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Question Number 25283 Answers: 2 Comments: 1

Question Number 25280 Answers: 1 Comments: 0

Find the limit off(x) _(x→4) =(((x+2)/(x^2 −4)))

$${Find}\:{the}\:{limit}\:{off}\left({x}\right)\underset{{x}\rightarrow\mathrm{4}} {\:}=\left(\frac{{x}+\mathrm{2}}{{x}^{\mathrm{2}} −\mathrm{4}}\right) \\ $$

Question Number 25275 Answers: 0 Comments: 0

Question Number 25273 Answers: 0 Comments: 0

If x, y, z are in HP, then log (x+z)+log (x−2y+z) is equal to

$$\mathrm{If}\:\:{x},\:{y},\:{z}\:\mathrm{are}\:\mathrm{in}\:\mathrm{HP},\:\mathrm{then}\: \\ $$$$\mathrm{log}\:\left({x}+{z}\right)+\mathrm{log}\:\left({x}−\mathrm{2}{y}+{z}\right)\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 25254 Answers: 1 Comments: 0

A charged sphere of mass 3×10^(−4) kg is suspended from a string.An electrical force acting horizontally on the sphere so that the string makes an angle 37° with the vertical when at rest. Find a)magnitude of the electric force b)the tension in the string.

$${A}\:{charged}\:{sphere}\:{of}\:{mass}\:\mathrm{3}×\mathrm{10}^{−\mathrm{4}} {kg}\:{is} \\ $$$${suspended}\:{from}\:{a}\:{string}.{An} \\ $$$${electrical}\:{force}\:{acting}\:{horizontally} \\ $$$${on}\:{the}\:{sphere}\:{so}\:{that}\:{the}\:{string} \\ $$$${makes}\:{an}\:{angle}\:\mathrm{37}°\:{with}\:{the}\:{vertical} \\ $$$${when}\:{at}\:{rest}.\:{Find} \\ $$$$\left.{a}\right){magnitude}\:{of}\:{the}\:{electric}\:{force} \\ $$$$\left.{b}\right){the}\:{tension}\:{in}\:{the}\:{string}. \\ $$

Question Number 25253 Answers: 1 Comments: 1

A 100kg man lowers himself to the ground from a height of 10m by means of a rope passed over a frictionless pulley and the other end attached to a 70kg sandbag. a)with what speed does the man hit the ground? b)could he have done anything to reduce the speed?

$${A}\:\mathrm{100}{kg}\:{man}\:{lowers}\:{himself}\:{to} \\ $$$${the}\:{ground}\:{from}\:{a}\:{height}\:{of}\:\mathrm{10}{m} \\ $$$${by}\:{means}\:{of}\:{a}\:{rope}\:{passed}\:{over}\:{a} \\ $$$${frictionless}\:{pulley}\:{and}\:{the}\:{other} \\ $$$${end}\:{attached}\:{to}\:{a}\:\mathrm{70}{kg}\:{sandbag}. \\ $$$$\left.{a}\right){with}\:{what}\:{speed}\:{does}\:{the}\:{man}\: \\ $$$${hit}\:{the}\:{ground}? \\ $$$$\left.{b}\right){could}\:{he}\:{have}\:{done}\:{anything}\:{to} \\ $$$${reduce}\:{the}\:{speed}? \\ $$

Question Number 25252 Answers: 1 Comments: 0

The mass of earth is 5.98×10^(24) kg. If the earth′s gravitational force causes a 60kg student to accelerate downwards at 9.8m/s^2 .Calculate the upward acceleration of the earth resulting from the student′s gravitational reaction force actinv on the earth.

$${The}\:{mass}\:{of}\:{earth}\:{is}\:\mathrm{5}.\mathrm{98}×\mathrm{10}^{\mathrm{24}} {kg}. \\ $$$${If}\:{the}\:{earth}'{s}\:{gravitational}\:{force} \\ $$$${causes}\:{a}\:\mathrm{60}{kg}\:{student}\:{to}\:{accelerate} \\ $$$${downwards}\:{at}\:\mathrm{9}.\mathrm{8}{m}/{s}^{\mathrm{2}} .{Calculate} \\ $$$${the}\:{upward}\:{acceleration}\:{of}\:{the} \\ $$$${earth}\:{resulting}\:{from}\:{the}\:{student}'{s} \\ $$$${gravitational}\:{reaction}\:{force}\:{actinv} \\ $$$${on}\:{the}\:{earth}. \\ $$

