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Question Number 31143 Answers: 1 Comments: 0

A cyclist is travelling down a hill at a speed of 9.2m/s . The hillside makes an angle of 6.3° with the horizontal .Calculate, for the cyclist: (i)the vertical speed (ii)horizontal speed

$${A}\:{cyclist}\:{is}\:{travelling}\:{down}\:{a} \\ $$$${hill}\:{at}\:{a}\:{speed}\:{of}\:\mathrm{9}.\mathrm{2}{m}/{s}\:.\:{The} \\ $$$${hillside}\:{makes}\:{an}\:{angle}\:{of}\:\mathrm{6}.\mathrm{3}° \\ $$$${with}\:{the}\:{horizontal}\:.{Calculate}, \\ $$$${for}\:{the}\:{cyclist}: \\ $$$$\left({i}\right){the}\:{vertical}\:{speed} \\ $$$$\left({ii}\right){horizontal}\:{speed} \\ $$

Question Number 31141 Answers: 1 Comments: 0

using the limit defination find the area of f(x)= cos(x) [0,π/2]

$$\boldsymbol{{using}}\:\boldsymbol{{the}}\:\boldsymbol{{limit}}\:\boldsymbol{{defination}} \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{area}}\:\boldsymbol{{of}} \\ $$$$\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\:\boldsymbol{{cos}}\left(\boldsymbol{{x}}\right)\:\:\left[\mathrm{0},\pi/\mathrm{2}\right] \\ $$

Question Number 31004 Answers: 1 Comments: 0

Question Number 31003 Answers: 1 Comments: 0

Number of positive integers x for which f(x)=x^3 −8x^2 +20x−13 is a prime number are ?

$${Number}\:{of}\:{positive}\:{integers}\:{x}\:{for} \\ $$$${which}\:{f}\left({x}\right)={x}^{\mathrm{3}} −\mathrm{8}{x}^{\mathrm{2}} +\mathrm{20}{x}−\mathrm{13}\:{is}\:\:{a}\: \\ $$$${prime}\:{number}\:{are}\:? \\ $$

Question Number 30994 Answers: 0 Comments: 3

Question Number 30990 Answers: 1 Comments: 0

Question Number 30984 Answers: 0 Comments: 3

Question Number 30986 Answers: 1 Comments: 0

Question Number 30961 Answers: 0 Comments: 13

Question Number 30958 Answers: 1 Comments: 4

Question Number 30957 Answers: 1 Comments: 0

Question Number 30956 Answers: 1 Comments: 0

Question Number 30939 Answers: 1 Comments: 0

If x^2 +y^2 +z^2 = r^2 , then tan^(−1) (((xy)/(zr)))+tan^(−1) (((yz)/(xr)))+tan^(−1) (((xz)/(yr))) =

$$\mathrm{If}\:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\:{r}^{\mathrm{2}} \:,\:\mathrm{then} \\ $$$$\mathrm{tan}^{−\mathrm{1}} \left(\frac{{xy}}{{zr}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{{yz}}{{xr}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{{xz}}{{yr}}\right)\:= \\ $$

Question Number 30936 Answers: 0 Comments: 0

find ∫^a _0 ((sinx)/(√(1+x^2 )))dx .

$${find}\:\:\:\underset{\mathrm{0}} {\int}^{{a}} \:\:\frac{{sinx}}{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{dx}\:. \\ $$

Question Number 30933 Answers: 1 Comments: 0

Question Number 30929 Answers: 2 Comments: 1

Σ_(n=0) ^∞ tan^(−1) (n+(1/2))−tan^(−1) (n−(1/2))= ?

$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\mathrm{tan}^{−\mathrm{1}} \left({n}+\frac{\mathrm{1}}{\mathrm{2}}\right)−\mathrm{tan}^{−\mathrm{1}} \left({n}−\frac{\mathrm{1}}{\mathrm{2}}\right)=\:? \\ $$

Question Number 30918 Answers: 1 Comments: 0

Question Number 30917 Answers: 0 Comments: 0

Question Number 30916 Answers: 1 Comments: 1

Question Number 30913 Answers: 0 Comments: 0

Question Number 30897 Answers: 1 Comments: 1

(44x+28y)2

$$\left(\mathrm{44}{x}+\mathrm{28}{y}\right)\mathrm{2} \\ $$

Question Number 30875 Answers: 1 Comments: 1

Question Number 30871 Answers: 1 Comments: 2

If 2f(x)+f(−x)=(1/x)sin (x−(1/x)) Find ∫_(1/e) ^( e) f(x)dx .

$${If}\:\:\:\mathrm{2}{f}\left({x}\right)+{f}\left(−{x}\right)=\frac{\mathrm{1}}{{x}}\mathrm{sin}\:\left({x}−\frac{\mathrm{1}}{{x}}\right) \\ $$$${Find}\:\:\:\int_{\mathrm{1}/{e}} ^{\:\:{e}} {f}\left({x}\right){dx}\:\:. \\ $$

Question Number 30866 Answers: 0 Comments: 8

Question Number 30858 Answers: 2 Comments: 0

∫_0 ^1 x∣x−4∣dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{x}\mid\mathrm{x}−\mathrm{4}\mid\mathrm{dx} \\ $$

Question Number 30862 Answers: 1 Comments: 0

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