Wasi Husain
@Wasi
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@Wasi
solving...
\[\cot\left(4\arctan\left(1.5\right)-\frac{5}{4}\pi\right)=?\]
A cannonball was fired from the surface of Earth with a velocity of \(12kms^{-1}\) perpendicular to the surface of Earth.  If \(e_1\) is the eccentricity of the conic section formed by its orbit. Find \(\lfloor 10e_1\rfloor\) **Assume:** - Mass of Earth = \(5.972\times 10^{24} kg\) - Radius of Earth =\(6.371\times 10^6 m\) - \(G=6.6743\times 10^{-11}Nm^2kg^{-2}\) - Only gravitational forces are involved
 The graph above is of \(\ln^2(x)-\ln^2(y)=\frac{1}{e}\) , the equation is not graphable in between the two colored points. If length of the line segment joining the points is \(e^a-e^{-a}\) find \(\ln a\)
An isosceles trapezium has a perimeter of \(80\), and an area of \(250\). Let \(\theta\) be the angle between any two adjacent sides. If the minimum of \(\sin\theta\) can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, submit your answer as \(a+b\)
A circle with centre point O and radius R is drawn. Point \(P_1\) is lying out of the circle such that \(\overline{OP_1}=3\). \(\overline{P_1B}\) is a tangent to the circle. Point \(P_2, P_3, ... \) till \((\infty)\) are taken on \(\overline{P_1B}\) such that \(\forall n\in\mathbb{N} P_{n+1}\) is mid point of \(\overline{P_nB}\) \(\forall n\in\mathbb{N}\overline{P_nA_n}\) is a tangent to the circle different from \(\overline{P_nB}\). If: \[\sum_{n=1}^{\infty}ar(BP_nA_nO)=2\sqrt{14}\] Fin...
What is the greatest possible perimeter of a right-angled triangle with integers side lengths if one of the sides has length \(12\)?
\[\left\{\lfloor x\rfloor + \frac{x}{\sqrt{3}}\right\} - \left\{\frac{\sqrt{3}}{x}\right\}=0; 1\leq x\leq 2\] If twice the sum of all possible real values of \(x\) satisfying the equation above is of the form \(\sqrt{a} + \sqrt{ab}\), where \(a,b\) are integers, find the value of \(a+b\) **Notations:** - \(\lfloor\cdot\rfloor\) denoted the floor function - \(\{\cdot\}\) denotes the fractional part function
[](https://postimg.cc/PND14hnh) In the above pulley-mass system the mass m constantly decreases with a rate of \(0.01gs ^{−1}\) If initially both the masses \(m,M\) were equal to \(1\) Kg, then find the distance travelled by the mass M in meters in \(30s\) assuming that the mass \(m\) didn't reached the top end in those \(30s\) and acceleration due to gravity of earth \(\approx 10ms ^{−2}\)
What is the sum of all the integers \(x\) such that \(x+38\) and \(x+19\) are both square numbers?
A circle with radius \(r\) is tangent internally to a larger circle with centre \(A\) and radius \(3\) at a point \(B\). Points \(P\) and \(Q\) on the larger circle are such that \(\overline{AP}\) and \(\overline{AQ}\) are tangent to the smaller circle. If the area of \(\triangle APQ\) is , the sum of all possible values of r can be expressed as \(a\sqrt[b]{c} + d\), where a, b, c, and d are integers. Find the smallest value of \(a+b+c+d\)