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Question Number 51549    Answers: 0   Comments: 0

A and B are two points from the plan (P) with AB=4 define and draw the locus of points M ∈(P) wich verify MA +MB =8 .

$${A}\:{and}\:{B}\:{are}\:{two}\:{points}\:{from}\:{the}\:{plan}\:\left({P}\right)\:{with}\:{AB}=\mathrm{4}\:{define}\:{and}\:{draw} \\ $$$${the}\:{locus}\:{of}\:{points}\:{M}\:\in\left({P}\right)\:{wich}\:{verify}\:\:\:{MA}\:+{MB}\:=\mathrm{8}\:. \\ $$

Question Number 51539    Answers: 2   Comments: 1

Question Number 51535    Answers: 1   Comments: 1

Question Number 51526    Answers: 1   Comments: 1

Question Number 51510    Answers: 1   Comments: 0

Question Number 51508    Answers: 0   Comments: 0

A man walking due to west along a level road observes a school in a direction N 72° E. After walking 1500 yards, he observes it in a direction N 67° E. How far is the school from the road.

$$\mathrm{A}\:\mathrm{man}\:\mathrm{walking}\:\mathrm{due}\:\mathrm{to}\:\mathrm{west}\:\mathrm{along}\:\mathrm{a}\:\mathrm{level}\:\mathrm{road}\:\mathrm{observes}\:\mathrm{a}\:\mathrm{school}\:\mathrm{in}\:\mathrm{a}\:\mathrm{direction}\:\mathrm{N}\:\mathrm{72}°\:\mathrm{E}.\:\mathrm{After}\:\mathrm{walking}\:\mathrm{1500}\:\mathrm{yards},\: \\ $$$$\mathrm{he}\:\mathrm{observes}\:\mathrm{it}\:\mathrm{in}\:\mathrm{a}\:\mathrm{direction}\:\mathrm{N}\:\mathrm{67}°\:\mathrm{E}.\:\mathrm{How}\:\mathrm{far}\:\mathrm{is}\:\mathrm{the}\:\mathrm{school}\:\mathrm{from}\:\mathrm{the}\:\mathrm{road}. \\ $$

Question Number 51502    Answers: 0   Comments: 1

Question Number 51501    Answers: 1   Comments: 0

Question Number 51507    Answers: 0   Comments: 0

^• 739 is a prime number and its reversed number 937 is also prime. Determine 4-digit prime numbers whose reversed be also prime. ^• If number of such primes is a function of number of digits, determine that the function is increasing or not.

$$\:^{\bullet} \mathrm{739}\:{is}\:{a}\:\:{prime}\:{number}\:{and} \\ $$$${its}\:{reversed}\:{number}\:\mathrm{937}\:{is}\:{also} \\ $$$${prime}. \\ $$$${Determine}\:\mathrm{4}-{digit}\:{prime}\:{numbers} \\ $$$${whose}\:{reversed}\:{be}\:{also}\:{prime}. \\ $$$$\:^{\bullet} {If}\:{number}\:{of}\:{such}\:{primes}\:{is}\:{a} \\ $$$${function}\:{of}\:{number}\:{of}\:{digits}, \\ $$$${determine}\:{that}\:{the}\:{function}\:{is} \\ $$$${increasing}\:{or}\:{not}. \\ $$

Question Number 51494    Answers: 0   Comments: 2

Solve: (t^2 + 1) (dp/dt) = p^t

$$\mathrm{Solve}:\:\:\:\:\:\:\:\:\left(\mathrm{t}^{\mathrm{2}} \:+\:\mathrm{1}\right)\:\frac{\mathrm{dp}}{\mathrm{dt}}\:\:=\:\:\mathrm{p}^{\mathrm{t}} \\ $$

Question Number 51492    Answers: 1   Comments: 0

For ellipse 16x^2 +4y^2 +96x−8y−84=0 find i)centre ii)verteces iii)focus iv)directrix v)length of major and minor axis vi)ecentricity vii)graph the ellipse

$${For}\:{ellipse}\: \\ $$$$\mathrm{16}{x}^{\mathrm{2}} +\mathrm{4}{y}^{\mathrm{2}} +\mathrm{96}{x}−\mathrm{8}{y}−\mathrm{84}=\mathrm{0} \\ $$$${find} \\ $$$$\left.{i}\right){centre} \\ $$$$\left.{ii}\right){verteces} \\ $$$$\left.{iii}\right){focus} \\ $$$$\left.{iv}\right){directrix} \\ $$$$\left.{v}\right){length}\:{of}\:{major}\: \\ $$$${and}\:{minor}\:{axis} \\ $$$$\left.{vi}\right){ecentricity} \\ $$$$\left.{vii}\right){graph}\:{the}\:{ellipse} \\ $$

