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Question Number 32792 Answers: 1 Comments: 2

the equation 3x− 5=15 represents a straight line. a) find one point on this line. b)find the coordinates of the points when the line cuts the x−axis and the y−axis c)find the gradient of this line.

$${the}\:{equation}\: \\ $$$$\mathrm{3}{x}−\:\mathrm{5}=\mathrm{15}\:{represents}\:{a}\:{straight}\:{line}. \\ $$$$\left.{a}\right)\:{find}\:{one}\:{point}\:{on}\:{this}\:{line}. \\ $$$$\left.{b}\right){find}\:{the}\:{coordinates}\:{of}\:{the}\:{points}\:{when} \\ $$$${the}\:{line}\:{cuts}\:{the}\:{x}−{axis}\:{and}\:{the}\:{y}−{axis} \\ $$$$\left.{c}\right){find}\:{the}\:{gradient}\:{of}\:{this}\:{line}. \\ $$$$ \\ $$

Question Number 32682 Answers: 1 Comments: 0

If x_1 and x_(2 ) are roots of the equation acos 2x+bsin x = c and 2sin x_1 sinx_2 = sin x_1 +sinx_2 . Then the value of (b/(c−a)) is ?

$$\boldsymbol{{I}}{f}\:{x}_{\mathrm{1}} \:{and}\:{x}_{\mathrm{2}\:} \:{are}\:{roots}\:{of}\:{the}\:{equation} \\ $$$${acos}\:\mathrm{2}{x}+{bsin}\:{x}\:=\:{c}\:{and}\: \\ $$$$\mathrm{2}{sin}\:{x}_{\mathrm{1}} {sinx}_{\mathrm{2}} =\:{sin}\:{x}_{\mathrm{1}} +{sinx}_{\mathrm{2}} .\:\boldsymbol{{T}}{hen}\: \\ $$$${the}\:{value}\:{of}\:\:\frac{{b}}{{c}−{a}}\:{is}\:? \\ $$

Question Number 32681 Answers: 0 Comments: 2

Total no. of polynomials of the form x^3 +ax^2 +bx+c that are divisible by x^2 +1, where a,b,c∈1,2,3,....,10 is 1) 10 2) 15 3) 5 4) 8

$$\boldsymbol{{T}}{otal}\:{no}.\:{of}\:{polynomials}\:{of}\:{the}\:{form} \\ $$$${x}^{\mathrm{3}} +{ax}^{\mathrm{2}} +{bx}+{c}\:\:{that}\:{are}\:{divisible}\:{by}\: \\ $$$${x}^{\mathrm{2}} +\mathrm{1},\:{where}\:{a},{b},{c}\in\mathrm{1},\mathrm{2},\mathrm{3},....,\mathrm{10}\:{is}\: \\ $$$$\left.\mathrm{1}\right)\:\mathrm{10} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{15} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{5} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{8} \\ $$

Question Number 32793 Answers: 1 Comments: 0

Given that the point (−3^ ,2) lies on the line y=2x + c.find the coordinates of the point of intersection of this line and the y−axis

$${Given}\:{that}\:{the}\:{point}\:\left(−\bar {\mathrm{3}},\mathrm{2}\right)\:{lies}\:{on}\:{the} \\ $$$${line}\:\:\:\:{y}=\mathrm{2}{x}\:+\:\mathrm{c}.{find}\:{the}\:{coordinates}\: \\ $$$${of}\:{the}\:{point}\:{of}\:{intersection}\:{of}\:{this}\:{line}\:{and}\:{the}\:{y}−{axis} \\ $$

Question Number 32679 Answers: 0 Comments: 0

If 4a^2 −5b^2 +6a+1=0 and the line ax+by+1=0 touches a fixed circle then the correct statement is : 1) centre of circle is at (3,0) 2) radius of circle is (√3). 3) circle passes through (1,0). 4) none of these.

$${If}\:\mathrm{4}{a}^{\mathrm{2}} −\mathrm{5}{b}^{\mathrm{2}} +\mathrm{6}{a}+\mathrm{1}=\mathrm{0}\:{and}\:{the}\:{line} \\ $$$${ax}+{by}+\mathrm{1}=\mathrm{0}\:{touches}\:{a}\:{fixed}\:{circle} \\ $$$${then}\:{the}\:{correct}\:{statement}\:{is}\:: \\ $$$$\left.\mathrm{1}\right)\:{centre}\:{of}\:{circle}\:{is}\:{at}\:\left(\mathrm{3},\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{radius}\:{of}\:{circle}\:{is}\:\sqrt{\mathrm{3}}. \\ $$$$\left.\mathrm{3}\right)\:{circle}\:{passes}\:{through}\:\left(\mathrm{1},\mathrm{0}\right). \\ $$$$\left.\mathrm{4}\right)\:{none}\:{of}\:{these}. \\ $$