Question Number 25251 Answers: 0 Comments: 1

state the domain and range in intervals for the following when they are said the be continuous at a point: a)a polynomial function b)a rational function c)an absolute value function d)a trig function

$${state}\:{the}\:{domain}\:{and}\:{range}\:{in}\: \\ $$$${intervals}\:{for}\:{the}\:{following}\:{when} \\ $$$${they}\:{are}\:{said}\:{the}\:{be}\:{continuous}\:{at} \\ $$$${a}\:{point}: \\ $$$$\left.{a}\right){a}\:{polynomial}\:{function} \\ $$$$\left.{b}\right){a}\:{rational}\:{function} \\ $$$$\left.{c}\right){an}\:{absolute}\:{value}\:{function} \\ $$$$\left.{d}\right){a}\:{trig}\:{function} \\ $$$$ \\ $$

Question Number 25246 Answers: 1 Comments: 0

8x^(3/(2n)) −8x^((−3)/(2n)) =63

$$\mathrm{8x}^{\frac{\mathrm{3}}{\mathrm{2n}}} −\mathrm{8x}^{\frac{−\mathrm{3}}{\mathrm{2n}}} \:=\mathrm{63} \\ $$

Question Number 25245 Answers: 2 Comments: 0

yadi kisi equilatter triangle ke parivrit aur antahvrit ke areas ka difference 44cm^2 hai to triangle ka area kya hoga?

$$\mathrm{yadi}\:\mathrm{kisi}\:\mathrm{equilatter}\:\mathrm{triangle}\:\mathrm{ke}\: \\ $$$$\mathrm{parivrit}\:\mathrm{aur}\:\mathrm{antahvrit}\:\mathrm{ke}\:\mathrm{areas}\:\mathrm{ka}\: \\ $$$$\mathrm{difference}\:\mathrm{44cm}^{\mathrm{2}} \:\mathrm{hai}\:\mathrm{to}\:\mathrm{triangle}\:\mathrm{ka}\: \\ $$$$\mathrm{area}\:\mathrm{kya}\:\mathrm{hoga}? \\ $$

Question Number 25278 Answers: 0 Comments: 4

Find the number of solutions of log∣x∣ = e^x

$${Find}\:{the}\:{number}\:{of}\:{solutions}\:{of} \\ $$$$\mathrm{log}\mid{x}\mid\:=\:{e}^{{x}} \\ $$

Question Number 25279 Answers: 2 Comments: 0

Find the domain and range of f(x)=(√((((x−5)/(x−3)))))

$${Find}\:{the}\:{domain}\:{and}\:{range}\:{of} \\ $$$${f}\left({x}\right)=\sqrt{\left(\frac{{x}−\mathrm{5}}{{x}−\mathrm{3}}\right)} \\ $$

Question Number 25237 Answers: 0 Comments: 1

prooove that 0!=1

$${prooove}\:{that}\:\mathrm{0}!=\mathrm{1} \\ $$

Question Number 25236 Answers: 0 Comments: 1

Question Number 25230 Answers: 1 Comments: 0

Let X is natural number . Multification of its digits is X^2 − 97X + 2020 . Find the value of X_(maximum) + X_(minimum) .

$${Let}\:\:{X}\:\:{is}\:{natural}\:\:{number}\:. \\ $$$${Multification}\:\:{of}\:\:{its}\:\:{digits}\:\:{is}\:\:{X}^{\mathrm{2}} \:−\:\mathrm{97}{X}\:+\:\mathrm{2020}\:. \\ $$$${Find}\:\:{the}\:\:{value}\:\:{of}\:\:{X}_{{maximum}} \:\:+\:\:{X}_{{minimum}} \:\:. \\ $$

Question Number 25229 Answers: 0 Comments: 1

∫(1/(√(x^2 +1)))dx

$$\int\frac{\mathrm{1}}{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}{dx} \\ $$

