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For complex number z, the minimum value of |z| + |z - cosa - i sina|+|z - 2(cosa + i sina )| is..? Solution) |z| + |z-(e^ia)| + |z-2(e^ia)| we see.....oigin , e^ia , 2e^ia , forms a straight line.and for minimum value..... z must coincide with e^iahence the equation becomes:=|e^ia| + 0 + |-e^ia|=1 + 0 + 1=2(ANS)
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a+b.
Suppose a fluid (say, water) occupies a domain D? R^(3 ) and has velocity field V=V(x, t). A substance (say, a day) is suspended into the fluid and will be transported by the fluid
Calucations of gradients find f Graph some level curve f=const. f=9x^2 = 4y^2
From a point P, two tangents PA are drawn to a circle with center O.If OP=diameter of the circle show that triangle APB is equilateral. Ans: PA=PB (length of tangents
Finding the Slope of a Line, Given Two Points on it ? Find the slope of the line passing through the pairs of points (-5, -2) and (2, 4). One way to find the slope is
How do i divide 200 by 4
Inverse Functions : In the last instance from the previous section we looked at the two functions f ( x ) = 3x - 2 and g ( x ) = x /3+ 2/3 and saw that ( f o g ) ( x )
A baseball card was worth $5.00 in 1940. It doubled in value every decade. How much was it worth in 2000?
You are given the following regression results estimating the demand for widgets based on time series data for the past 40 months. Q t = 2.5 - 0.3 x P t + 12 x M t Where Q
I need help with my calculus work
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