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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 man invest ?13500 partly in shares paying 6% at ?140 and partly in 5% at 125.If he is tolal income is 560, how much has he invested in each?
(a) Using interpolation, give a polynomial f ∈ F 11 [x] of degree at most 3 satisfying f(0) = 2; f(2) = 3; f(3) = 1; f(7) = 6 (b) What are all the polynomials in F 11 [x] which
A company makes 2 products, Product A and Product B. The product characteristics are shown in the following table. Product A B
how do i write a conjecture about the sum of two negative integers.
Decimal representations of some basic angles: As a last quick topic let's note that it will, on occasion, be useful to remember the decimal representations of some basic angles. S
Solve the inequation: |x|
what is the LCM of 18, 56 and 104 show working
Correlation coefficient - These are numerical measures of the correlations existing between the independent and the dependent variables - These are better measures of corre
Can I have simplify radicals for Alebgera 2
Differentiate following. Solution : It requires the product rule & each derivative in the product rule will need a chain rule application as well. T ′ ( x ) =1/1+(2x) 2
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