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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
Lucy's youth group increased $1,569 for charity. They decided to split the money evenly between 3 charities. How much will each charity receive? Divide the money raised through
a die was rooled 500 times and number of times 4 came up was noted if the imperical probability calculated from this information 7_10
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What is 2 5 ? 2 5 = 2 ×2 ×2 ×2 ×2 = 32
The probability that a leap year will have 53 sunday is ? and how please explain it ? (a)1/7 (b) 2/7 (c) 5/7 (d)6/7 Sol) A leap year has 366 days, therefore 52 weeks i.e
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1. A direction ?eld for a differential equation is shown. Draw, with a ruler, the graphs of the Euler approximations to the solution curve that passes through the origin. Use step
Eduardo is merging two 6-inch pieces of wood with a piece in which measures 4 inches. How many total inches of wood does he have? This problem translates to the expression 6 ×
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