To add a complex number on a complex plane, the points needed to be plotted first. Learn about the real part and the imaginary part of a complex number, about similarities between complex and Cartesian planes, and how to add complex numbers in an equation...
Let R be the region in the xy-plane bounded by xy = 1,xy = 4,yx=1,andyx=3. Evaluate the double integral. ∫∫RexydA Double Integrals: Integral defined over an area in thexy- plane has to be integrated twice. Double ...
Find the area of the surface. The portion of the cone z = 2*sqrt(x^2 + y^2) inside the cylinder x^2 + y^2 = 4. Find the surface area of the part of the cone z = \sqrt{x^2 + y^2} that lies under the plane z = R. Do yo...
Calculate the volume of the region below the plane z=x+4 and over the region of the x-y plane bounded by the parabola y= 4-x^2 and the line y= 3x. Find the total area of the region formed by the parabola f(x)=x^2 - 4x +...
(a ≠ 0, c ≠ 0) 2a^-2 b^3/ 4a^3 c^-4 = 1b^3/2a^3+2= b^3 c^4/ 2a^5 31. What is the distance between the points (6,-5) and (2,3) in a standard (x,y) coordinate plane? d = √(x2 - x1)^2 + (y2-y1)^2d = √(2-6)^2 + (3-(-5))^2d = √(...
Let E is the region bounded by the surface z=x2+y2 and the plane z = 1. Evaluate the integral. ∫∫E∫(x2+y2)dV Application of Triple Integrals: Not that we can use the triple integrals formula in cylindrical coordinat...
Answer to: Let D be the region in the xy plane bounded by the graphs of: x^2-y^2 =1, x^2 -y^2 = 9, xy =2 and xy = 4. Evaluate the integral...
Give the x-coordinate of the point of intersection of the plane x+2y+z=6 and the line through the point (1,0,1) and (2,-1,1). Find the point of intersection for \\ y = x^2 \\ and \\ y =4x - 3 Find Point of intersection of y = ...
Let C be the circumference of a circle of radius 3 in the plane 2x + y + 2z = 8, oriented counterclockwise when viewed from the origin. Compute \int_C (5x + 6y) \vec i + (4y - 2z) \vec j + (32 + x)\ ...
How to prove the basis of a vector space? Let a, b and c be any three vectors in space. Argue that the vector a (a * b) is perpendicular to a and lies in the plane of b and c. Consider th...