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AlgebraQuestion and Answers: Page 228

Question Number 123894 Answers: 2 Comments: 0

Question Number 123886 Answers: 1 Comments: 0

Let l^− z+lz^− +m=0 be a straight line in the complex plane and P(z_0 ) be a point in the plane. Then the equation of the line passing through P(z_0 ) and perpendicular to the given line is ___

$$\mathrm{Let}\:\overset{−} {{l}z}+{l}\overset{−} {{z}}+{m}=\mathrm{0}\:\mathrm{be}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line}\:\mathrm{in}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{plane} \\ $$$$\mathrm{and}\:{P}\left({z}_{\mathrm{0}} \right)\:\mathrm{be}\:\mathrm{a}\:\mathrm{point}\:\mathrm{in}\:\mathrm{the}\:\mathrm{plane}.\:\mathrm{Then}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:\mathrm{passing}\:\mathrm{through}\:{P}\left({z}_{\mathrm{0}} \right)\:\mathrm{and}\:\mathrm{perpendicular} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{given}\:\mathrm{line}\:\mathrm{is}\:\_\_\_ \\ $$

Question Number 123824 Answers: 1 Comments: 1

Show that for all real numbers (x/y/z) satisfying x+y+z=0 and xy +yz+zx=−3 the value of expression x^3 y+y^3 z +z^3 x is a constant

$${Show}\:{that}\:{for}\:{all}\:{real}\:{numbers}\:\left({x}/{y}/{z}\right)\:{satisfying}\:\: \\ $$$${x}+{y}+{z}=\mathrm{0}\:{and}\:{xy}\:+{yz}+{zx}=−\mathrm{3}\:\:\:{the}\:{value}\:{of} \\ $$$${expression}\:{x}^{\mathrm{3}} {y}+{y}^{\mathrm{3}} {z}\:+{z}^{\mathrm{3}} {x}\:\:\:{is}\:{a}\:{constant} \\ $$

Question Number 123746 Answers: 0 Comments: 1

Question Number 123638 Answers: 0 Comments: 1

show that if x∈R then x and −x cannot be positive

$$\mathrm{show}\:\mathrm{that}\:\mathrm{if}\:\mathrm{x}\in\mathbb{R}\:\mathrm{then}\:\mathrm{x}\:\mathrm{and}\:−\mathrm{x}\:\mathrm{cannot}\:\mathrm{be}\:\mathrm{positive} \\ $$

Question Number 123626 Answers: 0 Comments: 0

Question Number 123595 Answers: 0 Comments: 1

For real numbers (a/b/c) define s_n =a^n +b^n +c^n Suppose s_1 =2 s_2 =6 and s_(3 ) =14.Prove that ∣s_n ^2 −s_(n−1) s_(n+1) ∣=8=holds ∀ n>1

$${For}\:{real}\:{numbers}\:\left({a}/{b}/{c}\right)\:{define}\:{s}_{{n}} ={a}^{{n}} +{b}^{{n}} +{c}^{{n}} \\ $$$${Suppose}\:{s}_{\mathrm{1}} =\mathrm{2}\:{s}_{\mathrm{2}} =\mathrm{6}\:{and}\:{s}_{\mathrm{3}\:} =\mathrm{14}.{Prove}\:{that}\: \\ $$$$\mid{s}_{{n}} ^{\mathrm{2}} −{s}_{{n}−\mathrm{1}} {s}_{{n}+\mathrm{1}} \mid=\mathrm{8}={holds}\:\forall\:{n}>\mathrm{1} \\ $$

Question Number 123591 Answers: 0 Comments: 2

Question Number 123576 Answers: 1 Comments: 2

Question Number 123574 Answers: 1 Comments: 0

Question Number 123548 Answers: 1 Comments: 1

a man 6 ft tall walks at a rate of 7 ft/sec away from a lamppost that is 14 ft hight. at what rate is the lenght of his shadow charging when he is 30 ft away from the lamppost

$${a}\:{man}\:\mathrm{6}\:{ft}\:{tall}\:{walks}\:{at}\:{a}\:{rate} \\ $$$${of}\:\mathrm{7}\:{ft}/{sec}\:{away}\:{from}\:{a}\:{lamppost} \\ $$$${that}\:{is}\:\mathrm{14}\:{ft}\:{hight}. \\ $$$${at}\:{what}\:{rate}\:{is}\:{the}\:{lenght}\:{of}\:{his} \\ $$$${shadow}\:{charging}\:{when}\:{he}\:{is}\:\mathrm{30}\:{ft}\: \\ $$$${away}\:{from}\:{the}\:{lamppost} \\ $$

Question Number 123510 Answers: 0 Comments: 0

sorry −(π/2)

$${sorry}\:−\frac{\pi}{\mathrm{2}} \\ $$

Question Number 123509 Answers: 1 Comments: 0

∫_(−(π/)2) ^(π/2) ∣cosx∣=?

$$\underset{−\frac{\pi}{}\mathrm{2}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\mid{cosx}\mid=? \\ $$

Question Number 123426 Answers: 0 Comments: 5

find the radii of all circles with center C tangenting the curve h C= ((5),(1) ) h: x^2 −y^2 =1

$$\mathrm{find}\:\mathrm{the}\:\mathrm{radii}\:\mathrm{of}\:\mathrm{all}\:\mathrm{circles}\:\mathrm{with}\:\mathrm{center}\:{C} \\ $$$$\mathrm{tangenting}\:\mathrm{the}\:\mathrm{curve}\:{h} \\ $$$${C}=\begin{pmatrix}{\mathrm{5}}\\{\mathrm{1}}\end{pmatrix} \\ $$$${h}:\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{1} \\ $$

Question Number 123409 Answers: 1 Comments: 0

x^4 +12x−5=0 show that the sum of two roots of the equation is 2