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The curve for which (dy/dx)=a(x−p)(x−q), where a, p and q are constants, has turning points at (2,0) and (1,1). i) state the value of p and q. ii) using these values, determine the value of a

$$\mathrm{The}\:\mathrm{curve}\:\mathrm{for}\:\mathrm{which}\:\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{a}\left(\mathrm{x}−\mathrm{p}\right)\left(\mathrm{x}−\mathrm{q}\right), \\ $$$$\mathrm{where}\:\mathrm{a},\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\mathrm{are}\:\mathrm{constants},\:\mathrm{has}\:\mathrm{turning} \\ $$$$\mathrm{points}\:\mathrm{at}\:\left(\mathrm{2},\mathrm{0}\right)\:\mathrm{and}\:\left(\mathrm{1},\mathrm{1}\right). \\ $$$$\left.\mathrm{i}\right)\:\mathrm{state}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}. \\ $$$$\left.\mathrm{ii}\right)\:\mathrm{using}\:\mathrm{these}\:\mathrm{values},\:\mathrm{determine}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:{a} \\ $$

Question Number 171761 Answers: 0 Comments: 0

solve: ((sin(10+x))/(sin(13+x)))=((sin27sin39)/(sin24sin57))

$${solve}: \\ $$$$\frac{{sin}\left(\mathrm{10}+{x}\right)}{{sin}\left(\mathrm{13}+{x}\right)}=\frac{{sin}\mathrm{27}{sin}\mathrm{39}}{{sin}\mathrm{24}{sin}\mathrm{57}} \\ $$

Question Number 171759 Answers: 1 Comments: 0

solve: ((√(x^2 −5x+6)) + (√(x^2 −5x+4)) )^(x/2) + ((√(x^2 −5x+6)) − (√(x^2 −5x+4)))^(x/2) = 2^((x+2)/4) . find x

$${solve}: \\ $$$$\left(\sqrt{{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{6}}\:+\:\sqrt{{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{4}}\:\right)^{\frac{{x}}{\mathrm{2}}} \:+\:\left(\sqrt{{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{6}}\:−\:\sqrt{{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{4}}\right)^{\frac{{x}}{\mathrm{2}}} \:=\:\mathrm{2}^{\frac{{x}+\mathrm{2}}{\mathrm{4}}} .\:{find}\:{x} \\ $$

Question Number 171757 Answers: 0 Comments: 0

find (2n)!

$${find}\:\left(\mathrm{2}{n}\right)! \\ $$

Question Number 171756 Answers: 0 Comments: 4

solve for real numbers: 2x^2 +3y^2 +z^2 =7 x^2 +y^2 +z^2 =(√2) z(x+y)

$${solve}\:{for}\:{real}\:{numbers}: \\ $$$$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\mathrm{7} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\sqrt{\mathrm{2}}\:{z}\left({x}+{y}\right) \\ $$

Question Number 171755 Answers: 0 Comments: 0

make R the subject of the formula if P=(M/5)(X+R^2 )+2.

$${make}\:{R}\:{the}\:{subject}\:{of}\:{the}\:{formula}\:{if} \\ $$$${P}=\frac{{M}}{\mathrm{5}}\left({X}+{R}^{\mathrm{2}} \right)+\mathrm{2}. \\ $$

Question Number 171749 Answers: 2 Comments: 0

if a+b+c=3,a^2 +b^2 +c^2 =5,a^3 +b^3 +c^3 =27. find a^(100) +b^(100) +c^(100) .

$${if}\:{a}+{b}+{c}=\mathrm{3},{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{5},{a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} =\mathrm{27}.\:{find}\:{a}^{\mathrm{100}} +{b}^{\mathrm{100}} +{c}^{\mathrm{100}} . \\ $$

Question Number 171742 Answers: 0 Comments: 3

solve: (1+n)!+2(n)!=(n+2)!−4n!

$${solve}:\:\left(\mathrm{1}+{n}\right)!+\mathrm{2}\left({n}\right)!=\left({n}+\mathrm{2}\right)!−\mathrm{4}{n}! \\ $$

Question Number 171739 Answers: 0 Comments: 2

the result of dividing ((x^a /x^b ))^(a+b) by ((x^(a+b) /x^(a−b) ))^(a^2 /(b )) is

$${the}\:{result}\:{of}\:{dividing}\:\left(\frac{{x}^{{a}} }{{x}^{{b}} }\right)^{{a}+{b}} {by}\:\left(\frac{{x}^{{a}+{b}} }{{x}^{{a}−{b}} }\right)^{\frac{{a}^{\mathrm{2}} }{{b}\:}} {is} \\ $$

Question Number 171730 Answers: 1 Comments: 0

solve((8^x −2^x )/(6^x −3^(x ) ))=2. find x

$${solve}\frac{\mathrm{8}^{{x}} −\mathrm{2}^{{x}} }{\mathrm{6}^{{x}} −\mathrm{3}^{{x}\:} }=\mathrm{2}.\:{find}\:{x} \\ $$$$ \\ $$

Question Number 171728 Answers: 1 Comments: 0

((x^3 +y^3 )/(x+y))=7 ((x^3 −y^3 )/(x−y))=19. find x and y

$$\frac{{x}^{\mathrm{3}} +{y}^{\mathrm{3}} }{{x}+{y}}=\mathrm{7} \\ $$$$\frac{{x}^{\mathrm{3}} −{y}^{\mathrm{3}} }{{x}−{y}}=\mathrm{19}.\:{find}\:{x}\:{and}\:{y} \\ $$

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