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Question Number 113976 Answers: 0 Comments: 1

A ball of mass 0.25kg is moving to the right at a speed of 7.4m/s. it strikes a wall at 90^0 and rebounds from the wall leaving it with a speed of 5.8n/s moving to the left. Find the direction and magnitude of the change in direction

$$\mathrm{A}\:\mathrm{ball}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{0}.\mathrm{25kg}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{to}\:\mathrm{the}\:\mathrm{right}\:\mathrm{at} \\ $$$$\mathrm{a}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{7}.\mathrm{4m}/\mathrm{s}.\:\mathrm{it}\:\mathrm{strikes}\:\mathrm{a}\:\mathrm{wall}\:\mathrm{at}\:\mathrm{90}^{\mathrm{0}} \mathrm{and}\: \\ $$$$\mathrm{rebounds}\:\mathrm{from}\:\mathrm{the}\:\mathrm{wall}\:\mathrm{leaving}\:\mathrm{it}\:\mathrm{with}\:\mathrm{a}\:\mathrm{speed} \\ $$$$\mathrm{of}\:\mathrm{5}.\mathrm{8n}/\mathrm{s}\:\mathrm{moving}\:\mathrm{to}\:\mathrm{the}\:\mathrm{left}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{direction}\: \\ $$$$\mathrm{and}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{change}\:\mathrm{in}\:\mathrm{direction} \\ $$

Question Number 113975 Answers: 1 Comments: 0

Find the nth term: 1, 0, − 1, 0, 1, 0, − 1, 0, ...

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}:\:\:\:\mathrm{1},\:\:\mathrm{0},\:\:−\:\mathrm{1},\:\:\mathrm{0},\:\:\mathrm{1},\:\:\mathrm{0},\:\:−\:\mathrm{1},\:\:\mathrm{0},\:\:... \\ $$

Question Number 113970 Answers: 0 Comments: 0

Question Number 113959 Answers: 1 Comments: 0

if a,b areal number such that a>b ,c<0 then (1)c.b≥c.a (2) c.b>c.a (3) c.a>c.b chouse the right answer

$${if}\:{a},{b}\:{areal}\:{number}\:{such}\:{that}\:{a}>{b}\:,{c}<\mathrm{0}\:{then}\: \\ $$$$ \\ $$$$\left(\mathrm{1}\right){c}.{b}\geqslant{c}.{a}\:\:\:\:\left(\mathrm{2}\right)\:{c}.{b}>{c}.{a}\:\:\:\:\left(\mathrm{3}\right)\:{c}.{a}>{c}.{b} \\ $$$$ \\ $$$${chouse}\:{the}\:{right}\:{answer} \\ $$

Question Number 113957 Answers: 0 Comments: 0

the sequence ........... is partial from sequence ⟨(1/(n+1))⟩_(n∈N) (1)⟨((1−n)/n)⟩ (2)⟨(1/(2n−1))⟩ (3)⟨(1/(2n))⟩ chouse the right answer

$${the}\:{sequence}\:...........\:{is}\:{partial}\:{from}\:{sequence}\:\langle\frac{\mathrm{1}}{{n}+\mathrm{1}}\rangle_{{n}\in{N}} \\ $$$$ \\ $$$$\left(\mathrm{1}\right)\langle\frac{\mathrm{1}−{n}}{{n}}\rangle\:\:\:\:\:\:\:\left(\mathrm{2}\right)\langle\frac{\mathrm{1}}{\mathrm{2}{n}−\mathrm{1}}\rangle\:\:\:\:\:\:\left(\mathrm{3}\right)\langle\frac{\mathrm{1}}{\mathrm{2}{n}}\rangle\: \\ $$$$ \\ $$$${chouse}\:{the}\:{right}\:{answer} \\ $$

Question Number 113954 Answers: 2 Comments: 1

x^y =y^x { (x),(y) :}=?

$${x}^{{y}} ={y}^{{x}} \:\:\:\: \\ $$$$\begin{cases}{\mathrm{x}}\\{\mathrm{y}}\end{cases}=? \\ $$