Question Number 32794 Answers: 1 Comments: 0

given that the point (t^ ,0) lies on the curve y=2x^2 −x. find the value of t.

$${given}\:{that}\:{the}\:{point}\:\left(\bar {{t}},\mathrm{0}\right)\:{lies}\:{on}\:{the} \\ $$$${curve}\:{y}=\mathrm{2}{x}^{\mathrm{2}} −{x}.\:{find}\:{the}\:{value}\:{of}\:{t}. \\ $$

Question Number 32707 Answers: 1 Comments: 0

1)find u the value of u if Σ_(n=1) ^4 2u.2^(n−1) =64 2) find k if Σ_(n=1) ^∞ k.((1/3))^(n−1) =(2/3)

$$\left.\mathrm{1}\right)\mathrm{find}\:\mathrm{u}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{u}\:\mathrm{if} \\ $$$$\sum_{\mathrm{n}=\mathrm{1}} ^{\mathrm{4}} \mathrm{2}{u}.\mathrm{2}^{{n}−\mathrm{1}} =\mathrm{64} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{k}\:\mathrm{if}\: \\ $$$$\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \mathrm{k}.\left(\frac{\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{n}−\mathrm{1}} =\frac{\mathrm{2}}{\mathrm{3}} \\ $$

Question Number 32705 Answers: 0 Comments: 1

let give f(x)= ∫_0 ^∞ ln(1 +(x/t^2 ))dt with ∣x∣<1 find a simple form of f(x).

$${let}\:{give}\:\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:{ln}\left(\mathrm{1}\:+\frac{{x}}{{t}^{\mathrm{2}} }\right){dt}\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right). \\ $$

Question Number 32704 Answers: 0 Comments: 0

find ∫_0 ^∞ (((x+1)(√x))/(2+x^2 ))dx.

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\left({x}+\mathrm{1}\right)\sqrt{{x}}}{\mathrm{2}+{x}^{\mathrm{2}} }{dx}. \\ $$

Question Number 32675 Answers: 1 Comments: 1

Question Number 32663 Answers: 0 Comments: 0

Question Number 32708 Answers: 0 Comments: 1

let give f(x)=∫_0 ^(π/2) ((ln(1+xtant))/(tant))dt find a simple form of f(x) 2)calculate ∫_0 ^(π/2) ((ln(1+2tant))/(tant))dt .

$${let}\:{give}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{ln}\left(\mathrm{1}+{xtant}\right)}{{tant}}{dt} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{ln}\left(\mathrm{1}+\mathrm{2}{tant}\right)}{{tant}}{dt}\:. \\ $$

Question Number 32659 Answers: 1 Comments: 1

Question Number 32650 Answers: 2 Comments: 0

f(x)=8x−34(√(25−4 (3/2)))

$${f}\left({x}\right)=\mathrm{8}{x}−\mathrm{34}\sqrt{\mathrm{25}−\mathrm{4}\:\frac{\mathrm{3}}{\mathrm{2}}} \\ $$

Question Number 32666 Answers: 0 Comments: 2

Question Number 32648 Answers: 1 Comments: 0

Question Number 32647 Answers: 1 Comments: 0

Question Number 32640 Answers: 1 Comments: 0

Given the function f:x→ ((x +1)/(3x)) and g : x → x−1.Find a) fg b)f°g c) gf^(−1) (x)

$${Given}\:{the}\:{function}\:{f}:{x}\rightarrow\:\frac{{x}\:+\mathrm{1}}{\mathrm{3}{x}} \\ $$$${and}\:{g}\::\:{x}\:\rightarrow\:{x}−\mathrm{1}.\mathrm{Find}\: \\ $$$$\left.\mathrm{a}\right)\:\mathrm{fg} \\ $$$$\left.\mathrm{b}\right)\mathrm{f}°\mathrm{g} \\ $$$$\left.\mathrm{c}\right)\:{gf}^{−\mathrm{1}} \left({x}\right) \\ $$

Question Number 32637 Answers: 1 Comments: 0

Question Number 32635 Answers: 0 Comments: 1

Question Number 32633 Answers: 0 Comments: 1

Question Number 32632 Answers: 0 Comments: 2

Question Number 32629 Answers: 1 Comments: 0

If x^2 +y^2 =9 , 4a^2 +9b^2 =16, then maximum value of 4a^2 x^2 +9b^2 y^2 −12abxy is ?