Question Number 51489    Answers: 1   Comments: 0

Given that y=mx+c is equation of tangent to the ellipse (x^2 /a^(2 ) )+(y^2 /b^2 )=1 find coordinate of point of contact.

$${Given}\:{that}\:{y}={mx}+{c} \\ $$$${is}\:{equation}\:{of}\:\:{tangent} \\ $$$${to}\:{the}\:{ellipse}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}\:} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1} \\ $$$${find}\:{coordinate}\:{of}\: \\ $$$${point}\:{of}\:{contact}. \\ $$

Question Number 51485    Answers: 0   Comments: 1

Question Number 51520    Answers: 1   Comments: 1

Question Number 51448    Answers: 0   Comments: 3

Question Number 51446    Answers: 1   Comments: 0

f(x)=(√((1−x^2 )/(x^2 +1))) f^′ (−2)=...

$${f}\left({x}\right)=\sqrt{\frac{\mathrm{1}−{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} +\mathrm{1}}} \\ $$$${f}^{'} \left(−\mathrm{2}\right)=... \\ $$

Question Number 51436    Answers: 1   Comments: 0

If y = (((e^x + e^(−x) ). tanh x)/(e^x − sinh x)) prove that y′ = 2 sech^2 x

$$\mathrm{If}\:\:\:\:\mathrm{y}\:=\:\frac{\left(\mathrm{e}^{\mathrm{x}} \:+\:\mathrm{e}^{−\mathrm{x}} \right).\:\mathrm{tanh}\:\mathrm{x}}{\mathrm{e}^{\mathrm{x}} \:−\:\mathrm{sinh}\:\mathrm{x}} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\:\:\:\:\:\:\mathrm{y}'\:\:=\:\:\mathrm{2}\:\mathrm{sech}^{\mathrm{2}} \:\mathrm{x} \\ $$

Question Number 51431    Answers: 3   Comments: 3

Find x and y x^2 + y^2 = 25 ...... (i) x^3 + y^3 = 91 ....... (ii)

$$\mathrm{Find}\:\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$$$\:\:\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:\:=\:\:\mathrm{25}\:\:\:\:\:......\:\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:\:=\:\:\mathrm{91}\:\:\:.......\:\left(\mathrm{ii}\right) \\ $$

Question Number 51466    Answers: 1   Comments: 5

Question Number 51465    Answers: 2   Comments: 4

Question Number 51456    Answers: 1   Comments: 0

∫ (x^8 /(x^6 + 64)) dx

$$\int\:\:\:\frac{\mathrm{x}^{\mathrm{8}} }{\mathrm{x}^{\mathrm{6}} \:+\:\mathrm{64}}\:\mathrm{dx} \\ $$

Question Number 51421    Answers: 2   Comments: 3

∫ ((tan^(−1) x)/x^2 ) dx

$$\int\:\:\frac{\mathrm{tan}^{−\mathrm{1}} \mathrm{x}}{\mathrm{x}^{\mathrm{2}} }\:\:\mathrm{dx} \\ $$

Question Number 51420    Answers: 2   Comments: 0

∫ (e^(3x) /(1 + e^x )) dx

$$\int\:\:\frac{\mathrm{e}^{\mathrm{3x}} }{\mathrm{1}\:+\:\mathrm{e}^{\mathrm{x}} }\:\mathrm{dx} \\ $$

Question Number 51419    Answers: 1   Comments: 0

∫ ((√x)/(1 + (x)^(1/3) )) dx

$$\int\:\frac{\sqrt{\mathrm{x}}}{\mathrm{1}\:+\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}}}\:\mathrm{dx} \\ $$

Question Number 51394    Answers: 1   Comments: 0

∫ (1/(1 + (√(tan x)))) dx

$$\int\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\sqrt{\mathrm{tan}\:\mathrm{x}}}\:\:\mathrm{dx} \\ $$

Question Number 51389    Answers: 1   Comments: 2

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