Determine the center and the radius
Determine the center and the radius of each circle:
(May you show me the steps for completing the square into standard form too?)
1) x^2+y^2=12x-12y
2) x^2+y^2-6y=0
3) x^2+1/2x+y^2+1/2y=1/8
4) x^2+y^2=3/2y
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Suppose a three-state single period economy with three base assets: the zero coupon bond with price St(1) = Bt, a stock with price St(2) = St, and call upon the stock with price St(3) = Ct = Ct(St,K), where t is between 0 and T. Let St(w1) = S+, S
Assume you're using the secant method to find a root x * of a nonlinear equation (x) 0 f = . Show that if at any iteration it happens to be the case that x k = x * , then it will also be true that x k+1 = x *.
Let a, b and n be three positive integers with gcd(a,n) = 1 and gcd(b,n) = 1. Show that gcd(ab,n) = 1
Let n > 1. Show that there exists n consecutive composite numbers. (Hint: consider (n+1)!+k for 2?k?n+1, where n!=n*(n-1)* ...2*1)
Write each of the following equation in one of the forms: y=a(x-h)^2+k, x=a(y-h)^2+k, [((x-h)^2/a^2)+((y-k)^2/b^2)=1] or (x-h)^2 +
Verify the origin is regular singularity. Show the roots of the indicial equation do not differ by an integer. Find, by the method of Frobenius, two independent solutions of:
The ratio for Nacys class is girl to boy 3:5, the ratio of bills class is girl to boy 3:1 is the number of students in Nancys class a multiple of 8? if thetwo classes were combined what would be the new girl:boy ratio?
Whenever multiplying two positive fractions, the product is less than starting numbers? Sometimes? Always? Never? Why?
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