$$\boldsymbol{{I}}{f}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{9}\:,\:\mathrm{4}{a}^{\mathrm{2}} +\mathrm{9}{b}^{\mathrm{2}} =\mathrm{16}, \\ $$$${then}\:\boldsymbol{{maximum}}\:{value}\:{of}\: \\ $$$$\mathrm{4}{a}^{\mathrm{2}} {x}^{\mathrm{2}} +\mathrm{9}{b}^{\mathrm{2}} {y}^{\mathrm{2}} −\mathrm{12}{abxy}\:{is}\:? \\ $$

Question Number 32627 Answers: 0 Comments: 1

plzz help ne differentiate between ∫sin(2x)= −(1/2)cox(2x)+c is not change to ∫2sin(x)cos(x) but ∫_b ^a sin(2x)= is change to ∫_b ^a 2sin(x)cos(x)

$${plzz}\:{help}\:{ne}\:{differentiate}\: \\ $$$${between} \\ $$$$\int{sin}\left(\mathrm{2}{x}\right)=\:−\frac{\mathrm{1}}{\mathrm{2}}{cox}\left(\mathrm{2}{x}\right)+{c}\: \\ $$$${is}\:{not}\:{change}\:{to}\:\int\mathrm{2}{sin}\left({x}\right){cos}\left({x}\right) \\ $$$${but}\:\underset{{b}} {\overset{{a}} {\int}}{sin}\left(\mathrm{2}{x}\right)=\:{is}\:{change}\:{to} \\ $$$$\underset{{b}} {\overset{{a}} {\int}}\mathrm{2}{sin}\left({x}\right){cos}\left({x}\right) \\ $$

Question Number 32610 Answers: 0 Comments: 1

2. Find the number of ordered triples (a, b, c) of integers satisfying 0 ≤ a, b, c ≤ 1000 for which a^3 + b^3 + c^3 ≡ 3abc + 1 (mod 1001)

$$\mathrm{2}.\:\:{Find}\:\:{the}\:\:{number}\:\:{of}\:\:{ordered}\:\:{triples}\:\:\left({a},\:{b},\:{c}\right)\:\:{of}\:\:{integers}\:\:{satisfying}\:\:\:\:\mathrm{0}\:\leqslant\:\:{a},\:{b},\:{c}\:\:\leqslant\:\:\mathrm{1000}\:\:\:{for}\:\:{which} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}^{\mathrm{3}} \:+\:{b}^{\mathrm{3}} \:+\:{c}^{\mathrm{3}} \:\:\equiv\:\:\mathrm{3}{abc}\:+\:\mathrm{1}\:\:\:\left({mod}\:\:\mathrm{1001}\right)\: \\ $$

Question Number 32609 Answers: 0 Comments: 0

1. Suppose that a, b, and c are real numbers such that a < b < c and a^3 − 3a + 1 = b^3 − 3b + 1 = c^3 − 3c + 1 = 0 . Then (1/(a^2 + b)) + (1/(b^2 + c)) + (1/(c^2 + a)) can be written as (p/q) for relatively prime of positive integers p and q. Find 100p + q

$$\mathrm{1}.\:{Suppose}\:\:{that}\:\:{a},\:{b},\:{and}\:\:{c}\:\:{are}\:\:{real}\:\:{numbers}\:\:{such}\:\:{that}\:\:{a}\:<\:{b}\:<\:{c}\:\:{and}\:\:\:{a}^{\mathrm{3}} \:−\:\mathrm{3}{a}\:+\:\mathrm{1}\:\:=\:\:{b}^{\mathrm{3}} \:−\:\mathrm{3}{b}\:+\:\mathrm{1}\:\:=\:\:{c}^{\mathrm{3}} \:−\:\mathrm{3}{c}\:+\:\mathrm{1}\:=\:\:\mathrm{0}\:. \\ $$$$\:\:\:\:{Then}\:\:\:\frac{\mathrm{1}}{{a}^{\mathrm{2}} \:+\:{b}}\:+\:\frac{\mathrm{1}}{{b}^{\mathrm{2}} \:+\:{c}}\:+\:\frac{\mathrm{1}}{{c}^{\mathrm{2}} \:+\:{a}}\:\:\:\:{can}\:{be}\:\:{written}\:\:{as}\:\:\:\frac{{p}}{{q}}\:\:\:{for}\:\:{relatively}\:\:{prime}\:\:{of}\:\:{positive}\:\:{integers}\:\:\boldsymbol{{p}}\:\:{and}\:\:\:\boldsymbol{{q}}.\:\:\:{Find}\:\:\:\mathrm{100}{p}\:+\:{q} \\ $$

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