}}}{\mathrm{4}}}\\{\mathrm{18}°}&{\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{4}}}&{\frac{\sqrt{\mathrm{5}+\sqrt{\mathrm{5}}}}{\mathrm{2}\sqrt{\mathrm{2}}}}\\{\mathrm{30}°}&{\frac{\mathrm{1}}{\mathrm{2}}}&{\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}}\\{\mathrm{36}°}&{\frac{\sqrt{\mathrm{5}−\sqrt{\mathrm{5}}}}{\mathrm{2}\sqrt{\mathrm{2}}}}&{\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{4}}}\\{\mathrm{45}°}&{\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}}&{\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}}\\{\mathrm{54}°}&{\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{4}}}&{\frac{\sqrt{\mathrm{5}−\sqrt{\mathrm{5}}}}{\mathrm{2}\sqrt{\mathrm{2}}}}\\{\mathrm{60}°}&{\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}}&{\frac{\mathrm{1}}{\mathrm{2}}}\\{\mathrm{72}°}&{\frac{\sqrt{\mathrm{5}+\sqrt{\mathrm{5}}}}{\mathrm{2}\sqrt{\mathrm{2}}}}&{\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{4}}}\\{\mathrm{75}°}&{\frac{\sqrt{\mathrm{6}}+\sqrt{\mathrm{2}}}{\mathrm{4}}}&{\frac{\sqrt{\mathrm{6}}−\sqrt{\mathrm{2}}}{\mathrm{4}}}\\{\mathrm{90}°}&{\mathrm{1}}&{\mathrm{0}}\end{bmatrix} \\ $$$$\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\theta}\right)=\boldsymbol{\mathrm{cos}}\left(\mathrm{90}°−\boldsymbol{\theta}\right) \\ $$

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