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If the distances from origin of the centres of 3 circles x2+y2+2alphaix= a2 (i=1,2,3) are in G.P. , then length of the tangents drawn to them frm any point on the circles x2+y2 = a2 are in :(a) A.P (b) G.P (c) H.P (d) None of theseAns) Ccentres of the 3 circles are (-alphai,0) (i= 1,2,3)Distances of thes from origin are alpha1, alpha2, alpha 3now (alpha2)^2= (alpha1)(alpha3)Also general point on x2+y2=a2 is (a costheta, a sintheta) length of tangent from this point on the given circle issqrt( (a cos theta)2+(a sintheta)2 +2alphai(a costheta) -a2)) = sqrt ( 2alphai(a costheta))now as alpha 1, alpha 2, alpha 3 are in GPthen sqrt alpha 1, sqrt alpha 2, sqrt alpha 3 are in gp then sqrt 2acos theta alpha 1 , 2acos theta alpha 2 and sqrt 2acos theta alpha 3 are also in GP
A large pipe dispenses 750 gallons of water in 50 seconds. At this rate, how long will it take to dispense 330 gallons? Find out the number of gallons per second by dividing 75
For the given function recognize the intervals where the function is increasing and decreasing and the intervals where the function is concave up & concave down. Utilizes this info
Distinguish between Mealy and Moore Machine? Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1''''s encountered is even or odd.on..
Manuel is a cross-country runner for his school’s team. He jogged along the perimeter of a rectangular field at his school. The track is a rectangle that has a length that is 3 tim
Three Dimensional geometry Intorduction In earlier classes we studied about the coordinates in two planes that is the XY plane. Here we are going to study in detail about th
The owner of TMH Hospital wants to open a new facility in a certain area. He usually builds 25-, 50-, or 100-bed facilities, depending on whether anticipated demand is low, medium
Tangent Lines : The first problem which we're going to study is the tangent line problem. Before getting into this problem probably it would be best to define a tangent line.
Variation of Parameters Notice there the differential equation, y′′ + q (t) y′ + r (t) y = g (t) Suppose that y 1 (t) and y 2 (t) are a fundamental set of solutions for
without using a calculator how would you know is cos theta(20) is greater than cos theta (35)
Importance of positioning
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