Question Number 113952 Answers: 2 Comments: 4

find all asymptotes of function f(x)=(((x^2 +4x−5)/(x^2 +x+3)))^(x+5)

$${find}\:{all}\:{asymptotes}\:{of}\:{function} \\ $$$${f}\left({x}\right)=\left(\frac{{x}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{5}}{{x}^{\mathrm{2}} +{x}+\mathrm{3}}\right)^{{x}+\mathrm{5}} \\ $$

Question Number 113931 Answers: 1 Comments: 2

∣ x ∣=2⇒ x=2 ∨ x=−2 OR ∣ x ∣=2⇒ x=2 ∧ x=−2 ?

$$\mid\:{x}\:\mid=\mathrm{2}\Rightarrow\:{x}=\mathrm{2}\:\vee\:{x}=−\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{OR} \\ $$$$\mid\:{x}\:\mid=\mathrm{2}\Rightarrow\:{x}=\mathrm{2}\:\wedge\:{x}=−\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:? \\ $$

Question Number 113929 Answers: 2 Comments: 4

∫(x+1)^2 (1−x)^5 dx

$$\int\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{5}} \mathrm{dx}\: \\ $$$$ \\ $$

Question Number 113928 Answers: 1 Comments: 0

Find the remainder when x^(2006) −1 is divided by x^4 +x^3 +2x^2 +x+1.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:{x}^{\mathrm{2006}} −\mathrm{1}\: \\ $$$$\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:{x}^{\mathrm{4}} +{x}^{\mathrm{3}} +\mathrm{2}{x}^{\mathrm{2}} +{x}+\mathrm{1}. \\ $$

Question Number 113919 Answers: 2 Comments: 0

Given a set data : 2,2,3,4,5,5,5,8,8,9,11,14. find the value of Q_1

$${Given}\:{a}\:{set}\:{data}\:\: \\ $$$$:\:\mathrm{2},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{5},\mathrm{5},\mathrm{8},\mathrm{8},\mathrm{9},\mathrm{11},\mathrm{14}. \\ $$$${find}\:{the}\:{value}\:{of}\:{Q}_{\mathrm{1}} \\ $$

Question Number 113913 Answers: 3 Comments: 0

Find the square root of (√(50))+(√(48))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{square}\:\mathrm{root}\:\mathrm{of}\:\sqrt{\mathrm{50}}+\sqrt{\mathrm{48}} \\ $$

Question Number 113910 Answers: 4 Comments: 0

(1)∫_0 ^π ((sin^4 x)/((1+cos x)^2 )) dx ? (2) lim_(x→∞) ((√(1−cos (((2π)/x))))/(1/x)) ?

$$\left(\mathrm{1}\right)\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{\mathrm{sin}\:^{\mathrm{4}} {x}}{\left(\mathrm{1}+\mathrm{cos}\:{x}\right)^{\mathrm{2}} }\:{dx}\:? \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}−\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{{x}}\right)}}{\frac{\mathrm{1}}{{x}}}\:? \\ $$

Question Number 113907 Answers: 1 Comments: 0

∫ (√x) cos ((√x)) dx

$$\int\:\sqrt{{x}}\:\mathrm{cos}\:\left(\sqrt{{x}}\right)\:{dx} \\ $$

Question Number 113904 Answers: 1 Comments: 0

If { ((f(x)=(√(2x−5)))),((g(x)=x^2 +1)) :} find (f^(−1) ○g)^(−1) (x)

$${If}\:\begin{cases}{{f}\left({x}\right)=\sqrt{\mathrm{2}{x}−\mathrm{5}}}\\{{g}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{1}}\end{cases} \\ $$$${find}\:\left({f}^{−\mathrm{1}} \circ{g}\right)^{−\mathrm{1}} \left({x}\right) \\ $$

Question Number 113901 Answers: 0 Comments: 4

when do I use ∣x∣ for (√x^2 )?

$${when}\:{do}\:{I}\:{use}\:\mid{x}\mid \\ $$$${for}\:\sqrt{{x}^{\mathrm{2}} }? \\ $$

