Question and Answers Forum

A line is formed by joining the points A(7,0) and B(0,2). Obtain the equation of the straight line joining AC such that the x−axis bisects the angle BAC.

$$\boldsymbol{{A}}\:\boldsymbol{{line}}\:\boldsymbol{{is}}\:\boldsymbol{{formed}}\:\boldsymbol{{by}}\:\boldsymbol{{joining}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{points}}\:\boldsymbol{{A}}\left(\mathrm{7},\mathrm{0}\right)\:\boldsymbol{{and}}\:\boldsymbol{{B}}\left(\mathrm{0},\mathrm{2}\right).\:\boldsymbol{{Obtain}} \\ $$$$\boldsymbol{{the}}\:\boldsymbol{{equation}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{straight}}\:\boldsymbol{{line}} \\ $$$$\boldsymbol{{joining}}\:\boldsymbol{{AC}}\:\boldsymbol{{such}}\:\boldsymbol{{that}}\:\boldsymbol{{the}}\:\boldsymbol{{x}}−\boldsymbol{{axis}} \\ $$$$\boldsymbol{{bisects}}\:\boldsymbol{{the}}\:\boldsymbol{{angle}}\:\boldsymbol{{BAC}}. \\ $$

Question Number 170427 Answers: 1 Comments: 0

14^b =7^(b−a) 49^(a/b) =?

$$\mathrm{14}^{{b}} =\mathrm{7}^{{b}−{a}} \\ $$$$\mathrm{49}^{\frac{{a}}{{b}}} =? \\ $$

Question Number 170426 Answers: 2 Comments: 0

Question Number 170416 Answers: 2 Comments: 0

∫(√(4−x^2 ))dx Mastermind

$$\int\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }{dx} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 170415 Answers: 1 Comments: 0

Given x^y =e^(x−y) . find (dy/dx)? Mastermind

$$\mathrm{Given}\:\mathrm{x}^{\mathrm{y}} =\mathrm{e}^{\mathrm{x}−\mathrm{y}} .\:\mathrm{find}\:\frac{\mathrm{dy}}{\mathrm{dx}}? \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 170413 Answers: 1 Comments: 0

Use Trapezoidal rule with ordinate 1, 1.5, 2, 2.5, 3 to compute ∫_1 ^3 ((√(x+1))/x)dx. Mastermind

$${Use}\:{Trapezoidal}\:{rule}\:{with}\:{ordinate} \\ $$$$\mathrm{1},\:\mathrm{1}.\mathrm{5},\:\mathrm{2},\:\mathrm{2}.\mathrm{5},\:\mathrm{3}\:{to}\:{compute} \\ $$$$\int_{\mathrm{1}} ^{\mathrm{3}} \frac{\sqrt{{x}+\mathrm{1}}}{{x}}{dx}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 170412 Answers: 2 Comments: 0

If part of the curve y=x+1 from x=1 and x=2 is rotated completely about the y−axis. find the volume of the solid form. Mastermind

$${If}\:{part}\:{of}\:{the}\:{curve}\:{y}={x}+\mathrm{1}\:{from}\:{x}=\mathrm{1} \\ $$$${and}\:{x}=\mathrm{2}\:{is}\:{rotated}\:{completely}\:{about} \\ $$$${the}\:{y}−{axis}.\:{find}\:{the}\:{volume}\:{of}\:{the} \\ $$$${solid}\:{form}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 170411 Answers: 1 Comments: 0

The position of a body at time t (in seconds) is given by s=t^3 −4, what is the velocity and acceleration of the object at time t=5 ? Mastermind

$${The}\:{position}\:{of}\:{a}\:{body}\:{at}\:{time}\:{t}\:\left({in}\right. \\ $$$$\left.{seconds}\right)\:{is}\:{given}\:{by}\:{s}={t}^{\mathrm{3}} −\mathrm{4},\:{what}\:{is} \\ $$$${the}\:{velocity}\:{and}\:{acceleration}\:{of}\:{the} \\ $$$${object}\:{at}\:{time}\:{t}=\mathrm{5}\:? \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 170410 Answers: 2 Comments: 0

Given y=xe^(−x) , show that (d^2 y/dx^2 )+2(dy/dx)+y=0 Mastermind

$${Given}\:{y}={xe}^{−{x}} ,\:{show}\:{that} \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\mathrm{2}\frac{{dy}}{{dx}}+{y}=\mathrm{0} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 170407 Answers: 0 Comments: 0

Question Number 170405 Answers: 0 Comments: 0

Question Number 170404 Answers: 0 Comments: 0

Question Number 170389 Answers: 1 Comments: 7

solve for x∈R x^3 +((3−x))^(1/3) −3=0

$${solve}\:{for}\:{x}\in{R} \\ $$$${x}^{\mathrm{3}} +\sqrt[{\mathrm{3}}]{\mathrm{3}−{x}}−\mathrm{3}=\mathrm{0} \\ $$

Question Number 170388 Answers: 0 Comments: 0

Question Number 170386 Answers: 1 Comments: 2

Find the volume of tetrahedron whose vertices are the points A(2, −1, −3), B(4, 1, 3), C(3, 2, −1) and D(1, 4, 2). Mastermind

$${Find}\:{the}\:{volume}\:{of}\:{tetrahedron}\:{whose} \\ $$$${vertices}\:{are}\:{the}\:{points}\:{A}\left(\mathrm{2},\:−\mathrm{1},\:−\mathrm{3}\right), \\ $$$${B}\left(\mathrm{4},\:\mathrm{1},\:\mathrm{3}\right),\:{C}\left(\mathrm{3},\:\mathrm{2},\:−\mathrm{1}\right)\:{and}\:{D}\left(\mathrm{1},\:\mathrm{4},\:\mathrm{2}\right). \\ $$$$ \\ $$$${Mastermind} \\ $$

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