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Equation of line joining(0,0)and point of intersection of X2+Y2+2XY=4 , 3x2+5y2-xy=7 is solution) The two equations above represent pair of straight lines. We can complete the square and arrive at the 4 line equatons and find their point of intersecrtion.Simple method (by mere observation) we can say X=1&Y=1 satisfies both the equation.therfore, Line passing through origin and (1,1) is :X=Y.=>X=Y is the reqd line equation
A two-digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the original number. Find the original number.
Solve 4 cos(t )= 3 on[-8,10]. Solution : Here the first step is identical to the problems in the previous section. First we need to isolate the cosine on one side by itself & t
Integrate following. ∫ -2 2 4x 4 - x 2 + 1dx Solution In this case the integrand is even & the interval is accurate so, ∫ -2 2 4x 4 - x 2 + 1dx = 2∫ o
examples of plane figures
calculate the vector LM given l(4,3),m(-1,2)
Jessica has a picture in a frame with a total area of 288 in2. The dimension of the picture without the frame is 12 in through 14 in. What is the larger dimension, in inches, of th
There's a nice way to show why the expresion for the area of a circle of radius R is: Pi * R 2 . It has an comman relationship with the experation for the circumference of a
Utilizes the second derivative test to classify the critical points of the function, h ( x ) = 3x 5 - 5x 3 + 3 Solution T
Solve sin (α /7) =0 . Solution By Using a unit circle it isn't too difficult to see that the solutions to this equation are, α /7 = 0 + 2 ? n ⇒ α = 14 ? n
An elliptical galaxy has gravitational boundaries defiend by 9x 2 +16y 2 +144z 2 =144. A black hole at the center of the galaxy is interacting with dark matter producing a radiatio
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