Question Number 25224 Answers: 1 Comments: 0

∫(2x−1)(√(x×x−x+1 dx))

$$\int\left(\mathrm{2}{x}−\mathrm{1}\right)\sqrt{{x}×{x}−{x}+\mathrm{1}\:\:\:{dx}} \\ $$

Question Number 25226 Answers: 1 Comments: 0

Show that if x=3−(√3).Show that x^2 +((36)/x^2 )=24

$${Show}\:{that}\:{if}\:{x}=\mathrm{3}−\sqrt{\mathrm{3}}.{Show}\:{that}\:{x}^{\mathrm{2}} +\frac{\mathrm{36}}{{x}^{\mathrm{2}} }=\mathrm{24} \\ $$

Question Number 25221 Answers: 1 Comments: 0

Find the lim_(x→∞) (e^x /(√(e^(2x) +1)))

$$\mathrm{Find}\:\mathrm{the}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\:\frac{\mathrm{e}^{\mathrm{x}} }{\sqrt{\mathrm{e}^{\mathrm{2x}} +\mathrm{1}}} \\ $$

Question Number 25215 Answers: 0 Comments: 1

Question Number 25209 Answers: 1 Comments: 0

∫cosec(√(4x^2 ))dx

$$\int{cosec}\sqrt{\mathrm{4}{x}^{\mathrm{2}} }{dx} \\ $$$$ \\ $$

Question Number 25203 Answers: 1 Comments: 1

Question Number 25201 Answers: 1 Comments: 0

Question Number 25200 Answers: 1 Comments: 0

The point A has coordinate (− 1, − 5) and the point B has coordinates (7, 1). The perpendicular bisector of AB meets the x − axis at C and the y − axis at D. Calculate the length of CD

$$\mathrm{The}\:\mathrm{point}\:\mathrm{A}\:\mathrm{has}\:\mathrm{coordinate}\:\left(−\:\mathrm{1},\:\:−\:\mathrm{5}\right)\:\mathrm{and}\:\mathrm{the}\:\mathrm{point}\:\mathrm{B}\:\mathrm{has}\:\mathrm{coordinates}\:\left(\mathrm{7},\:\mathrm{1}\right). \\ $$$$\mathrm{The}\:\mathrm{perpendicular}\:\mathrm{bisector}\:\mathrm{of}\:\mathrm{AB}\:\mathrm{meets}\:\mathrm{the}\:\mathrm{x}\:−\:\mathrm{axis}\:\mathrm{at}\:\mathrm{C}\:\mathrm{and}\:\mathrm{the}\:\mathrm{y}\:−\:\mathrm{axis}\:\mathrm{at} \\ $$$$\mathrm{D}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{CD} \\ $$

Question Number 25199 Answers: 1 Comments: 1

A line has equation y = 2x − 7 and a curve has equation y = x^2 − 4x + c, where c is a constant. Find the set of possible values of c for which the line does not intersect the curve.

$$\mathrm{A}\:\mathrm{line}\:\mathrm{has}\:\mathrm{equation}\:\mathrm{y}\:=\:\mathrm{2x}\:−\:\mathrm{7}\:\mathrm{and}\:\mathrm{a}\:\mathrm{curve}\:\mathrm{has}\:\mathrm{equation}\:\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\mathrm{c}, \\ $$$$\mathrm{where}\:\mathrm{c}\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\mathrm{c}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\:\mathrm{line} \\ $$$$\mathrm{does}\:\mathrm{not}\:\mathrm{intersect}\:\mathrm{the}\:\mathrm{curve}. \\ $$

Question Number 25198 Answers: 0 Comments: 0

Given sin (K + L) cos M = 2 sin K cos (L − M) Prove that tan M = ((sin (L − K))/(2 sin K sin L))

$$\mathrm{Given} \\ $$$$\mathrm{sin}\:\left({K}\:+\:{L}\right)\:\mathrm{cos}\:{M}\:=\:\mathrm{2}\:\mathrm{sin}\:{K}\:\mathrm{cos}\:\left({L}\:−\:{M}\right) \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{tan}\:{M}\:=\:\frac{\mathrm{sin}\:\left({L}\:−\:{K}\right)}{\mathrm{2}\:\mathrm{sin}\:{K}\:\mathrm{sin}\:{L}} \\ $$

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