Question Number 113897 Answers: 1 Comments: 0

Question Number 113894 Answers: 2 Comments: 1

Question Number 113885 Answers: 1 Comments: 0

Question Number 113886 Answers: 3 Comments: 0

Question Number 113876 Answers: 4 Comments: 0

If 2^x =4^y =8^z and xyz=288, then find (1/(2x))+(1/(4y))+(1/(8z))

$$\mathrm{If}\:\mathrm{2}^{\mathrm{x}} =\mathrm{4}^{\mathrm{y}} =\mathrm{8}^{\mathrm{z}} \:\mathrm{and}\:\mathrm{xyz}=\mathrm{288},\:\mathrm{then}\:\mathrm{find} \\ $$$$\frac{\mathrm{1}}{\mathrm{2x}}+\frac{\mathrm{1}}{\mathrm{4y}}+\frac{\mathrm{1}}{\mathrm{8z}} \\ $$

Question Number 113868 Answers: 0 Comments: 1

Find the area between the circle ρ=2acosθ and cardiode ρ=a(1+cosθ)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{between}\:\mathrm{the}\:\mathrm{circle}\:\rho=\mathrm{2acos}\theta\:\mathrm{and}\: \\ $$$$\mathrm{cardiode}\:\rho=\mathrm{a}\left(\mathrm{1}+\mathrm{cos}\theta\right) \\ $$

Question Number 113867 Answers: 1 Comments: 0

∫_3 ^6 ((x+1)/(x^3 +x^2 −6x))dx

$$\int_{\mathrm{3}} ^{\mathrm{6}} \frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} −\mathrm{6x}}\mathrm{dx} \\ $$

Question Number 113865 Answers: 0 Comments: 0

Consider the series I_n =∫_1 ^e x(lnx)^n dx and I_0 =∫_1 ^e xdx Which of the following is true ? a\ 0≤I_n ≤(e^2 /(n+2)) b\1≤I_n ≤(e^2 /(n+1)) c\I_n is negative

$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{series}\:\mathrm{I}_{\mathrm{n}} =\int_{\mathrm{1}} ^{\mathrm{e}} \mathrm{x}\left(\mathrm{lnx}\right)^{\mathrm{n}} \mathrm{dx}\:\mathrm{and}\:\mathrm{I}_{\mathrm{0}} =\int_{\mathrm{1}} ^{\mathrm{e}} \mathrm{xdx} \\ $$$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{true}\:? \\ $$$$\mathrm{a}\backslash\:\mathrm{0}\leqslant\mathrm{I}_{\mathrm{n}} \leqslant\frac{\mathrm{e}^{\mathrm{2}} }{\mathrm{n}+\mathrm{2}}\:\:\:\:\mathrm{b}\backslash\mathrm{1}\leqslant\mathrm{I}_{\mathrm{n}} \leqslant\frac{\mathrm{e}^{\mathrm{2}} }{\mathrm{n}+\mathrm{1}}\:\:\mathrm{c}\backslash\mathrm{I}_{\mathrm{n}} \:\mathrm{is}\:\mathrm{negative} \\ $$

Question Number 113862 Answers: 1 Comments: 0

Question Number 113854 Answers: 1 Comments: 0

if f(x)=2x^2 −12x+10. (i) sketch the graph of y=∣f(x)∣ for −1≤x≤7. (ii) find the set of values of k for which the equation ∣f(x)∣=k has 4 distinct roots.

$${if}\:{f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{2}} −\mathrm{12}{x}+\mathrm{10}.\: \\ $$$$\left({i}\right)\:{sketch}\:{the}\:{graph}\:{of}\:{y}=\mid{f}\left({x}\right)\mid\:{for} \\ $$$$−\mathrm{1}\leqslant{x}\leqslant\mathrm{7}. \\ $$$$\left({ii}\right)\:{find}\:{the}\:{set}\:{of}\:{values}\:{of}\:{k}\:{for} \\ $$$${which}\:{the}\:{equation}\:\mid{f}\left({x}\right)\mid={k}\:{has}\:\mathrm{4} \\ $$$${distinct}\:{roots}. \\ $$

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