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3d ago

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Continue Learning about Trigonometry

What is subdominant triad of B major?

There is no such thing as B major. There is B minor and B flat major. The subdominant triad of B minor ( I'm pretty sure) is E minor.


What are five trigonometric identities?

All others can be derived from these and a little calculus: sin2x+cos2x=1 sec2x-tan2x=1 sin(a+b)=sin(a)cos(b)+sin(b)sin(a) cos(a+b)=cos(a)cos(b)-sin(a)sin(b) eix=cos(x)+i*sin(x)


What is tan20tan32 plus tan32tan38 plus tan38tan20?

This may not be the most efficient method but ... Let the three angle be A, B and C. Then note that A + B + C = 20+32+38 = 90 so that C = 90-A+B. Therefore, sin(C) = sin[(90-(A+B) = cos(A+B) and cos(C) = cos[(90-(A+B) = sin(A+B). So that tan(C) = sin(C)/cos(C) = cos(A+B) / sin(A+B) = cot(A+B) Now, tan(A+B) = [tan(A)+tan(B)] / [1- tan(A)*tan(B)] so cot(A+B) = [1- tan(A)*tan(B)] / [tan(A)+tan(B)] The given expressin is tan(A)*tan(B) + tan(B)*tan(C) + tan(C)*tan(A) = tan(A)*tan(B) + [tan(B) + tan(A)]*cot(A+B) substituting for cot(A+B) gives = tan(A)*tan(B) + [tan(B) + tan(A)]*[1- tan(A)*tan(B)]/[tan(A)+tan(B)] cancelling [tan(B) + tan(A)] and [tan(A) + tan(B)], which are equal, in the second expression. = tan(A)*tan(B) + [1- tan(A)*tan(B)] = 1


In a triangle ABC b equals 15 cm and c equals 25 cm and also angle B equals 32'15'Find the side a and other angles?

By the sine rule, sin(C)/c = sin(B)/b so sin(C) = 25/15*sin(32d15m) = 0.8894 so C = 62.8 deg or 117.2 deg. Therefore, A = 180 - (B+C) = 85.0 deg or 30.5 deg and then, using the sine rule again, a/sin(A) = b/sin(B) so a = sin(A)*b/sin(B) = 28 or a = 14.3


What is the square root of Pythagoras?

Pythagoras was a Classical Greek mathemtician. He gave us the equation. h^(2) = a^(2)+ b^(2) To take the 'square root (sqrt) of this equation we write. sqrt[h^(2)] = sqrt[ a^(2) + b^(2) ] or h = sqrt[a^(2) + b^(2)] Note the use of square brackets to indicate on the RHS that the sum of the squared numbered is square rooted.; NOT the individual numbers. The Pyrthagorean Eq'n refers to Right-Angles triangles. 'h' is the hypotenuse ; the angle opposite the right angle. 'a' & 'b' are the two sides that make up the right angle.